GCL_allosteric_responses.ipynb

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  "metadata": {
    "colab": {
      "name": "GCL_allosteric_responses.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "machine_shape": "hm"
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    },
    "accelerator": "GPU",
    "gpuClass": "standard"
  },
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "FMcM8qfoXF9z"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import random\n",
        "import networkx as nx\n",
        "import torch\n",
        "import torch.nn as nn\n",
        "import matplotlib.pyplot as plt\n",
        "%matplotlib inline\n",
        "\n",
        "torch.cuda.get_device_name(0)\n",
        "DEVICE = torch.device(\"cuda:0\" if torch.cuda.is_available() else \"cpu\")\n",
        "\n",
        "#from google.colab import drive\n",
        "#drive.mount('/content/drive')\n"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# ________________________ALL FUNCTIONS AND CLASSES ___________________________\n",
        "\n",
        "\n",
        "def make_network(m,n, noise_low, noise_high):\n",
        "    O = nx.triangular_lattice_graph(m,n, periodic=False, with_positions=True, create_using=None)\n",
        "    G = nx.convert_node_labels_to_integers(O)\n",
        "    #nx.draw(G, with_labels=True)\n",
        "    #plt.show()\n",
        "    print(G)\n",
        "    pos_dict = nx.get_node_attributes(G, \"pos\")\n",
        "\n",
        "    num_nodes = len(G.nodes)\n",
        "    num_springs = len(G.edges)\n",
        "    \n",
        "    x = torch.zeros(num_nodes, 2)\n",
        "    values = list(pos_dict.values())\n",
        "    for i in range(len(values)):\n",
        "        x[i][0] = values[i][0]\n",
        "        x[i][1] = values[i][1]\n",
        "    \n",
        "    # add noise to initial layout\n",
        "    torch.random.manual_seed(8)\n",
        "    base_x = x.detach().clone()\n",
        "    noise = (noise_low - noise_high) * torch.rand(num_nodes, 2) + noise_high\n",
        "    x = x+noise\n",
        "    \n",
        "    x.requires_grad = True\n",
        "    \n",
        "    indices = []\n",
        "    for i, (node1,node2) in enumerate(G.edges):\n",
        "        indices.append([node1,node2])\n",
        "\n",
        "    return num_nodes, num_springs, x, indices, base_x\n",
        "\n",
        "def make_incidence(indices, num_vertices):\n",
        "    # this creates a dense matrix (incidence), but\n",
        "    # sparse matrices or convolutions might be more appropriate\n",
        "    # in certain cases\n",
        "    num_springs = len(indices)\n",
        "    incidence = torch.zeros(num_springs, num_vertices, dtype=torch.float32)\n",
        "    for i, item in enumerate(indices):\n",
        "        i1, i2 = item\n",
        "        incidence[i, i1] = 1\n",
        "        incidence[i, i2] = -1\n",
        "    return incidence\n",
        "\n",
        "def get_l0(num_springs, range_num, noise_scale = 0):\n",
        "    l0 = torch.rand(num_springs) * range_num\n",
        "    # add noise\n",
        "    noise = (-noise_scale - noise_scale) * torch.rand(num_springs) + noise_scale\n",
        "    buffer = torch.ones(num_springs) * noise_scale\n",
        "    l0 = l0 + noise + buffer\n",
        "    return l0\n",
        "\n",
        "def get_k(num_springs, range_num):\n",
        "    k = torch.rand(num_springs) * range_num\n",
        "    #k = torch.ones(num_springs, dtype=torch.float32)\n",
        "    #k = k + noise\n",
        "    return k\n",
        "\n",
        "def get_source_springs(nsprings, nsource_springs):\n",
        "    s_springs = np.random.choice(nsprings, size=nsource_springs, replace=False, p=None)\n",
        "    return s_springs\n",
        "\n",
        "def get_target_springs(nsprings, ntarget_springs, s_springs):\n",
        "    to_exclude = s_springs # cannot be the same springs as the source springs\n",
        "    t_springs = random.sample(list(set([x for x in range(nsprings)]) - set(to_exclude)), k = ntarget_springs)\n",
        "    return t_springs\n",
        "\n",
        "def create_spring_mask(s_springs, t_springs, indices, nodes, free_mode=True):\n",
        "    # using the random springs, get the corresponding nodes and create a mask\n",
        "    mask = np.zeros(nodes,)\n",
        "    for spring_index in s_springs:\n",
        "        node1, node2 = indices[spring_index]\n",
        "        mask[node1] = 1\n",
        "        mask[node2] = 1\n",
        "    if free_mode == False:\n",
        "        for spring_index in t_springs:\n",
        "            node1, node2 = indices[spring_index]\n",
        "            mask[node1] = 1\n",
        "            mask[node2] = 1\n",
        "    return mask\n",
        "\n",
        "\n",
        "def clamp_s_spring_length(spring_network, input_strain, spring, indices, x):\n",
        "    \n",
        "    input_length = input_strain + 1\n",
        "    \n",
        "    # get the corresponding nodes for the spring\n",
        "    node1, node2 = indices[spring]\n",
        "        \n",
        "    x1 = x[node1][0]\n",
        "    x2 = x[node2][0]\n",
        "        \n",
        "    y1 = x[node1][1]\n",
        "    y2 = x[node2][1]\n",
        "        \n",
        "    delta_y = y2 - y1\n",
        "    delta_x = x2 - x1\n",
        "    \n",
        "    current_length = spring_network.measure_spring_length(x, spring)\n",
        "    ratio = input_length / current_length\n",
        "    \n",
        "    new_y = ratio * delta_y\n",
        "    new_x = ratio * delta_x\n",
        "    \n",
        "    with torch.no_grad():\n",
        "        x[node2][1] = x[node1][1] + new_y\n",
        "        x[node2][0] = x[node1][0] + new_x\n",
        "    \n",
        "    return x\n",
        "\n",
        "def clamp_spring_length2(spring_network, input_strain, spring, indices, x, l0):\n",
        "    \n",
        "    input_length = (l0[spring]*(input_strain + 1))\n",
        "    \n",
        "    # get the corresponding nodes for the spring\n",
        "    node1, node2 = indices[spring]\n",
        "        \n",
        "    x1 = x[node1][0]\n",
        "    x2 = x[node2][0]\n",
        "        \n",
        "    y1 = x[node1][1]\n",
        "    y2 = x[node2][1]\n",
        "        \n",
        "    delta_y = y2 - y1\n",
        "    delta_x = x2 - x1\n",
        "    \n",
        "    current_length = spring_network.measure_spring_length(x, spring)\n",
        "    ratio = input_length / current_length\n",
        "    \n",
        "    new_y = ratio * delta_y\n",
        "    new_x = ratio * delta_x\n",
        "    \n",
        "    with torch.no_grad():\n",
        "        x[node2][1] = x[node1][1] + new_y\n",
        "        x[node2][0] = x[node1][0] + new_x\n",
        "        \n",
        "        l0[spring] = input_length\n",
        "        k[spring] = 1e10\n",
        "    \n",
        "    return x\n",
        "\n",
        "def clamp_spring_length(spring_network, input_strain, spring, indices, x, l0):\n",
        " \n",
        "    input_length = input_strain\n",
        "    \n",
        "    # get the corresponding nodes for the spring\n",
        "    node1, node2 = indices[spring]\n",
        "        \n",
        "    x1 = x[node1][0]\n",
        "    x2 = x[node2][0]\n",
        "        \n",
        "    y1 = x[node1][1]\n",
        "    y2 = x[node2][1]\n",
        "        \n",
        "    delta_y = y2 - y1\n",
        "    delta_x = x2 - x1\n",
        "    \n",
        "    current_length = spring_network.measure_spring_length(x, spring)\n",
        "    ratio = input_length / current_length\n",
        "    \n",
        "    new_y = ratio * delta_y\n",
        "    new_x = ratio * delta_x\n",
        "    \n",
        "    with torch.no_grad():\n",
        "        x[node2][1] = x[node1][1] + new_y\n",
        "        x[node2][0] = x[node1][0] + new_x\n",
        "        \n",
        "        l0[spring] = input_length\n",
        "        k[spring] = 1e10\n",
        "    \n",
        "    return x\n",
        "\n",
        "# main simulation loop\n",
        "def run_to_equil(mask, x, optimizer, network, iterations):\n",
        "    \n",
        "  energies = np.zeros(iterations)\n",
        "  for i in range(iterations):\n",
        "    #if i > 1000:\n",
        "    #    optimizer = torch.optim.Adam([x], lr=1e-3)\n",
        "    optimizer.zero_grad()\n",
        "    loss = network.energy(x).sum() # sum for total energy\n",
        "    loss.backward()\n",
        "    #x.grad[mask !=0] = torch.zeros_like(x.grad[mask !=0])\n",
        "    optimizer.step()\n",
        "    energies[i] = loss\n",
        "  return energies\n",
        "\n",
        "class MSD(nn.Module):\n",
        "    def __init__(self, indices, l0, k, num_vertices):\n",
        "        super().__init__()\n",
        "        self.indices = indices\n",
        "        self.register_buffer(\"incidence\", make_incidence(self.indices, num_vertices))\n",
        "        self.register_buffer(\"l0\", l0)\n",
        "        self.register_buffer(\"k\", k)\n",
        "    \n",
        "    def measure_spring_length(self, x, spring_index):\n",
        "        d = self.incidence.mm(x)\n",
        "        q = d.pow(2).sum(1)\n",
        "        l = q.sqrt() \n",
        "        l = l[spring_index] # get the length of a particular spring by indexing\n",
        "        return l\n",
        "        \n",
        "    def measure_spring_strain(self, x, spring_index):\n",
        "        # strain = change in length / original length\n",
        "        d = self.incidence.mm(x)\n",
        "        q = d.pow(2).sum(1)\n",
        "        l = q.sqrt()\n",
        "        strain = (l / self.l0) - 1\n",
        "        #dl = (l - self.l0)\n",
        "        strain = strain[spring_index] # get the strain of a particular spring by indexing\n",
        "        return strain\n",
        "    \n",
        "    def measure_length_change(self, x):\n",
        "        d = self.incidence.mm(x)\n",
        "        q = d.pow(2).sum(1)\n",
        "        l = q.sqrt()\n",
        "        dl = (l - self.l0)\n",
        "        return dl\n",
        "        \n",
        "    \n",
        "    def energy(self, x):\n",
        "        d = self.incidence.float().mm(x) \n",
        "        q = d.pow(2).sum(1)\n",
        "        l = q.sqrt()\n",
        "        #l = (q + 1e-6).sqrt()\n",
        "        dl = l - self.l0\n",
        "        #e = 0.5 * (self.k * dl.pow(2)).sum()\n",
        "        e = 0.5 * (self.k * dl.pow(2)) # without summing, returns vector of size = num_springs\n",
        "        return e\n",
        "    \n",
        "    def partial_e(self, x):\n",
        "      # k * (x - l)\n",
        "      d = self.incidence.float().mm(x) \n",
        "      q = d.pow(2).sum(1)\n",
        "      l = q.sqrt()\n",
        "      dl = l - self.l0\n",
        "      partial_e = self.k * dl\n",
        "      return partial_e\n",
        "\n",
        "    def partial_e_k(self, x):\n",
        "      # k * (x - l)^2\n",
        "      d = self.incidence.float().mm(x) \n",
        "      q = d.pow(2).sum(1)\n",
        "      l = q.sqrt()\n",
        "      dl = l - self.l0\n",
        "      partial_e_k = self.k * dl.pow(2)\n",
        "      return partial_e_k"
      ],
      "metadata": {
        "id": "kdKqFM0qbhKH"
      },
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "#_______________________________ INIT NETWORK__________________________________\n",
        "\n",
        "# set seeds if you want the same network everytime\n",
        "seed = 8\n",
        "torch.random.manual_seed(seed)\n",
        "np.random.seed(seed)\n",
        "random.seed(seed)\n",
        "\n",
        "# create network\n",
        "noise_low=-0.1\n",
        "noise_high=0.1\n",
        "num_nodes, num_springs, x, indices, base_x = make_network(3, 3, noise_low=noise_low, noise_high=noise_high)\n",
        "num_springs = len(indices)\n",
        "\n",
        "# copy initial conditions so that the network can be reinitialised each time\n",
        "x_init = x.detach().clone()\n",
        "\n",
        "# initialise learning degrees of freedom\n",
        "# noise scale should not be greater than 1\n",
        "l0 = get_l0(num_springs, 10, noise_scale=10)\n",
        "k = get_k(num_springs, 50)\n",
        "#l0 = torch.ones(num_springs)\n",
        "#k = torch.ones(num_springs)\n",
        "\n",
        "\n",
        "# select source springs\n",
        "num_source_springs = 1\n",
        "s_springs = get_source_springs(num_springs, num_source_springs)\n",
        "print(s_springs) \n",
        "# source spring equil length needs to always be 1\n",
        "l0[s_springs] = 1\n",
        "\n",
        "\n",
        "# select target springs \n",
        "num_targets = 1 # if we are only doing MNIST with 0s and 1s...\n",
        "t_springs = get_target_springs(num_springs, num_targets, s_springs)\n",
        "#set_value = 13\n",
        "#t_springs = np.array([set_value])\n",
        "print(t_springs)\n",
        "\n",
        "mask1 = create_spring_mask(s_springs, t_springs, indices, num_nodes)\n",
        "mask2 = create_spring_mask(s_springs, t_springs, indices, num_nodes, free_mode=False)\n",
        "\n",
        "# instantiate network\n",
        "spring_network = MSD(indices, l0, k, num_nodes)"
      ],
      "metadata": {
        "id": "ZPPiR1kox6FP",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "b1c144ff-bfe2-4427-8b90-357f30d909c3"
      },
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Graph with 10 nodes and 18 edges\n",
            "[14]\n",
            "[7]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "\n",
        "\"\"\"\n",
        "_________________COUPLED LEARNING RULE: ALLOSTERY______________________\n",
        "\"\"\"\n",
        "    \n",
        "def get_nudged_target(free_strain, desired_strain, eta):\n",
        "    error = 0.5 * torch.pow((desired_strain - free_strain), 2)\n",
        "    if (free_strain > desired_strain):\n",
        "        error = error * -1\n",
        "        \n",
        "    # or could just do \n",
        "    nudged_strain = free_strain + (eta* (desired_strain-free_strain))\n",
        "    length = l0[t_springs[0]] * (nudged_strain + 1)\n",
        "    #length = free_strain + (eta * error)\n",
        "    return length, error\n",
        "\n",
        "\n",
        "l0_init_s = l0[s_springs[0]].detach().clone()\n",
        "l0_init_t = l0[t_springs[0]].detach().clone()\n",
        "\n",
        "\n",
        "#alpha = 5e-4\n",
        "alpha = 1e-3 \n",
        "\n",
        "eta = 1e-1\n",
        "epochs = 100\n",
        "#run_time = 200000\n",
        "run_time = 20000\n",
        "\n",
        "mu, sigma = 0, 2.5\n",
        "factor =  np.random.normal(mu, sigma, 1)[0]\n",
        "#print(factor)\n",
        "input_strain = factor + 5\n",
        "sigma2 = 0.2*sigma\n",
        "factor2 =  np.random.normal(mu, sigma2, 1)[0]\n",
        "#print(factor2)\n",
        "target = factor2 + 5\n",
        "\n",
        "print('s and t')\n",
        "print(input_strain)\n",
        "print(target)\n",
        "\n",
        "\n",
        "lengths_list = np.zeros(epochs)\n",
        "target_l0s = np.zeros(epochs)\n",
        "\n",
        "errors = np.zeros(epochs)\n",
        "energies_list = np.zeros(epochs)\n",
        "partial_energies_list = np.zeros(epochs)\n",
        "\n",
        "for i in range(epochs):\n",
        "\n",
        "    print(f'iteration no.: {i}')\n",
        "\n",
        "    print('l0 of the target spring', l0[t_springs[0]])\n",
        "\n",
        "    target_l0s[i] = l0[t_springs[0]].item()\n",
        "    \n",
        "    with torch.no_grad():\n",
        "      # reset x\n",
        "      x = x_init.detach().clone()\n",
        "      x.requires_grad = True\n",
        "\n",
        "    # PHASE 1: run to equilibrium (free state)\n",
        "    \n",
        "    k_orig = k.detach().clone()\n",
        "    l0_orig = l0.detach().clone()\n",
        "    \n",
        "    # clamp source inputs \n",
        "    x = clamp_spring_length(spring_network, input_strain, s_springs[0], indices, x, l0)\n",
        "\n",
        "    # instantiate the optimizer    \n",
        "    optimizer = torch.optim.Adagrad([x], lr=1e-1)\n",
        "\n",
        "    # inference\n",
        "    energies = run_to_equil(mask1, x, optimizer, spring_network, iterations=run_time)\n",
        "    energies_list[i] = energies[-1]\n",
        "    partial_energies_list[i] = spring_network.partial_e(x).sum()\n",
        "    free_state_energy = spring_network.energy(x).sum()\n",
        "    #print(energies[0], energies[-1])\n",
        "    #print(spring_network.measure_spring_strain(x, t_springs))\n",
        "    free_target_len = spring_network.measure_spring_length(x, t_springs)\n",
        "    free_target_strain = spring_network.measure_spring_strain(x, t_springs)\n",
        "    print('length',free_target_len.item())\n",
        "\n",
        "    lengths_list[i] = free_target_len.item()\n",
        "\n",
        "    print('strain',free_target_strain.item())\n",
        "    free_state_dl = spring_network.measure_length_change(x)\n",
        "    print('free_state_energy',free_state_energy)\n",
        "    \n",
        "    # PHASE 2: now clamp target at nudged length and run to second equilibrium\n",
        "\n",
        "    # clamp target\n",
        "    #target_len_nudged, error = get_nudged_target(free_target_len, target, eta)\n",
        "    target_len_nudged, error = get_nudged_target(free_target_strain, target, eta)\n",
        "\n",
        "    print('_________error', error.item())\n",
        "    errors[i] = error.item()\n",
        "\n",
        "    x = clamp_spring_length(spring_network, target_len_nudged, t_springs[0], indices, x, l0)\n",
        "   \n",
        "    energies2 = run_to_equil(mask1, x, optimizer, spring_network, iterations=run_time)\n",
        "    \"\"\"\n",
        "    take this below bit out as biologically implausible - if it has no affect?\n",
        "    \"\"\"\n",
        "    # reinstate the original ks and l0s to get a measure of the energy function\n",
        "    with torch.no_grad():\n",
        "        k[t_springs[0]] = k_orig[t_springs[0]] \n",
        "        l0[t_springs[0]] = l0_orig[t_springs[0]]\n",
        "    \n",
        "    spring_network.l0 = l0\n",
        "    spring_network.k = k\n",
        "    clamp_state_energy = spring_network.energy(x).sum()\n",
        "    print('clamp_state_energy',clamp_state_energy)\n",
        "    \n",
        "    # PHASE 3: weight update \n",
        "    \n",
        "    clamped_state_dl = spring_network.measure_length_change(x)\n",
        "    \n",
        "    with torch.no_grad():\n",
        "        dls = free_state_dl - clamped_state_dl\n",
        "        #dls = np.linalg.norm(free_state_dl - clamped_state_dl)\n",
        "        all_strains = torch.mul(k, dls)\n",
        "\n",
        "        # __________if I want to check whether its worse at learning when target cannot learn...\n",
        "        #target_springs_l0 = l0[t_springs[0]].detach().clone()\n",
        "\n",
        "        # weight update\n",
        "        l0 = l0 + (alpha * (1/eta)* all_strains)\n",
        "        l0[l0<0] = 1e-6\n",
        "\n",
        "        # __________if I want to check whether its worse at learning when target cannot learn...\n",
        "        #l0[t_springs[0]] = target_springs_l0\n",
        "\n",
        "\n",
        "    spring_network.l0 = l0\n",
        "   \n",
        "\n",
        "\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "0EFyO-HmajOi",
        "outputId": "0c6967d7-748f-4ede-ca2b-e35dbe8cbb9e"
      },
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "s and t\n",
            "8.936084809721873\n",
            "5.130911414813278\n",
            "iteration no.: 0\n",
            "l0 of the target spring tensor(5.5966)\n",
            "length 7.969210624694824\n",
            "strain 0.42392992973327637\n",
            "free_state_energy tensor(346.3716, grad_fn=<SumBackward0>)\n",
            "_________error 11.077837944030762\n",
            "clamp_state_energy tensor(368.1424, grad_fn=<SumBackward0>)\n",
            "iteration no.: 1\n",
            "l0 of the target spring tensor(5.2536)\n",
            "length 7.527449131011963\n",
            "strain 0.43280911445617676\n",
            "free_state_energy tensor(331.5425, grad_fn=<SumBackward0>)\n",
            "_________error 11.036081314086914\n",
            "clamp_state_energy tensor(346.2207, grad_fn=<SumBackward0>)\n",
            "iteration no.: 2\n",
            "l0 of the target spring tensor(4.9323)\n",
            "length 7.107660293579102\n",
            "strain 0.44105613231658936\n",
            "free_state_energy tensor(317.1154, grad_fn=<SumBackward0>)\n",
            "_________error 10.997370719909668\n",
            "clamp_state_energy tensor(323.7551, grad_fn=<SumBackward0>)\n",
            "iteration no.: 3\n",
            "l0 of the target spring tensor(4.6311)\n",
            "length 6.707282066345215\n",
            "strain 0.4483211040496826\n",
            "free_state_energy tensor(302.8032, grad_fn=<SumBackward0>)\n",
            "_________error 10.963326454162598\n",
            "clamp_state_energy tensor(304.0668, grad_fn=<SumBackward0>)\n",
            "iteration no.: 4\n",
            "l0 of the target spring tensor(4.3487)\n",
            "length 6.333877086639404\n",
            "strain 0.45649242401123047\n",
            "free_state_energy tensor(289.4363, grad_fn=<SumBackward0>)\n",
            "_________error 10.92509651184082\n",
            "clamp_state_energy tensor(285.4753, grad_fn=<SumBackward0>)\n",
            "iteration no.: 5\n",
            "l0 of the target spring tensor(4.0840)\n",
            "length 5.988511562347412\n",
            "strain 0.4663194417953491\n",
            "free_state_energy tensor(277.1380, grad_fn=<SumBackward0>)\n",
            "_________error 10.8792085647583\n",
            "clamp_state_energy tensor(268.3698, grad_fn=<SumBackward0>)\n",
            "iteration no.: 6\n",
            "l0 of the target spring tensor(3.8360)\n",
            "length 5.657739162445068\n",
            "strain 0.47490668296813965\n",
            "free_state_energy tensor(264.7930, grad_fn=<SumBackward0>)\n",
            "_________error 10.839190483093262\n",
            "clamp_state_energy tensor(252.5508, grad_fn=<SumBackward0>)\n",
            "iteration no.: 7\n",
            "l0 of the target spring tensor(3.6034)\n",
            "length 5.352540969848633\n",
            "strain 0.4853947162628174\n",
            "free_state_energy tensor(253.4804, grad_fn=<SumBackward0>)\n",
            "_________error 10.790410995483398\n",
            "clamp_state_energy tensor(238.1290, grad_fn=<SumBackward0>)\n",
            "iteration no.: 8\n",
            "l0 of the target spring tensor(3.3855)\n",
            "length 5.068360328674316\n",
            "strain 0.49708497524261475\n",
            "free_state_energy tensor(242.8672, grad_fn=<SumBackward0>)\n",
            "_________error 10.736172676086426\n",
            "clamp_state_energy tensor(224.5772, grad_fn=<SumBackward0>)\n",
            "iteration no.: 9\n",
            "l0 of the target spring tensor(3.1812)\n",
            "length 4.800642013549805\n",
            "strain 0.5090548992156982\n",
            "free_state_energy tensor(232.5876, grad_fn=<SumBackward0>)\n",
            "_________error 10.680779457092285\n",
            "clamp_state_energy tensor(213.2444, grad_fn=<SumBackward0>)\n",
            "iteration no.: 10\n",
            "l0 of the target spring tensor(2.9898)\n",
            "length 4.559117794036865\n",
            "strain 0.5248996019363403\n",
            "free_state_energy tensor(223.7315, grad_fn=<SumBackward0>)\n",
            "_________error 10.607672691345215\n",
            "clamp_state_energy tensor(202.3559, grad_fn=<SumBackward0>)\n",
            "iteration no.: 11\n",
            "l0 of the target spring tensor(2.8105)\n",
            "length 4.330521583557129\n",
            "strain 0.540848970413208\n",
            "free_state_energy tensor(215.0410, grad_fn=<SumBackward0>)\n",
            "_________error 10.534335136413574\n",
            "clamp_state_energy tensor(192.5247, grad_fn=<SumBackward0>)\n",
            "iteration no.: 12\n",
            "l0 of the target spring tensor(2.6425)\n",
            "length 4.118027210235596\n",
            "strain 0.5583770275115967\n",
            "free_state_energy tensor(206.9287, grad_fn=<SumBackward0>)\n",
            "_________error 10.454035758972168\n",
            "clamp_state_energy tensor(184.2928, grad_fn=<SumBackward0>)\n",
            "iteration no.: 13\n",
            "l0 of the target spring tensor(2.4852)\n",
            "length 3.924370050430298\n",
            "strain 0.579106330871582\n",
            "free_state_energy tensor(199.8004, grad_fn=<SumBackward0>)\n",
            "_________error 10.359464645385742\n",
            "clamp_state_energy tensor(176.6902, grad_fn=<SumBackward0>)\n",
            "iteration no.: 14\n",
            "l0 of the target spring tensor(2.3379)\n",
            "length 3.7441232204437256\n",
            "strain 0.6014927625656128\n",
            "free_state_energy tensor(193.1520, grad_fn=<SumBackward0>)\n",
            "_________error 10.25781536102295\n",
            "clamp_state_energy tensor(169.7918, grad_fn=<SumBackward0>)\n",
            "iteration no.: 15\n",
            "l0 of the target spring tensor(2.2000)\n",
            "length 3.5762925148010254\n",
            "strain 0.6255741119384766\n",
            "free_state_energy tensor(186.9533, grad_fn=<SumBackward0>)\n",
            "_________error 10.149031639099121\n",
            "clamp_state_energy tensor(162.6933, grad_fn=<SumBackward0>)\n",
            "iteration no.: 16\n",
            "l0 of the target spring tensor(2.0710)\n",
            "length 3.416091203689575\n",
            "strain 0.6495194435119629\n",
            "free_state_energy tensor(180.6931, grad_fn=<SumBackward0>)\n",
            "_________error 10.041437149047852\n",
            "clamp_state_energy tensor(157.3362, grad_fn=<SumBackward0>)\n",
            "iteration no.: 17\n",
            "l0 of the target spring tensor(1.9501)\n",
            "length 3.2709155082702637\n",
            "strain 0.677288293838501\n",
            "free_state_energy tensor(175.3602, grad_fn=<SumBackward0>)\n",
            "_________error 9.917378425598145\n",
            "clamp_state_energy tensor(151.2832, grad_fn=<SumBackward0>)\n",
            "iteration no.: 18\n",
            "l0 of the target spring tensor(1.8370)\n",
            "length 3.1317317485809326\n",
            "strain 0.7047731876373291\n",
            "free_state_energy tensor(169.8781, grad_fn=<SumBackward0>)\n",
            "_________error 9.795348167419434\n",
            "clamp_state_energy tensor(146.0632, grad_fn=<SumBackward0>)\n",
            "iteration no.: 19\n",
            "l0 of the target spring tensor(1.7312)\n",
            "length 3.0021684169769287\n",
            "strain 0.7341866493225098\n",
            "free_state_energy tensor(164.7736, grad_fn=<SumBackward0>)\n",
            "_________error 9.665594100952148\n",
            "clamp_state_energy tensor(141.3036, grad_fn=<SumBackward0>)\n",
            "iteration no.: 20\n",
            "l0 of the target spring tensor(1.6321)\n",
            "length 2.8814759254455566\n",
            "strain 0.7655419111251831\n",
            "free_state_energy tensor(160.0180, grad_fn=<SumBackward0>)\n",
            "_________error 9.52822494506836\n",
            "clamp_state_energy tensor(136.5777, grad_fn=<SumBackward0>)\n",
            "iteration no.: 21\n",
            "l0 of the target spring tensor(1.5393)\n",
            "length 2.76751446723938\n",
            "strain 0.797906756401062\n",
            "free_state_energy tensor(155.3674, grad_fn=<SumBackward0>)\n",
            "_________error 9.387463569641113\n",
            "clamp_state_energy tensor(132.3884, grad_fn=<SumBackward0>)\n",
            "iteration no.: 22\n",
            "l0 of the target spring tensor(1.4525)\n",
            "length 2.661365270614624\n",
            "strain 0.8323228359222412\n",
            "free_state_energy tensor(151.0356, grad_fn=<SumBackward0>)\n",
            "_________error 9.238932609558105\n",
            "clamp_state_energy tensor(128.9453, grad_fn=<SumBackward0>)\n",
            "iteration no.: 23\n",
            "l0 of the target spring tensor(1.3712)\n",
            "length 2.563844919204712\n",
            "strain 0.8698351383209229\n",
            "free_state_energy tensor(147.2155, grad_fn=<SumBackward0>)\n",
            "_________error 9.078384399414062\n",
            "clamp_state_energy tensor(125.6415, grad_fn=<SumBackward0>)\n",
            "iteration no.: 24\n",
            "l0 of the target spring tensor(1.2951)\n",
            "length 2.472888469696045\n",
            "strain 0.9094376564025879\n",
            "free_state_energy tensor(143.6556, grad_fn=<SumBackward0>)\n",
            "_________error 8.910420417785645\n",
            "clamp_state_energy tensor(123.3132, grad_fn=<SumBackward0>)\n",
            "iteration no.: 25\n",
            "l0 of the target spring tensor(1.2239)\n",
            "length 2.390249490737915\n",
            "strain 0.9529744386672974\n",
            "free_state_energy tensor(140.7013, grad_fn=<SumBackward0>)\n",
            "_________error 8.727579116821289\n",
            "clamp_state_energy tensor(120.1843, grad_fn=<SumBackward0>)\n",
            "iteration no.: 26\n",
            "l0 of the target spring tensor(1.1573)\n",
            "length 2.3109230995178223\n",
            "strain 0.9967823028564453\n",
            "free_state_energy tensor(137.5791, grad_fn=<SumBackward0>)\n",
            "_________error 8.545511245727539\n",
            "clamp_state_energy tensor(117.6085, grad_fn=<SumBackward0>)\n",
            "iteration no.: 27\n",
            "l0 of the target spring tensor(1.0950)\n",
            "length 2.2369353771209717\n",
            "strain 1.0428135395050049\n",
            "free_state_energy tensor(134.6699, grad_fn=<SumBackward0>)\n",
            "_________error 8.356270790100098\n",
            "clamp_state_energy tensor(115.2423, grad_fn=<SumBackward0>)\n",
            "iteration no.: 28\n",
            "l0 of the target spring tensor(1.0367)\n",
            "length 2.1679162979125977\n",
            "strain 1.091090440750122\n",
            "free_state_energy tensor(131.9576, grad_fn=<SumBackward0>)\n",
            "_________error 8.160075187683105\n",
            "clamp_state_energy tensor(113.8962, grad_fn=<SumBackward0>)\n",
            "iteration no.: 29\n",
            "l0 of the target spring tensor(0.9822)\n",
            "length 2.1059482097625732\n",
            "strain 1.1440987586975098\n",
            "free_state_energy tensor(129.8648, grad_fn=<SumBackward0>)\n",
            "_________error 7.9473371505737305\n",
            "clamp_state_energy tensor(111.4821, grad_fn=<SumBackward0>)\n",
            "iteration no.: 30\n",
            "l0 of the target spring tensor(0.9312)\n",
            "length 2.0458171367645264\n",
            "strain 1.19692063331604\n",
            "free_state_energy tensor(127.4867, grad_fn=<SumBackward0>)\n",
            "_________error 7.7381415367126465\n",
            "clamp_state_energy tensor(109.6247, grad_fn=<SumBackward0>)\n",
            "iteration no.: 31\n",
            "l0 of the target spring tensor(0.8835)\n",
            "length 1.9897716045379639\n",
            "strain 1.2520930767059326\n",
            "free_state_energy tensor(125.2716, grad_fn=<SumBackward0>)\n",
            "_________error 7.522615432739258\n",
            "clamp_state_energy tensor(107.5698, grad_fn=<SumBackward0>)\n",
            "iteration no.: 32\n",
            "l0 of the target spring tensor(0.8389)\n",
            "length 1.9365285634994507\n",
            "strain 1.308415174484253\n",
            "free_state_energy tensor(123.0123, grad_fn=<SumBackward0>)\n",
            "_________error 7.30573844909668\n",
            "clamp_state_energy tensor(106.1671, grad_fn=<SumBackward0>)\n",
            "iteration no.: 33\n",
            "l0 of the target spring tensor(0.7971)\n",
            "length 1.8879470825195312\n",
            "strain 1.368380069732666\n",
            "free_state_energy tensor(121.1061, grad_fn=<SumBackward0>)\n",
            "_________error 7.0783209800720215\n",
            "clamp_state_energy tensor(105.8251, grad_fn=<SumBackward0>)\n",
            "iteration no.: 34\n",
            "l0 of the target spring tensor(0.7581)\n",
            "length 1.8456114530563354\n",
            "strain 1.4345390796661377\n",
            "free_state_energy tensor(119.9089, grad_fn=<SumBackward0>)\n",
            "_________error 6.8315839767456055\n",
            "clamp_state_energy tensor(105.0589, grad_fn=<SumBackward0>)\n",
            "iteration no.: 35\n",
            "l0 of the target spring tensor(0.7216)\n",
            "length 1.8063981533050537\n",
            "strain 1.5032925605773926\n",
            "free_state_energy tensor(118.8120, grad_fn=<SumBackward0>)\n",
            "_________error 6.579809188842773\n",
            "clamp_state_energy tensor(103.2914, grad_fn=<SumBackward0>)\n",
            "iteration no.: 36\n",
            "l0 of the target spring tensor(0.6875)\n",
            "length 1.7670332193374634\n",
            "strain 1.5701370239257812\n",
            "free_state_energy tensor(117.2335, grad_fn=<SumBackward0>)\n",
            "_________error 6.339556694030762\n",
            "clamp_state_energy tensor(102.1472, grad_fn=<SumBackward0>)\n",
            "iteration no.: 37\n",
            "l0 of the target spring tensor(0.6556)\n",
            "length 1.730473279953003\n",
            "strain 1.6393280029296875\n",
            "free_state_energy tensor(115.7649, grad_fn=<SumBackward0>)\n",
            "_________error 6.095577239990234\n",
            "clamp_state_energy tensor(101.0979, grad_fn=<SumBackward0>)\n",
            "iteration no.: 38\n",
            "l0 of the target spring tensor(0.6258)\n",
            "length 1.696523904800415\n",
            "strain 1.7107858657836914\n",
            "free_state_energy tensor(114.4039, grad_fn=<SumBackward0>)\n",
            "_________error 5.848628997802734\n",
            "clamp_state_energy tensor(100.1396, grad_fn=<SumBackward0>)\n",
            "iteration no.: 39\n",
            "l0 of the target spring tensor(0.5980)\n",
            "length 1.6650307178497314\n",
            "strain 1.7844610214233398\n",
            "free_state_energy tensor(113.1437, grad_fn=<SumBackward0>)\n",
            "_________error 5.599364757537842\n",
            "clamp_state_energy tensor(100.0064, grad_fn=<SumBackward0>)\n",
            "iteration no.: 40\n",
            "l0 of the target spring tensor(0.5719)\n",
            "length 1.6378834247589111\n",
            "strain 1.8638465404510498\n",
            "free_state_energy tensor(112.3889, grad_fn=<SumBackward0>)\n",
            "_________error 5.336856365203857\n",
            "clamp_state_energy tensor(98.8619, grad_fn=<SumBackward0>)\n",
            "iteration no.: 41\n",
            "l0 of the target spring tensor(0.5476)\n",
            "length 1.6108318567276\n",
            "strain 1.9416823387145996\n",
            "free_state_energy tensor(111.2975, grad_fn=<SumBackward0>)\n",
            "_________error 5.085590839385986\n",
            "clamp_state_energy tensor(98.1251, grad_fn=<SumBackward0>)\n",
            "iteration no.: 42\n",
            "l0 of the target spring tensor(0.5248)\n",
            "length 1.5858176946640015\n",
            "strain 2.0214693546295166\n",
            "free_state_energy tensor(110.2891, grad_fn=<SumBackward0>)\n",
            "_________error 4.834314823150635\n",
            "clamp_state_energy tensor(98.3535, grad_fn=<SumBackward0>)\n",
            "iteration no.: 43\n",
            "l0 of the target spring tensor(0.5036)\n",
            "length 1.5652153491973877\n",
            "strain 2.1080493927001953\n",
            "free_state_energy tensor(109.8615, grad_fn=<SumBackward0>)\n",
            "_________error 4.568847179412842\n",
            "clamp_state_energy tensor(97.1843, grad_fn=<SumBackward0>)\n",
            "iteration no.: 44\n",
            "l0 of the target spring tensor(0.4838)\n",
            "length 1.5434339046478271\n",
            "strain 2.190368175506592\n",
            "free_state_energy tensor(108.9046, grad_fn=<SumBackward0>)\n",
            "_________error 4.323397159576416\n",
            "clamp_state_energy tensor(96.6965, grad_fn=<SumBackward0>)\n",
            "iteration no.: 45\n",
            "l0 of the target spring tensor(0.4653)\n",
            "length 1.5238004922866821\n",
            "strain 2.2751822471618652\n",
            "free_state_energy tensor(108.1075, grad_fn=<SumBackward0>)\n",
            "_________error 4.07759428024292\n",
            "clamp_state_energy tensor(96.2003, grad_fn=<SumBackward0>)\n",
            "iteration no.: 46\n",
            "l0 of the target spring tensor(0.4480)\n",
            "length 1.5057599544525146\n",
            "strain 2.3613932132720947\n",
            "free_state_energy tensor(107.3747, grad_fn=<SumBackward0>)\n",
            "_________error 3.835115432739258\n",
            "clamp_state_energy tensor(96.9618, grad_fn=<SumBackward0>)\n",
            "iteration no.: 47\n",
            "l0 of the target spring tensor(0.4318)\n",
            "length 1.492624282836914\n",
            "strain 2.4567203521728516\n",
            "free_state_energy tensor(107.3872, grad_fn=<SumBackward0>)\n",
            "_________error 3.575648784637451\n",
            "clamp_state_energy tensor(95.7358, grad_fn=<SumBackward0>)\n",
            "iteration no.: 48\n",
            "l0 of the target spring tensor(0.4168)\n",
            "length 1.4765907526016235\n",
            "strain 2.5429515838623047\n",
            "free_state_energy tensor(106.5905, grad_fn=<SumBackward0>)\n",
            "_________error 3.3487677574157715\n",
            "clamp_state_energy tensor(96.6985, grad_fn=<SumBackward0>)\n",
            "iteration no.: 49\n",
            "l0 of the target spring tensor(0.4027)\n",
            "length 1.4663256406784058\n",
            "strain 2.64100980758667\n",
            "free_state_energy tensor(106.7142, grad_fn=<SumBackward0>)\n",
            "_________error 3.0998048782348633\n",
            "clamp_state_energy tensor(95.6895, grad_fn=<SumBackward0>)\n",
            "iteration no.: 50\n",
            "l0 of the target spring tensor(0.3897)\n",
            "length 1.453227162361145\n",
            "strain 2.729390859603882\n",
            "free_state_energy tensor(106.0952, grad_fn=<SumBackward0>)\n",
            "_________error 2.883650302886963\n",
            "clamp_state_energy tensor(95.4605, grad_fn=<SumBackward0>)\n",
            "iteration no.: 51\n",
            "l0 of the target spring tensor(0.3775)\n",
            "length 1.4417492151260376\n",
            "strain 2.8193626403808594\n",
            "free_state_energy tensor(105.6142, grad_fn=<SumBackward0>)\n",
            "_________error 2.671628713607788\n",
            "clamp_state_energy tensor(95.2144, grad_fn=<SumBackward0>)\n",
            "iteration no.: 52\n",
            "l0 of the target spring tensor(0.3661)\n",
            "length 1.4313620328903198\n",
            "strain 2.909511089324951\n",
            "free_state_energy tensor(105.1793, grad_fn=<SumBackward0>)\n",
            "_________error 2.4673094749450684\n",
            "clamp_state_energy tensor(96.3508, grad_fn=<SumBackward0>)\n",
            "iteration no.: 53\n",
            "l0 of the target spring tensor(0.3555)\n",
            "length 1.4261902570724487\n",
            "strain 3.0114097595214844\n",
            "free_state_energy tensor(105.5695, grad_fn=<SumBackward0>)\n",
            "_________error 2.2461435794830322\n",
            "clamp_state_energy tensor(95.4345, grad_fn=<SumBackward0>)\n",
            "iteration no.: 54\n",
            "l0 of the target spring tensor(0.3457)\n",
            "length 1.4173228740692139\n",
            "strain 3.099605083465576\n",
            "free_state_energy tensor(105.1194, grad_fn=<SumBackward0>)\n",
            "_________error 2.0631024837493896\n",
            "clamp_state_energy tensor(96.4802, grad_fn=<SumBackward0>)\n",
            "iteration no.: 55\n",
            "l0 of the target spring tensor(0.3366)\n",
            "length 1.4136077165603638\n",
            "strain 3.1999406814575195\n",
            "free_state_energy tensor(105.4773, grad_fn=<SumBackward0>)\n",
            "_________error 1.8643238544464111\n",
            "clamp_state_energy tensor(95.5952, grad_fn=<SumBackward0>)\n",
            "iteration no.: 56\n",
            "l0 of the target spring tensor(0.3281)\n",
            "length 1.4060505628585815\n",
            "strain 3.2852277755737305\n",
            "free_state_energy tensor(105.0180, grad_fn=<SumBackward0>)\n",
            "_________error 1.703273892402649\n",
            "clamp_state_energy tensor(97.4810, grad_fn=<SumBackward0>)\n",
            "iteration no.: 57\n",
            "l0 of the target spring tensor(0.3202)\n",
            "length 1.4065461158752441\n",
            "strain 3.392292022705078\n",
            "free_state_energy tensor(105.8457, grad_fn=<SumBackward0>)\n",
            "_________error 1.5113985538482666\n",
            "clamp_state_energy tensor(96.5582, grad_fn=<SumBackward0>)\n",
            "iteration no.: 58\n",
            "l0 of the target spring tensor(0.3130)\n",
            "length 1.401470422744751\n",
            "strain 3.4778084754943848\n",
            "free_state_energy tensor(105.6100, grad_fn=<SumBackward0>)\n",
            "_________error 1.3663746118545532\n",
            "clamp_state_energy tensor(96.3692, grad_fn=<SumBackward0>)\n",
            "iteration no.: 59\n",
            "l0 of the target spring tensor(0.3062)\n",
            "length 1.3966090679168701\n",
            "strain 3.560436248779297\n",
            "free_state_energy tensor(105.3147, grad_fn=<SumBackward0>)\n",
            "_________error 1.2331960201263428\n",
            "clamp_state_energy tensor(96.0233, grad_fn=<SumBackward0>)\n",
            "iteration no.: 60\n",
            "l0 of the target spring tensor(0.3000)\n",
            "length 1.3914942741394043\n",
            "strain 3.6385855674743652\n",
            "free_state_energy tensor(104.9007, grad_fn=<SumBackward0>)\n",
            "_________error 1.1135181188583374\n",
            "clamp_state_energy tensor(96.0223, grad_fn=<SumBackward0>)\n",
            "iteration no.: 61\n",
            "l0 of the target spring tensor(0.2942)\n",
            "length 1.3878555297851562\n",
            "strain 3.718132972717285\n",
            "free_state_energy tensor(104.6647, grad_fn=<SumBackward0>)\n",
            "_________error 0.9979713559150696\n",
            "clamp_state_energy tensor(96.0860, grad_fn=<SumBackward0>)\n",
            "iteration no.: 62\n",
            "l0 of the target spring tensor(0.2887)\n",
            "length 1.3852722644805908\n",
            "strain 3.7976012229919434\n",
            "free_state_energy tensor(104.5394, grad_fn=<SumBackward0>)\n",
            "_________error 0.8888579607009888\n",
            "clamp_state_energy tensor(96.1160, grad_fn=<SumBackward0>)\n",
            "iteration no.: 63\n",
            "l0 of the target spring tensor(0.2837)\n",
            "length 1.3831993341445923\n",
            "strain 3.875054359436035\n",
            "free_state_energy tensor(104.4377, grad_fn=<SumBackward0>)\n",
            "_________error 0.7885884046554565\n",
            "clamp_state_energy tensor(96.0414, grad_fn=<SumBackward0>)\n",
            "iteration no.: 64\n",
            "l0 of the target spring tensor(0.2791)\n",
            "length 1.3810982704162598\n",
            "strain 3.9485678672790527\n",
            "free_state_energy tensor(104.2730, grad_fn=<SumBackward0>)\n",
            "_________error 0.6989680528640747\n",
            "clamp_state_energy tensor(96.0286, grad_fn=<SumBackward0>)\n",
            "iteration no.: 65\n",
            "l0 of the target spring tensor(0.2748)\n",
            "length 1.3794479370117188\n",
            "strain 4.019935131072998\n",
            "free_state_energy tensor(104.1289, grad_fn=<SumBackward0>)\n",
            "_________error 0.6171340942382812\n",
            "clamp_state_energy tensor(96.0346, grad_fn=<SumBackward0>)\n",
            "iteration no.: 66\n",
            "l0 of the target spring tensor(0.2708)\n",
            "length 1.378207802772522\n",
            "strain 4.089037895202637\n",
            "free_state_energy tensor(104.0002, grad_fn=<SumBackward0>)\n",
            "_________error 0.5427501201629639\n",
            "clamp_state_energy tensor(96.1751, grad_fn=<SumBackward0>)\n",
            "iteration no.: 67\n",
            "l0 of the target spring tensor(0.2671)\n",
            "length 1.377826452255249\n",
            "strain 4.157594203948975\n",
            "free_state_energy tensor(103.9737, grad_fn=<SumBackward0>)\n",
            "_________error 0.47367313504219055\n",
            "clamp_state_energy tensor(96.1633, grad_fn=<SumBackward0>)\n",
            "iteration no.: 68\n",
            "l0 of the target spring tensor(0.2638)\n",
            "length 1.3773373365402222\n",
            "strain 4.221940517425537\n",
            "free_state_energy tensor(103.8763, grad_fn=<SumBackward0>)\n",
            "_________error 0.4131139814853668\n",
            "clamp_state_energy tensor(96.2041, grad_fn=<SumBackward0>)\n",
            "iteration no.: 69\n",
            "l0 of the target spring tensor(0.2606)\n",
            "length 1.3771817684173584\n",
            "strain 4.283886909484863\n",
            "free_state_energy tensor(103.7933, grad_fn=<SumBackward0>)\n",
            "_________error 0.3587251901626587\n",
            "clamp_state_energy tensor(96.3807, grad_fn=<SumBackward0>)\n",
            "iteration no.: 70\n",
            "l0 of the target spring tensor(0.2578)\n",
            "length 1.3777904510498047\n",
            "strain 4.345167636871338\n",
            "free_state_energy tensor(103.8070, grad_fn=<SumBackward0>)\n",
            "_________error 0.30869659781455994\n",
            "clamp_state_energy tensor(96.5232, grad_fn=<SumBackward0>)\n",
            "iteration no.: 71\n",
            "l0 of the target spring tensor(0.2551)\n",
            "length 1.3786561489105225\n",
            "strain 4.403805255889893\n",
            "free_state_energy tensor(103.8335, grad_fn=<SumBackward0>)\n",
            "_________error 0.2643416225910187\n",
            "clamp_state_energy tensor(97.8154, grad_fn=<SumBackward0>)\n",
            "iteration no.: 72\n",
            "l0 of the target spring tensor(0.2527)\n",
            "length 1.3842519521713257\n",
            "strain 4.477596282958984\n",
            "free_state_energy tensor(104.5850, grad_fn=<SumBackward0>)\n",
            "_________error 0.21341028809547424\n",
            "clamp_state_energy tensor(98.3855, grad_fn=<SumBackward0>)\n",
            "iteration no.: 73\n",
            "l0 of the target spring tensor(0.2506)\n",
            "length 1.3892563581466675\n",
            "strain 4.544562816619873\n",
            "free_state_energy tensor(105.1745, grad_fn=<SumBackward0>)\n",
            "_________error 0.17190229892730713\n",
            "clamp_state_energy tensor(98.2179, grad_fn=<SumBackward0>)\n",
            "iteration no.: 74\n",
            "l0 of the target spring tensor(0.2486)\n",
            "length 1.3909558057785034\n",
            "strain 4.594052791595459\n",
            "free_state_energy tensor(105.2296, grad_fn=<SumBackward0>)\n",
            "_________error 0.14410854876041412\n",
            "clamp_state_energy tensor(98.3951, grad_fn=<SumBackward0>)\n",
            "iteration no.: 75\n",
            "l0 of the target spring tensor(0.2469)\n",
            "length 1.3928852081298828\n",
            "strain 4.641246318817139\n",
            "free_state_energy tensor(105.2852, grad_fn=<SumBackward0>)\n",
            "_________error 0.11988592147827148\n",
            "clamp_state_energy tensor(98.5754, grad_fn=<SumBackward0>)\n",
            "iteration no.: 76\n",
            "l0 of the target spring tensor(0.2453)\n",
            "length 1.394918441772461\n",
            "strain 4.685731887817383\n",
            "free_state_energy tensor(105.3536, grad_fn=<SumBackward0>)\n",
            "_________error 0.09909237921237946\n",
            "clamp_state_energy tensor(98.6447, grad_fn=<SumBackward0>)\n",
            "iteration no.: 77\n",
            "l0 of the target spring tensor(0.2439)\n",
            "length 1.396600604057312\n",
            "strain 4.725777626037598\n",
            "free_state_energy tensor(105.3388, grad_fn=<SumBackward0>)\n",
            "_________error 0.08206667006015778\n",
            "clamp_state_energy tensor(98.7547, grad_fn=<SumBackward0>)\n",
            "iteration no.: 78\n",
            "l0 of the target spring tensor(0.2426)\n",
            "length 1.3983244895935059\n",
            "strain 4.763247013092041\n",
            "free_state_energy tensor(105.3378, grad_fn=<SumBackward0>)\n",
            "_________error 0.06758853048086166\n",
            "clamp_state_energy tensor(98.9924, grad_fn=<SumBackward0>)\n",
            "iteration no.: 79\n",
            "l0 of the target spring tensor(0.2415)\n",
            "length 1.4008251428604126\n",
            "strain 4.801324844360352\n",
            "free_state_energy tensor(105.4120, grad_fn=<SumBackward0>)\n",
            "_________error 0.05431363359093666\n",
            "clamp_state_energy tensor(98.9618, grad_fn=<SumBackward0>)\n",
            "iteration no.: 80\n",
            "l0 of the target spring tensor(0.2404)\n",
            "length 1.4023109674453735\n",
            "strain 4.832508087158203\n",
            "free_state_energy tensor(105.3342, grad_fn=<SumBackward0>)\n",
            "_________error 0.044522251933813095\n",
            "clamp_state_energy tensor(99.0111, grad_fn=<SumBackward0>)\n",
            "iteration no.: 81\n",
            "l0 of the target spring tensor(0.2395)\n",
            "length 1.4037930965423584\n",
            "strain 4.861446380615234\n",
            "free_state_energy tensor(105.2630, grad_fn=<SumBackward0>)\n",
            "_________error 0.036305684596300125\n",
            "clamp_state_energy tensor(99.9748, grad_fn=<SumBackward0>)\n",
            "iteration no.: 82\n",
            "l0 of the target spring tensor(0.2387)\n",
            "length 1.4095361232757568\n",
            "strain 4.906147480010986\n",
            "free_state_energy tensor(105.8047, grad_fn=<SumBackward0>)\n",
            "_________error 0.02525939792394638\n",
            "clamp_state_energy tensor(99.9275, grad_fn=<SumBackward0>)\n",
            "iteration no.: 83\n",
            "l0 of the target spring tensor(0.2380)\n",
            "length 1.4123111963272095\n",
            "strain 4.935144424438477\n",
            "free_state_energy tensor(105.8920, grad_fn=<SumBackward0>)\n",
            "_________error 0.019162343814969063\n",
            "clamp_state_energy tensor(100.1304, grad_fn=<SumBackward0>)\n",
            "iteration no.: 84\n",
            "l0 of the target spring tensor(0.2374)\n",
            "length 1.415156602859497\n",
            "strain 4.962299823760986\n",
            "free_state_energy tensor(105.9775, grad_fn=<SumBackward0>)\n",
            "_________error 0.014214923605322838\n",
            "clamp_state_energy tensor(100.3336, grad_fn=<SumBackward0>)\n",
            "iteration no.: 85\n",
            "l0 of the target spring tensor(0.2368)\n",
            "length 1.4179856777191162\n",
            "strain 4.987364768981934\n",
            "free_state_energy tensor(106.0681, grad_fn=<SumBackward0>)\n",
            "_________error 0.010302810929715633\n",
            "clamp_state_energy tensor(101.1025, grad_fn=<SumBackward0>)\n",
            "iteration no.: 86\n",
            "l0 of the target spring tensor(0.2364)\n",
            "length 1.423535943031311\n",
            "strain 5.022056579589844\n",
            "free_state_energy tensor(106.5396, grad_fn=<SumBackward0>)\n",
            "_________error 0.005924680735915899\n",
            "clamp_state_energy tensor(100.9949, grad_fn=<SumBackward0>)\n",
            "iteration no.: 87\n",
            "l0 of the target spring tensor(0.2361)\n",
            "length 1.4258804321289062\n",
            "strain 5.040535926818848\n",
            "free_state_energy tensor(106.5443, grad_fn=<SumBackward0>)\n",
            "_________error 0.0040838588029146194\n",
            "clamp_state_energy tensor(101.0112, grad_fn=<SumBackward0>)\n",
            "iteration no.: 88\n",
            "l0 of the target spring tensor(0.2358)\n",
            "length 1.4276409149169922\n",
            "strain 5.05511999130249\n",
            "free_state_energy tensor(106.4726, grad_fn=<SumBackward0>)\n",
            "_________error 0.002872165059670806\n",
            "clamp_state_energy tensor(101.2774, grad_fn=<SumBackward0>)\n",
            "iteration no.: 89\n",
            "l0 of the target spring tensor(0.2355)\n",
            "length 1.4305062294006348\n",
            "strain 5.073266983032227\n",
            "free_state_energy tensor(106.5579, grad_fn=<SumBackward0>)\n",
            "_________error 0.0016614365158602595\n",
            "clamp_state_energy tensor(101.4722, grad_fn=<SumBackward0>)\n",
            "iteration no.: 90\n",
            "l0 of the target spring tensor(0.2354)\n",
            "length 1.433349847793579\n",
            "strain 5.089910507202148\n",
            "free_state_energy tensor(106.6423, grad_fn=<SumBackward0>)\n",
            "_________error 0.0008405345724895597\n",
            "clamp_state_energy tensor(101.3528, grad_fn=<SumBackward0>)\n",
            "iteration no.: 91\n",
            "l0 of the target spring tensor(0.2352)\n",
            "length 1.4345386028289795\n",
            "strain 5.098216533660889\n",
            "free_state_energy tensor(106.4929, grad_fn=<SumBackward0>)\n",
            "_________error 0.0005344754899851978\n",
            "clamp_state_energy tensor(101.5201, grad_fn=<SumBackward0>)\n",
            "iteration no.: 92\n",
            "l0 of the target spring tensor(0.2351)\n",
            "length 1.4367198944091797\n",
            "strain 5.110091209411621\n",
            "free_state_energy tensor(106.4878, grad_fn=<SumBackward0>)\n",
            "_________error 0.00021673913579434156\n",
            "clamp_state_energy tensor(101.6253, grad_fn=<SumBackward0>)\n",
            "iteration no.: 93\n",
            "l0 of the target spring tensor(0.2351)\n",
            "length 1.4388322830200195\n",
            "strain 5.120734691619873\n",
            "free_state_energy tensor(106.4814, grad_fn=<SumBackward0>)\n",
            "_________error 5.178218998480588e-05\n",
            "clamp_state_energy tensor(101.8367, grad_fn=<SumBackward0>)\n",
            "iteration no.: 94\n",
            "l0 of the target spring tensor(0.2350)\n",
            "length 1.4414597749710083\n",
            "strain 5.132725238800049\n",
            "free_state_energy tensor(106.5548, grad_fn=<SumBackward0>)\n",
            "_________error -1.6450958355562761e-06\n",
            "clamp_state_energy tensor(102.4937, grad_fn=<SumBackward0>)\n",
            "iteration no.: 95\n",
            "l0 of the target spring tensor(0.2350)\n",
            "length 1.446625828742981\n",
            "strain 5.154556751251221\n",
            "free_state_energy tensor(106.9558, grad_fn=<SumBackward0>)\n",
            "_________error -0.00027955250698141754\n",
            "clamp_state_energy tensor(102.5086, grad_fn=<SumBackward0>)\n",
            "iteration no.: 96\n",
            "l0 of the target spring tensor(0.2351)\n",
            "length 1.449319839477539\n",
            "strain 5.164121627807617\n",
            "free_state_energy tensor(107.0161, grad_fn=<SumBackward0>)\n",
            "_________error -0.0005514612421393394\n",
            "clamp_state_energy tensor(102.5625, grad_fn=<SumBackward0>)\n",
            "iteration no.: 97\n",
            "l0 of the target spring tensor(0.2352)\n",
            "length 1.4512742757797241\n",
            "strain 5.1697678565979\n",
            "free_state_energy tensor(106.9961, grad_fn=<SumBackward0>)\n",
            "_________error -0.0007549140136688948\n",
            "clamp_state_energy tensor(102.4508, grad_fn=<SumBackward0>)\n",
            "iteration no.: 98\n",
            "l0 of the target spring tensor(0.2353)\n",
            "length 1.452028512954712\n",
            "strain 5.169852256774902\n",
            "free_state_energy tensor(106.8315, grad_fn=<SumBackward0>)\n",
            "_________error -0.0007581971003673971\n",
            "clamp_state_energy tensor(103.5888, grad_fn=<SumBackward0>)\n",
            "iteration no.: 99\n",
            "l0 of the target spring tensor(0.2355)\n",
            "length 1.4592461585998535\n",
            "strain 5.197379112243652\n",
            "free_state_energy tensor(107.4943, grad_fn=<SumBackward0>)\n",
            "_________error -0.0022089816629886627\n",
            "clamp_state_energy tensor(103.3278, grad_fn=<SumBackward0>)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#np.save(f\"drive/My Drive/project_data/cl_allostery/errors_folder/errors_{seed}_repeated\", errors)\n",
        "#np.save(f\"drive/My Drive/project_data/cl_allostery/l0s/target_l0s_{seed}_repeated\", target_l0s)\n",
        "#np.save(f\"drive/My Drive/project_data/cl_allostery/lens/lengths_list_{seed}_repeated\", lengths_list)\n",
        "#np.save(f\"drive/My Drive/project_data/cl_allostery/trained_l0s/final_l0s_{seed}_repeated\", spring_network.l0)\n"
      ],
      "metadata": {
        "id": "DvaI5aK8blH9"
      },
      "execution_count": 5,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "plt.plot(np.linspace(0,epochs,epochs), errors)\n",
        "plt.show()\n",
        "\n",
        "plt.plot(np.linspace(0,epochs,epochs), energies_list)\n",
        "plt.show()\n",
        "\n",
        "plt.plot(np.linspace(0,epochs,epochs), partial_energies_list)\n",
        "plt.show()"
      ],
      "metadata": {
        "id": "zJh13_RvY-Dl",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 761
        },
        "outputId": "563e3b73-3492-46b8-afc4-3687e7469601"
      },
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "strains_list = []\n",
        "lens_list = []\n",
        "\n",
        "inputs_list =  [1,2,3,4,5,6,7,8,9,10]\n",
        "\n",
        "spring_network.l0 = l0\n",
        "\n",
        "for inp in inputs_list:\n",
        "    \n",
        "    with torch.no_grad():\n",
        "      # reset x\n",
        "      x = x_init.detach().clone()\n",
        "      x.requires_grad = True\n",
        "\n",
        "    # PHASE 1: run to equilibrium (free state)\n",
        "    \n",
        "    k_orig = k.detach().clone()\n",
        "    l0_orig = l0.detach().clone()\n",
        "    \n",
        "    # clamp source inputs \n",
        "    x = clamp_spring_length(spring_network, inp, s_springs[0], indices, x, l0)\n",
        "\n",
        "    # instantiate the optimizer    \n",
        "    optimizer = torch.optim.Adagrad([x], lr=1e-1)\n",
        "\n",
        "    # inference\n",
        "    energies = run_to_equil(mask1, x, optimizer, spring_network, iterations=run_time)\n",
        "    free_target_len = spring_network.measure_spring_length(x, t_springs)\n",
        "    free_target_strain = spring_network.measure_spring_strain(x, t_springs)\n",
        "    #print('length',free_target_len.item())\n",
        "    lens_list.append(free_target_len.item())\n",
        "\n",
        "    #print('strain',free_target_strain.item())\n",
        "    strains_list.append(free_target_strain.item())\n"
      ],
      "metadata": {
        "id": "BgPXTavcXirP"
      },
      "execution_count": 7,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "plt.plot(inputs_list, strains_list)\n",
        "plt.xlabel(\"Source Spring Strain\")\n",
        "plt.ylabel(\"Target Spring Strain\")\n",
        "actual_strain = np.full(len(inputs_list),target)\n",
        "plt.plot(inputs_list,actual_strain)\n",
        "plt.show()\n",
        "\n",
        "plt.plot(inputs_list, lens_list)\n",
        "plt.show()"
      ],
      "metadata": {
        "id": "COq99qFyafDu",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 531
        },
        "outputId": "84e58889-2402-46d7-a41a-058efdd4314b"
      },
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        ""
      ],
      "metadata": {
        "id": "i55q4Li0Qz0H"
      },
      "execution_count": 8,
      "outputs": []
    }
  ]
}