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BINNs_EQL_Covasim Wiki

  Wiki for the BINNs_Covasim_EQL repository explaining the motivation, goals, methods, and results of this project as well as information of the computational pipeline for the project, "Incorporating Human Adaptive Behavior into Epidemiological Models using Equation Learning". The rough outline of the pipeline is: 1) Modifying the agent-based simulator, 2) Training Biologically-Informed Neural Networks on the data, and 3) Conducting Equation Learning on the trained parameter networks.

  This wiki is the guideline explaining and connecting our paper, "Incorporating Human Adaptive Behaviors into Epidemiological Models using Equation Learning", and our code repository. For more information on our project, please see [INSERT PAPER LINK].

Table of Contents

This wiki is structured in an order similar to the intended computational pipeline created.

Overview: This page gives the overarching idea behind the project and the table of contents guiding the reader through the content.

1. Data Generation: Learn about what an agent-based model (ABM) is, our ABM - Covasim, how to interact with Covasim, how to generate data, how to add an adaptive behavior, and why we chose masking as our adaptive behavior.
2. Biologically-Informed Neural Networks (BINNs): Learn about what BINNs are and the role they play in the equation learning process. Learn about our model's architecture, how it works, the different types of models available for our application, and why we designed it in this way.
3. Learned Parameter Equation Regression: This is the equation learning process done to find closed form equations that approximate the ODE system. Learn how to perform sparse regression on equations that infer the learned parameter networks, how our algorithm works, and how to interpret results.
4. Learned Parameter Surface Plotting: Learn how to plot the surfaces learned by the BINNs.
5. Evaluation Procedure: This portion of the process numerically solves the system of ODEs using the learned parameter networks and learned equations.
6. Sensitivity Analysis: Conduct sensitivity analysis to determine the important parameters in the learned equations and possibly perform further pruning.

That's it! Pages 2-7 take you through the entire computational pipeline we created. In reality, only pages 2-4 and 6 are required in order to perform equation learning. However, page 5 provides a visual interpretation for the learned networks and page 7 provides a quantifiable procedure for analyzing the learned equations and what components in those equations are important to describe the learned parameter.

Overview

  We extended an existing agent-based epidemiological model, Covasim, with an adaptive behavior and mathematically modeled it using novel equation learning techniques.

  Agent-based models (ABMs) are computational models that simulate actions of agents on an individual level. ABMs require large amounts of computations in order to effectively model complex systems. Although they can be effective, they can often be intractable. Additionally, they lack a big picture understanding of why things occur in a system.

  Differential equations, on the other hand, are mathematical models that do provide intuition and can be efficiently solved. However, traditional coarse-grained differential equations are often implausible for complex systems. This difficulty can be overcame by utilizing equation learning techniques that leverage computational power and broad mathematical models to inference systems of equations and generate an ODE approximation of the system.

  We use Biologically-Informed Neural Networks, an extension of Physics-Informed Neural Networks, to estimate parameters that can be arbitrarily complicated nonlinear functions. The caveat to this is that neural networks are non-interpretable models and do not provide mathematical insight into our system or model. We mitigate this by using sparse regression and sensitivity analysis to inference a closed form equation that approximates these learned parameters. This generates the final approximated mathematical model for the ABM which provides us the ability mathematically model more complicated real-world scenarios in disease spread.

  In principle, our process generalizes to any agent-based model. An important note to make is that our equation learning methods can be more broadly applied to any sets of data, experimental or simulated, however, effective equation learning on sparse and/or experimental data is a difficult problem that still has ongoing research in the math modeling community today.