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Zhenghao Peng (Team 00)
2022-09-19

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[1] Dwibedi, Debidatta, et al. "Counting out time: Class agnostic video repetition counting in the wild." Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2020.

[Peng, et al.] Peng, Zhenghao, et al. "Maybe you can also use other format for reference as you wish." Nature. 2022.

Data Rich and Physics Certain

Experiment Parameters Results Comments
DL + Data

| Predicting only velocity | Dataset size : 10000
Network : 2->5->5->1
activation: ReLU | ~100% accurate | Generalises well over various initial velocities | | Predicting only displacement | Dataset size : 10000
Network : 2->16->16->1
activation: ReLU | Reasonable | Better prediction for $u_0 \in dataset$, average prediction outside | | Predicting both $v_t, s_t$ | Dataset size : 10000
Network : 2->16->16->2
activation: tanh | Reasonable | Better prediction for $u_0 \in dataset$, poor prediction outside |

| DL + Physics | | Predicting both $v_t, s_t$, using Loss $L_{physics} = |v_{predicted}^2-u_{initial}^2-2gs_{predicted}|$ | Dataset size : 10000
Network : 2->16->16->1
activation: ReLU | ~0% accuracy | Expected result as no supervision of any kind is provided | | Predicting both $v_t, s_t$, using Loss $L_{velocity+phy} = (v_{predicted}-v_{actual})^2+\gamma*(v_{predicted}^2-u_{initial}^2-2gs_{predicted})^2$ | Dataset size : 10000
Network : 2->16->16->1
activation: ReLU | Reasonable | Prediction of $v_t$ is good. Was able to learn $s_t$ reasonably well without direct supervision | | Predicting both $v_t, s_t$, using Loss $L_{supervised+phy} = (v_{predicted}-v_{actual})^2+(s_{predicted}-s_{actual})^2+\gamma*(v_{predicted}^2-u_{initial}^2-2gs_{predicted})^2$ | Dataset size : 10000
Network : 2->16->16->1
activation: ReLU | Reasonable | Not a better result w.r.t direct supervision |

Observations :

  • Physics equations are certain in this case and are the best to use.
  • Both DL, Hybrid(DL+Physics) methods performance are equivalent (actual accuracy/loss varies based on fine training, random dataset generation)

Re running the above experiments with Dataset size of 200(Data Starvation), yielded the following observations

  • DL performance is comparable with 10000 dataset when trained on much mode epochs(5x)
  • Hybrid(DL+Physics) without direct supervision on $s_t$ has comparable/better closeness than DL only method for limited epochs($\sim$300) training.

Data Rich and Physics Uncertain

Experiment Parameters Results Comments
DL + Data \
Predicting both $v_t, s_t$ Dataset size : 10000
Network : 2->16->16->2
activation: tanh		 Reasonable Better prediction for $u_0 \in dataset$, poor prediction outside
DL + Physics
Predicting both $v_t, s_t$
using Loss $L_{physics} = |v_{predicted}^2-u_{initial}^2-2gs_{predicted}|$		 Dataset size : 10000
Network : 2->16->16->1
activation: ReLU		 ~0% accuracy Expected result as no supervision of any kind is provided
Predicting both $v_t, s_t$
using Loss $L_{velocity+phy} = (v_{predicted}-v_{actual})^2+\gamma*(v_{predicted}^2-u_{initial}^2-2gs_{predicted})^2$		 Dataset size : 10000
Network : 2->16->16->1
activation: ReLU		 Reasonable Prediction of $v_t$ is good. Was able to learn $s_t$ reasonably well without direct supervision
Predicting both $v_t, s_t$
using Loss $L_{supervised+phy} = (v_{predicted}-v_{actual})^2+(s_{predicted}-s_{actual})^2+\gamma*(v_{predicted}^2-u_{initial}^2-2gs_{predicted})^2$		 Dataset size : 10000
Network : 2->16->16->1
activation: ReLU		 Reasonable Not a better result w.r.t direct supervision, but bettr than DL when $u0$ is out of dataset

Observations :

  • Both DL, Hybrid(DL+Physics) methods performance are similar, Hybrid(DL+Physics) is better when $u0$ is out of dataset, DL is better for $u0$ in dataset.
  • Physics equations are not certain in this case and the above methods are better to use than Physics.

Data Starvation and Physics Uncertain

  • Similar observations as in data rich