This block is a brief introduction of your project and must be finished. The introduction will be shown in the main page of this website.

Main Content

Your article starts here. You can refer to the source code of lil’s blogs for article structure ideas or Markdown syntax. We’ve provided a sample post from Lilian Weng and you can find the source code here

Basic Syntax

Image

Please create a folder with the name of your team id under /assets/images/, put all your images into the folder and reference the images in your main content.

You can add an image to your survey like this: YOLO

Fig 1. YOLO: An object detection method in computer vision [1].

Please cite the image if it is taken from other people’s work.

Table

Here is an example for creating tables, including alignment syntax.

  column 1 column 2
row1 Text Text
row2 Text Text

Code Block

# This is a sample code block
import torch
print (torch.__version__)

Formula

Please use latex to generate formulas, such as:

\[\tilde{\mathbf{z}}^{(t)}_i = \frac{\alpha \tilde{\mathbf{z}}^{(t-1)}_i + (1-\alpha) \mathbf{z}_i}{1-\alpha^t}\]

or you can write in-text formula \(y = wx + b\).

More Markdown Syntax

You can find more Markdown syntax at this page.

Reference

Please make sure to cite properly in your work, for example:

[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 $L_{velocity+phy} = (v_{predicted}-v_{actual})^2+\gamma(v_{predicted}^2-u_{initial}^2-2g*s_{predicted})^2$ 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 $L_{supervised+phy} = (v_{predicted}-v_{actual})^2+(s_{predicted}-s_{actual})^2+\gamma(v_{predicted}^2-u_{initial}^2-2g*s_{predicted})^2$ 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 $L_{velocity+phy} = (v_{predicted}-v_{actual})^2+\gamma(v_{predicted}^2-u_{initial}^2-2g*s_{predicted})^2$		 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 $L_{supervised+phy} = (v_{predicted}-v_{actual})^2+(s_{predicted}-s_{actual})^2+\gamma(v_{predicted}^2-u_{initial}^2-2g*s_{predicted})^2$		 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