Deep Learning: From Theory to Applications

• Link- PDF, Code

• Suggested Reading links - Why Deep Neural Networks for Function Approximation , Universal approximation - Cybenko

• Assignment 1: "Our task is to predict house prices using Neural Networks. The dataset is publicly available at Kaggle (https://www.kaggle.com/c/house-prices-advanced-regression-techniques). Most of the house property features are categorical features, and one may have to use Embedding layers to convert them into real vectors of desired dimensions. There are separate training and test datasets. You are required to use train.csv to train your NN model, and evaluate it on the test set. Don't forget to use feature/data standardization. You may also refer to some of the sample submissions on data preparation. Happy learning!"

• PPT - Module2 , Repo for GCN- https://github.com/baranwa2/MetabolicPathwayPrediction

• Codes- AutoEncoder_example , AdversarialAutoEncoder_example , VariationalAutoEncoder_example

• Suggested Reading links - Auto-Encoding Variational Bayes , Adversarial Autoencoders , Semi-Supervised Classification with Graph Convolutional Networks

• Assignment 2 - Replicate the task given at: https://github.com/hrenski/Adversarial-Autoencoder-Experimients/blob/master/aae_faces_Gauss.ipynb "Experiment with generating new faces, and explore the role of generator and discriminator hyperparameters!"

• PPT - Module3 , Repo for Microbiome project - https://gitlab.eecs.umich.edu/mayank.baranwal/Microbiome

• Assignment 3 - "You are expected to learn to predict angular positions and velocities of the two links in a double-pendulum system. The equations describing the evolution of a double pendulum system are described in https://scipython.com/blog/the-double-pendulum/. Simulate the double-pendulum system for random initial conditions with $\theta_1, \theta_2\in (-\pi,pi]$ and $\dot{\theta}_1, \dot{\theta}_2 \in [-5,5]$. Set $m_1=2m_2=2$ and $l_1=0.5l_2=1$. Simulate this system 200 times with a randomly chosen initial condition. For each of the 200 scenarios, sample the outputs (angular positions and velocities) at $t=1,2,3,\dots,10$ time instants and store them, along with initial condition at $t=0$. Of the 200 examples, randomly sample 150 examples and make this your training set. The remaining 50 examples are kept as a test set. Train an LSTM model with teacher forcing to predict the outputs at all time instants given the initial condition, and validate your trained model on the test set."

• Code Link- Demo-NeuralODE.ipynb

• Assignment 4 - "You are expected to learn to predict angular positions and velocities of the two links in a double-pendulum system. The equations describing the evolution of a double pendulum system are described in https://scipython.com/blog/the-double-pendulum/. Simulate the double-pendulum system for random initial conditions with $\theta_1, \theta_2\in (-\pi,pi]$ and $\dot{\theta}_1, \dot{\theta}_2 \in [-5,5]$. Set $m_1=2m_2=2$ and $l_1=0.5l_2=1$. Simulate this system 200 times with a randomly chosen initial condition. For each of the 200 scenarios, sample the outputs (angular positions and velocities) at $t=1,2,3,\dots,10$ time instants and store them, along with initial condition at $t=0$. Of the 200 examples, randomly sample 150 examples and make this your training set. The remaining 50 examples are kept as a test set. Train an ODENet to predict the outputs at all time instants given the initial condition, and validate your trained model on the test set."

• Code Link- PINN_Example

• Assignment 5 - Consider the pde $u_t + x u_x = u$ with the initial condition $u(x,0) = x^2$. The analytical solution to this pde is $u(t,x) = x^2e^{-t}$. Simulate this system for $x\in[0,2]$ and $t\in[0,5]$. Randomly sample 100 points containing the tuple-$(t,x,u)$ such that $x\in[0,1]$ and $t\in[0,1]$. Create a simple NN that takes $x$ and $t$ as inputs and predicts $u$. Train this model using supervised loss. Validate this model for $x\in[1,2]$ and $t\in[2,5]$. Does the static model capture the evolution across the entire domain?

Now repeat the same process but this time include the Physics loss + IC loss, along with the supervised loss. Train a PINN to see if you're able to capture the trend overall.

• PPT - Module6

Assignment 1 : colab link1

Assignment 2 : colab link2

Assignment 3 : colab link3

Assignment 4 : colab link4

Assignment 5 : colab link5