Paper link

My Blog Post link

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Commands for replicating experiment results

All the experiments were done using Kaggle notebooks with GPU enabled.. This environment had Tensorflow 2.6 and other required libraries pre-installed .

MNIST experiments

For training CNN model: python train_mnist_example.py --backbone=cnn

For training Residual model: python train_mnist_example.py --backbone=residual

For training PDE model: python train_mnist_example.py --backbone=pde

CIFAR-10 experiments

For original Resnet32 training: python train_cifar.py --net='resnet'

For original PDENet training: python train_cifar.py --net='pdenet'

For PDENet training with advection disabled: python train_cifar.py --net='pdenet' --disable_advection True

For PDENet training with constant Dxy (Dx=1, Dy=1): python train_cifar.py --epochs 5 --net='pdenet' --constant_Dxy True

MNIST Confusion matrix comparison

Confusion matrices for CNN, Residual and PDE Models. It can be noted that the PDE model has lowest confusion b/w 3 & 5 among the three models. [Open in new tab to see the enlarged image.]

About the code

• train_cifar.py: This file can be used for training different networks on CIFAR-10 dataset. The training & evaluation loop and default training settings are defined in this file.
• train_mnist_example.py: Can be used to train cnn, residual cnn & PDENet depending on the user provided arguments.
• mnist_model.py: Toy models used for MNIST experiment are defined here.
• utils.py: Plotting, logging, metric calculators and other miscellaneous functions are defined in this file.
• resnet.py: Resnet32 model is defined here. Depending on user settings, different types of diffusion and anisotropic blocks are invoked here.
• global_layer.py: Contains implementation of Diffusion-Advection layer as proposed in the paper.
• loader.py: Functions for MNIST & CIFAR data loading and augmentation are defined here.
• viz_pde.py: This script can be used to visualize Dx, Dy and advection terms using trained model checkpoint weights.

Directory Structure of logsfolder

The expt_logs folder contains detailed logs for various experiments.
The directory structure is as follows:

--- expt_logs
    --- <expt_name>
        --- logs
            --- <model_name>
                --- images (contains confusion matrix/activation plots)
                --- train (contains tensorboard logs)                            

The logs folder also contains settings_log.txt file. This file contains the training/testing loss and accuracy.\