Lens Classification using ResNet-18 and Physics-Informed Neural Networks (PINN)

Overview

This repository contains the implementation of two models for classifying images of gravitational lenses using PyTorch. The first model employs a standard ResNet-18 architecture, while the second model enhances the ResNet-18 with a physics-informed neural network (PINN) that incorporates the gravitational lensing equation.

NOTE: You can find the detailed implementation of Self-supervised learning in this repo: SSL_results

Common Test: Multi-Class Classification

Task

Build a model for classifying images into lenses using PyTorch or Keras. The model should be trained and validated using a suitable approach to achieve high accuracy.

Approach

I utilized ResNet-18 for this task due to its ability to capture intricate patterns and features in the data, leading to better generalization and higher accuracy. The model was trained using 5-fold cross-validation, with each fold consisting of 5 epochs on a dataset of 30,000 training images and 7,500 test images.

Results

The model achieved an ROC-AUC score of 0.99 on the test data.

Notebook

You can find the detailed implementation and results of this approach in the following Jupyter notebook: ResNet-18 Approach

Specific Test V: Physics-Guided ML

Task

Build a model for classifying images into lenses using PyTorch or Keras. The architecture should take the form of a physics-informed neural network (PINN) that incorporates the gravitational lensing equation to improve network performance over the common test results.

Approach 1

For classifying gravitational lenses into three types (no lensing, vortex, and halo substructure), I incorporated the lens equation, which describes how light is bent by the gravitational field of a massive object. The mass distribution of the lensing object is assumed to follow a Singular Isothermal Sphere (SIS) model, with a proportionality parameter ( k ) to correct potential distortions.

Implementation Steps

1. Define the lens equation: β=θ−α where β is the apparent position of the source, θ is the observed position, and α is the deflection angle.

2. Incorporate the mass distribution due to galaxies and dark matter: β+cX=θ−kr^2

3. Utilize feature vectors θ and k from ResNet-18.

4. Apply three neural layers on the resulting vector to extract features for lens classification.

Results

The model achieved an ROC-AUC score of 0.92 on the test data.

Notebook

You can find the detailed implementation and results of this approach in the following Jupyter notebook: PINN Approach 1

Approach 2

In this approach, the original image vector I represents θ. Another feature vector k from ResNet-18 is used as follows: C=I−B(features)⋅r^2 A concatenated feature vector D is formed from another ResNet-18 feature vector A features and C . This vector is then processed through three neural layers to classify the lenses.

Notebook

You can find the detailed implementation and results of this approach in the following Jupyter notebook: PINN Approach 2

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