A Physics-Informed Machine Learning Approach for Heat Conduction Equation

Welcome to the PINNs project! This repository contains code and resources for solving the heat conduction equation in 2D and 3D using Physics-Informed Neural Networks (PINNs). Developed as part of a machine learning course FYS5429 at the university of Oslo.

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Project Overview

• Goal:
  Leverage PINNs to approximate solutions to the heat conduction equation in both two and three dimensions.
• Context:
  This project was completed as part of an advanced machine learning course FYS5429 at the university of Oslo, focusing on scientific machine learning and physics-based modeling.

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How It Works

Physics-Informed Neural Networks (PINNs) combine data-driven neural networks with the governing physical laws (expressed as PDEs). The loss function is augmented with the residuals of the heat equation, ensuring the model respects the underlying physics.

• 2D/3D Heat Equation:
  PINNs are trained to solve: $$-\nabla \cdot(\kappa\ \nabla T) = f$$ where T is temperature, kappa is thermal conductivity.

• Key Features:

  • Solves both 2D and 3D variants
  • Customizable boundary conditions
  • Trains using NVIDIa PhysicsNeMo

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Getting Started

1. Clone the repository:

   git clone https://github.com/AnthonyTSV/pinns.git
   cd pinns

2. Install requirements for NVIDIA PhysicsNeMo:

   docker pull nvcr.io/nvidia/physicsnemo/physicsnemo:25.03