This repository contains implementations and comparative studies of various Neural Operator architectures, including Fourier Neural Operators (FNO), Deep Operator Networks (DeepONet), and Physics-Informed Neural Operators (PINO).
The focus is on solving 1D physics problems, specifically the 1D Heat Equation and the 1D Bar (Elasticity) problem.
The goal of this project is to benchmark the performance and accuracy of data-driven and physics-informed approaches for solving differential equations. The repository explores:
- DeepONet: Learning operators for mapping input functions to solution functions.
- FNO: Using Fourier transforms to learn resolution-invariant operators.
- PINO: Combining the data efficiency of operators with the physical constraints of PINNs.
Scripts focused on solving the heat diffusion equation.
1D Heat Deep 1.py/1D Heat Deep 2.py: Implementation of DeepONet for the heat equation.1D Heat Deep Training.py: Training loop and configuration for the DeepONet heat model.1D_Heat Pino.py/Heat_1D_PINO.py: Implementation of Physics-Informed Neural Operators for the heat equation.1D Heat compare.py: Key Script. Compares the results of the different models (likely DeepONet vs. FNO/PINO).
Scripts focused on the 1D elastic bar deformation problem.
1D_Bar_PINO.py: Solving the bar problem using PINO.1D_Bar_PiDeepONet.py: Solving the bar problem using Physics-Informed DeepONet.1DBARDEEPONET.py: Standard DeepONet implementation for the bar.1DBAR DEEP vs FNO.py: Key Script. Comparative analysis between DeepONet and FNO performance on the bar topology.
1D_Wave.py: Preliminary experiments with the 1D Wave equation.PINO Error.py: Error analysis and metric calculation for PINO models.
- Clone the repository:
git clone [https://github.com/YourUsername/Neural-Operators-1D-Physics.git](https://github.com/YourUsername/Neural-Operators-1D-Physics.git)