#PI-DeepONet: Physics-Informed Deep Operator Network

This project implements a Physics-Informed Deep Operator Network (PI-DeepONet) to solve and analyze parametric partial differential equations (PDEs). The framework includes a Multi-Layer Perceptron (MLP) architecture for the branch and trunk networks, and supports different types of PDEs like the Fisher equation, Richards equation, and their variants. ##Folder Structure MeshData/: Initially empty. This folder is populated with dynamically generated mesh data during the training and simulation process. Data/: Contains the simulation data files (e.g., .mat files) used as inputs for the model. PI_DeepONet/: Main codebase for implementing and training the PI-DeepONet framework. ###Dataset Preparation Place the simulation data files (e.g., U_total_x.mat) into the Data/ folder. These files contain the required inputs for training. The MeshData/ folder will automatically populate with generated mesh files during training. The script dynamically generates triangular or circular meshes based on the dataset.