DeepONet
Neural network approximation of nonlinear operators for partial differential equations
Project Overview
DeepONet implements a neural architecture capable of learning operators that map between function spaces, with applications in solving partial differential equations (PDEs). Presented at the GT x Emory Scientific ML Competition, this project demonstrates how operator learning can achieve significantly better efficiency compared to traditional numerical methods for PDE approximation. The neural architecture generalizes across different input functions, making it a powerful tool for scientific computing applications.
Operator Learning
Traditional neural networks learn functions that map inputs to outputs. DeepONet learns operators - transformations that map entire functions to other functions.
This is particularly powerful for PDEs, where we need to solve equations for many different initial conditions or boundary conditions. Rather than solving each PDE instance separately, DeepONet learns the underlying operator that can generate solutions for any input function.
Technical Implementation
The implementation uses PyTorch to create a two-network architecture:
Branch Network: Encodes the input function (initial/boundary conditions)
Trunk Network: Encodes the evaluation locations
Operator Mapping: Combines both networks to approximate the PDE solution operator
The model was trained on various PDE families and demonstrated the ability to generalize to unseen input functions, showcasing the power of operator learning over traditional point-wise function approximation.
Competition Results
Presented at the Georgia Tech x Emory Scientific Machine Learning Competition, demonstrating:
10x faster inference compared to traditional numerical solvers
Generalization across different PDE families
Accuracy comparable to classical methods with significantly reduced computational cost
Real-time PDE solving capabilities for engineering applications
Skills & Technologies
Project Info
March 2025 - April 2025
Completed