To ensure long-term accessibility and improve communication with users, we have also archived the repository and selected experimental setups on Zenodo.
You can access the official Zenodo record here:
https://doi.org/10.5281/zenodo.15537454
This repository contains the implementation of Sensitivity-Constrained Fourier Neural Operators (SC-FNO), a novel approach to improve neural operators for parametric differential equations of the form (\frac{\partial u}{\partial t} = f(u, x, t, p)). SC-FNO enhances the Fourier Neural Operator (FNO) by addressing challenges in inverse problems, sensitivity calculations ((\frac{\partial u}{\partial p})), and concept drift using a sensitivity loss regularizer. It outperforms standard FNO and FNO with PINN regularization, offering superior accuracy in solution paths and parameter inversion, scalability (tested up to 82 parameters), and reduced training demands.
- High accuracy in forward and inverse problems
- Robustness to sparse data and complex parameter spaces
- Reduced training time and data requirements
- Applicable to various differential equations and neural operators
- Abdolmehdi Behroozi (amb10399@psu.edu)
Department of Civil and Environmental Engineering, Penn State University - Chaopeng Shen (Corresponding author, cxs1024@psu.edu)
Department of Civil and Environmental Engineering, Penn State University - Daniel Kifer (duk17@psu.edu)
School of Electrical Engineering and Computer Science, Penn State University
This work is Published as a conference paper at ICLR 2025. Please cite as:
Behroozi, A., Shen, C., & Kifer, D. (2025). Sensitivity-Constrained Fourier Neural Operators for Forward and Inverse Problems in Parametric Differential Equations. ICLR 2025.
- Python 3.x
- PyTorch
- Additional dependencies in
requirements.txt(TBD)
Instructions will be updated upon code release. Stay tuned!
TBD upon release.