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RAMS

The data and code for the paper RAMS: Residual‐Based Adversarial‐Gradient Moving Sample Method for Scientific Machine Learning in Solving Partial Differential Equations.

Data

Datasets are provided in the corresponding subfolders or can be generated using the scripts therein.

Code

This repository implements RAMS (Residual-based Adaptive Sampling) and related methods for physics-informed neural networks (PINNs) and operator learning. It supports multiple sampling strategies (e.g., RAR, RAD, R3, Random, LHS, Halton, Sobol) and compares their performance with or without trainable sampling.

Repository structure

• src/ — Core library: training loop, networks (FCNN, DeepONet, ResFCNN, CNN), samplers, visualization, and I/O.
• pinn/ — Physics-Informed Neural Networks: standard PINN benchmarks (e.g., Burgers’ equation) and experiments on high-dimensional PDEs.
• piol/ — Physics-Informed Operator Learning: physics-informed operator learning for the Poisson equation and a tricky ODE problem from arXiv:2402.11283, where conventional sampling methods perform poorly.
• ddol/ — Data-Driven Operator Learning: RAMS applied to a 1D wave equation and a 2D Burgers equation.

Detailed experimental setups are given in our paper: http://doi.org/10.1002/aidi.202500214.

How to run

1. Install dependencies (from project root):

   pip install -r requirements.txt

2. Run an experiment by executing the corresponding run.py from the project root, for example:

   python pinn/burgers/run.py
   python piol/ol_ode/run.py
   python ddol/wave_eq/run.py

   Each subfolder contains its own run.py, loss modules, and evaluation scripts.

Cite this work

If you use this data or code for academic research, you are encouraged to cite the following paper:

@article{author2000title,
  author  = {Weihang Ouyang, Min Zhu, Wei Xiong, Si-Wei Liu, and Lu Lu},
  title   = {RAMS: Residual‐Based Adversarial‐Gradient Moving Sample Method for Scientific Machine Learning in Solving Partial Differential Equations},
  journal = {Advanced Intelligent Discovery},
  year    = {2026},
  doi     = {http://doi.org/10.1002/aidi.202500214}
}

Questions

To get help on how to use the data or code, simply open an issue in the GitHub "Issues" section.