Generalize to New Dynamical Systems via Frequency Domain Adaptation

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This repository provides the official implementations and experiments for our research in generalizable neural surrogate for numerical solvers, introduced in FNSDA. The core code for implement our method can be found in models/fourier_solver.py. Please follow the steps to prepare running environment, and run our code.

Requirements

• python 3.9
• Pytorch 2.0 or above
• torchdiffeq
• Pyyaml

All the required packages can be installed via conda.

🚀 Quick Start

1. Running

# 1. Model training for the Lotka-Volterra dataset
python main.py --config_file ./configs/Fourier.yaml 

# 2. Model evaluation
  # please change the yaml file as follows
  mode: 'test'
  task: 'inter'  # for inter-trajectory adaptation task
  or
  task: 'extra'  # for extra-trajectory adaptation task

2. Other Datasets

To apply our method to other datasets, you need to specify the dataset info and modify several hyperparameters:

# Glycolitic-Oscillator dataset
  data_name: 'g_osci'
  output_dir: './logs/baseline/g_osci/FNSDA'

# Gray-Scott dataset
  data_name: 'gray'
  output_dir: './logs/baseline/gray/FNSDA'
  code_dim: 20

# Navier-Stokes dataset
  data_name: 'navier'
  output_dir: './logs/baseline/navier/FNSDA'
  code_dim: 20
  train_epochs: 100000

Citations

If you find this repo useful for your research, please cite the following papers:

@article{Qin2025FNSDA,
title={Generalizing to New Dynamical Systems via Frequency Domain Adaptation},
author={Tiexin Qin and Hong Yan and Haoliang Li},
journal={IEEE Transactions on Pattern Analysis and Machine Intelligence},
year={2025},
}