MJfadeaway/DAS-2

Deep Adaptive Sampling for Surrogate Modeling Without Labeled Data

DAS-2: Generalizing DAS for surrogate modeling of parametric differential equations

Official implementation for the paper Deep Adaptive Sampling for Surrogate Modeling Without Labeled Data

We propose a deep adaptive sampling approach for surrogate modeling of parametric differential equations without labeled data, i.e., DAS for surrogates ($\text{DAS}^2$). We demonstrate the efficiency of the proposed method with a series of numerical experiments, including the operator learning problem, the parametric optimal control problem, and the lid-driven 2D cavity flow problem with a continuous range of Reynolds numbers from 100 to 3200 (see the paper).

Requirements

PyTorch, Numpy, Scipy, pyDOE

Motivation

Surrogate modeling is of great practical significance for parametric differential equation systems. In contrast to classical numerical methods, using physics-informed deep learning-based methods to construct simulators for such systems is a promising direction due to its potential to handle high dimensionality, which requires minimizing a loss over a training set of random samples. However, the random samples introduce statistical errors, which may become the dominant errors for the approximation of low-regularity and high-dimensional problems.

Choosing a proper set of collocation points is crucial for solving low-regularity problems. Adaptive sampling is needed.

Train

See the paper for the details of settings. Here is a demo with a specific setting for example.

Operator learning

cd Operator_learning
python das_oplearning.py

Surrogate modeling for parametric optimal control

cd Optimal_control
python das_train.py

Surrogate modeling for the lid-driven cavity flow

cd Lid-driven_cavity_flow
python das_train.py

All-at-once solutions of parametric lid-driven cavity flow problems

Citation

If you find this repo useful for your research, please consider to cite our paper on arXiv or Journal of Scientific Computing

@article{wang2024deep,
  title={Deep adaptive sampling for surrogate modeling without labeled data},
  author={Wang, Xili and Tang, Kejun and Zhai, Jiayu and Wan, Xiaoliang and Yang, Chao},
  journal={arXiv preprint arXiv:2402.11283},
  year={2024}
}

@article{wang2024das2,
	title={Deep {A}daptive {S}ampling for {S}urrogate {M}odeling {W}ithout {L}abeled {D}ata},
	author={Wang, Xili and Tang, Kejun and Zhai, Jiayu and Wan, Xiaoliang and Yang, Chao},
	journal={Journal of Scientific Computing},
	volume={101},
	number={3},
	pages={77},
	year={2024},
	publisher={Springer}
}