Learning Dynamical Coupled Operator For High-dimensional Black-box Partial Differential Equations

Wang, Yichi; Huang, Tian; Huang, Dandan; Bai, Zhaohai; Wang, Xuan; Ma, Lin; Zhang, Haodi

doi:10.24963/ijcai.2025/1044

Learning Dynamical Coupled Operator For High-dimensional Black-box Partial Differential Equations

Yichi Wang, Tian Huang, Dandan Huang, Zhaohai Bai, Xuan Wang, Lin Ma, Haodi Zhang

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Proceedings of the Thirty-Fourth International Joint Conference on Artificial Intelligence. AI4Tech: AI Enabling Technologies. Pages 9393-9401.

https://doi.org/10.24963/ijcai.2025/1044

Keywords

Domain-specific AI4Tech: Other AI4Tech applications
Advanced AI4Tech: Data-driven AI4Tech

Abstract

The deep operator networks (DON), a class of neural operators that learn mappings between function spaces, have recently emerged as surrogate models for parametric partial differential equations (PDEs). However, their full potential for accurately approximating general black-box PDEs remains underexplored due to challenges in training stability and performance, primarily arising from difficulties in learning mappings between low-dimensional inputs and high-dimensional outputs. Furthermore, inadequate encoding of input functions and query positions limits the generalization ability of DONs. To address these challenges, we propose the Dynamical Coupled Operator (DCO), which incorporates temporal dynamics to learn coupled functions, reducing information loss and improving training robustness. Additionally, we introduce an adaptive spectral input function encoder based on empirical mode decomposition to enhance input function representation, as well as a hybrid location encoder to improve query location encoding. We provide theoretical guarantees on the universal expressiveness of DCO, ensuring its applicability to a wide range of PDE problems. Extensive experiments on real-world, high-dimensional PDE datasets demonstrate that DCO significantly outperforms DONs.

Yichi Wang, Tian Huang, Dandan Huang, Zhaohai Bai, Xuan Wang, Lin Ma, and Haodi Zhang. 2025. Learning Dynamical Coupled Operator For High-dimensional Black-box Partial Differential Equations. In Proceedings of the Thirty-Fourth International Joint Conference on Artificial Intelligence, IJCAI-25. IJCAI, 9393–9401. https://doi.org/10.24963/ijcai.2025/1044

@inproceedings{ijcai2025p1044,
  title     = {Learning Dynamical Coupled Operator For High-dimensional Black-box Partial Differential Equations},
  author    = {Wang, Yichi and Huang, Tian and Huang, Dandan and Bai, Zhaohai and Wang, Xuan and Ma, Lin and Zhang, Haodi},
  booktitle = {Proceedings of the Thirty-Fourth International Joint Conference on
               Artificial Intelligence, {IJCAI-25}},
  publisher = {International Joint Conferences on Artificial Intelligence Organization},
  editor    = {James Kwok},
  pages     = {9393--9401},
  year      = {2025},
  month     = {8},
  note      = {AI4Tech: AI Enabling Technologies},
  doi       = {10.24963/ijcai.2025/1044},
  url       = {https://doi.org/10.24963/ijcai.2025/1044},
}

TY  - CPAPER
TI  - Learning Dynamical Coupled Operator For High-dimensional Black-box Partial Differential Equations
AU  - Wang, Yichi
AU  - Huang, Tian
AU  - Huang, Dandan
AU  - Bai, Zhaohai
AU  - Wang, Xuan
AU  - Ma, Lin
AU  - Zhang, Haodi
T2  - Proceedings of the Thirty-Fourth International Joint Conference on Artificial Intelligence, IJCAI-25
PB  - International Joint Conferences on Artificial Intelligence Organization
PY  - 2025
SP  - 9393
EP  - 9401
DO  - 10.24963/ijcai.2025/1044
UR  - https://doi.org/10.24963/ijcai.2025/1044
ER  -