UNOP: Physics-Constrained Unsupervised Neural Operator for Long-Horizon PDE Learning on Generalized Geometries

Cheng, Xinrui; Zhao, Tianqi; Zhang, Zhaodong; Wong, Ngai; Wang, Zhongjie; Hu, Ruihan

doi:10.24963/ijcai.2026/469

UNOP: Physics-Constrained Unsupervised Neural Operator for Long-Horizon PDE Learning on Generalized Geometries

Xinrui Cheng, Tianqi Zhao, Zhaodong Zhang, Ngai Wong, Zhongjie Wang, Ruihan Hu

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Proceedings of the Thirty-Fifth International Joint Conference on Artificial Intelligence. Main Track. Pages 4215-4223.

https://doi.org/10.24963/ijcai.2026/469

Keywords

Machine Learning: Unsupervised learning
Machine Learning: Deep learning architectures
Multidisciplinary Topics and Applications: Physical sciences

Abstract

Unsupervised learning of neural operators is constrained by numerical instability, causing predictions to diverge in long-horizon rollouts. To address this, we present a physics-constrained unsupervised neural operator for long-horizon PDE learning on generalized geometries (UNOP). This framework replaces differential constraints with integral consistency for stable, label-free learning. Unlike prior works, UNOP is built upon Latent Integral Physics Embedding (LIPE), which enforces physical consistency through integral constraints. To extend integral formulations to generalized geometries, the Geometry-Agnostic Latent Adapter (GALA) projects them onto a unified latent grid of PDE inputs, providing a regularized domain for spatial integral evaluation. Based on this shared embedding, the Gated Spectral Evolution Operator (GSEO) performs stable temporal integration while retaining spatial regions with sharp gradients and fine-scale structures, with the evolution constrained by the LIPE objective. Experiments on 1D, 2D, and 3D benchmarks show UNOP outperforms state of the art methods, reducing error accumulation by up to 60% in

20-step rollouts. Code is available at https://github.com/chengxinrui/UNOP.

Xinrui Cheng, Tianqi Zhao, Zhaodong Zhang, Ngai Wong, Zhongjie Wang, and Ruihan Hu. 2026. UNOP: Physics-Constrained Unsupervised Neural Operator for Long-Horizon PDE Learning on Generalized Geometries. In Proceedings of the Thirty-Fifth International Joint Conference on Artificial Intelligence, IJCAI-26. IJCAI, 4215–4223. https://doi.org/10.24963/ijcai.2026/469

@inproceedings{ijcai2026p469,
  title     = {UNOP: Physics-Constrained Unsupervised Neural Operator for Long-Horizon PDE Learning on Generalized Geometries},
  author    = {Cheng, Xinrui and Zhao, Tianqi and Zhang, Zhaodong and Wong, Ngai and Wang, Zhongjie and Hu, Ruihan},
  booktitle = {Proceedings of the Thirty-Fifth International Joint Conference on
               Artificial Intelligence, {IJCAI-26}},
  publisher = {International Joint Conferences on Artificial Intelligence Organization},
  editor    = {Diego Calvanese},
  pages     = {4215--4223},
  year      = {2026},
  month     = {8},
  note      = {Main Track},
  doi       = {10.24963/ijcai.2026/469},
  url       = {https://doi.org/10.24963/ijcai.2026/469},
}

TY  - CPAPER
TI  - UNOP: Physics-Constrained Unsupervised Neural Operator for Long-Horizon PDE Learning on Generalized Geometries
AU  - Cheng, Xinrui
AU  - Zhao, Tianqi
AU  - Zhang, Zhaodong
AU  - Wong, Ngai
AU  - Wang, Zhongjie
AU  - Hu, Ruihan
T2  - Proceedings of the Thirty-Fifth International Joint Conference on Artificial Intelligence, IJCAI-26
PB  - International Joint Conferences on Artificial Intelligence Organization
PY  - 2026
SP  - 4215
EP  - 4223
DO  - 10.24963/ijcai.2026/469
UR  - https://doi.org/10.24963/ijcai.2026/469
ER  -