Origo: Interpretable Multi-physics PDE Foundation Model through Neural Operator Splitting

Li Sun, Hongbo Lv, Zhikai Jiang, Zhongtian Sun, Lanxu Yang, Philip S. Yu
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:116957-116975, 2026.

Abstract

Partial Differential Equations (PDEs) play a fundamental role in scientific computing, and recent efforts have sought to extend the success of foundation models to PDE solving. However, multi-physics PDE pre-training faces the unique challenge of disentangling dynamic heterogeneity to learn universal, elementary patterns that generalize to new PDEs. Additionally, cross-physics transfer lacks a theoretical framework for interpretability—specifically, understanding which pre-trained operator knowledge is effectively transferred to target PDEs. To bridge these gaps, we introduce the theory of neural operator splitting, which decomposes PDE evolution into a modulated global spectral operator and sparse local constitutive mechanisms. A key innovation is Origo, which provides a neural operator bank that enables the identification of operator-level generalization patterns. Extensive experiments demonstrate strong zero-shot generalization and mechanism-level interpretability on unseen PDEs.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-sun26aa, title = {Origo: Interpretable Multi-physics {PDE} Foundation Model through Neural Operator Splitting}, author = {Sun, Li and Lv, Hongbo and Jiang, Zhikai and Sun, Zhongtian and Yang, Lanxu and Yu, Philip S.}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {116957--116975}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/sun26aa/sun26aa.pdf}, url = {https://proceedings.mlr.press/v306/sun26aa.html}, abstract = {Partial Differential Equations (PDEs) play a fundamental role in scientific computing, and recent efforts have sought to extend the success of foundation models to PDE solving. However, multi-physics PDE pre-training faces the unique challenge of disentangling dynamic heterogeneity to learn universal, elementary patterns that generalize to new PDEs. Additionally, cross-physics transfer lacks a theoretical framework for interpretability—specifically, understanding which pre-trained operator knowledge is effectively transferred to target PDEs. To bridge these gaps, we introduce the theory of neural operator splitting, which decomposes PDE evolution into a modulated global spectral operator and sparse local constitutive mechanisms. A key innovation is Origo, which provides a neural operator bank that enables the identification of operator-level generalization patterns. Extensive experiments demonstrate strong zero-shot generalization and mechanism-level interpretability on unseen PDEs.} }
Endnote
%0 Conference Paper %T Origo: Interpretable Multi-physics PDE Foundation Model through Neural Operator Splitting %A Li Sun %A Hongbo Lv %A Zhikai Jiang %A Zhongtian Sun %A Lanxu Yang %A Philip S. Yu %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-sun26aa %I PMLR %P 116957--116975 %U https://proceedings.mlr.press/v306/sun26aa.html %V 306 %X Partial Differential Equations (PDEs) play a fundamental role in scientific computing, and recent efforts have sought to extend the success of foundation models to PDE solving. However, multi-physics PDE pre-training faces the unique challenge of disentangling dynamic heterogeneity to learn universal, elementary patterns that generalize to new PDEs. Additionally, cross-physics transfer lacks a theoretical framework for interpretability—specifically, understanding which pre-trained operator knowledge is effectively transferred to target PDEs. To bridge these gaps, we introduce the theory of neural operator splitting, which decomposes PDE evolution into a modulated global spectral operator and sparse local constitutive mechanisms. A key innovation is Origo, which provides a neural operator bank that enables the identification of operator-level generalization patterns. Extensive experiments demonstrate strong zero-shot generalization and mechanism-level interpretability on unseen PDEs.
APA
Sun, L., Lv, H., Jiang, Z., Sun, Z., Yang, L. & Yu, P.S.. (2026). Origo: Interpretable Multi-physics PDE Foundation Model through Neural Operator Splitting. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:116957-116975 Available from https://proceedings.mlr.press/v306/sun26aa.html.

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