PhysGuard: Fisher-Guided Gradient Projection for Sim-to-Real Neural PDE Surrogates

Abstract

Neural operator models trained on simulation data often lose accuracy when applied to experimental measurements due to the sim-to-real gap. Standard fine-tuning with limited real data can reduce this gap, but it may also damage the core physics-relevant representations learned during pretraining. Although knowledge-preserving adaptation has been widely investigated in vision or language tasks, it remains unclear whether these methods are suitable for neural operators whose architectures and protected knowledge are fundamentally different. Neural operators need to preserve core-scale physical structures rather than semantic or visual features. We propose PhysGuard, a physics-preserving framework for accurate sim-to-real adaptation of neural operators. Specifically, PhysGuard uses the empirical Fisher Information Matrix computed on simulation data to identify physics-critical parameter directions, then restricts fine-tuning updates to directions that do not interfere with them. A layer-wise Gram-matrix formulation makes this efficient for models with millions of parameters, while an adaptive threshold automatically determines the protected subspace size. A spectral probe experiment shows that the dominant Fisher directions are strongly associated with low-frequency output structures. Experiments on benchmark across four neural operator architectures and different physical systems show that PhysGuard performs strongly on most evaluation metrics compared to baselines. The benefits are most evident under severe domain shift, where it reduces low-frequency error by up to 32% compared to standard fine-tuning while maintaining adaptability. Our code is available at https://github.com/Data-Driven-Computational-Geotechnics/PhysGuard.

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BibTeX RIS

BibTeX

@misc{zhou2026physguard,
  title = {{PhysGuard: Fisher-Guided Gradient Projection for Sim-to-Real Neural PDE Surrogates}},
  author = {Changjian Zhou and Junfeng Fang and Negin Yousefpour and Peng Wu and Bin Yan and Guillermo A. Narsilio},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2606.16602},
  eprint = {2606.16602},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.16602},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - PhysGuard: Fisher-Guided Gradient Projection for Sim-to-Real Neural PDE Surrogates
AU  - Changjian Zhou
AU  - Junfeng Fang
AU  - Negin Yousefpour
AU  - Peng Wu
AU  - Bin Yan
AU  - Guillermo A. Narsilio
PY  - 2026
DA  - 2026/10/27
PB  - arXiv
DO  - 10.48550/arxiv.2606.16602
UR  - https://arxiv.org/abs/2606.16602
AB  - Neural operator models trained on simulation data often lose accuracy when applied to experimental measurements due to the sim-to-real gap. Standard fine-tuning with limited real data can reduce this gap, but it may also damage the core physics-relevant representations learned during pretraining. Although knowledge-preserving adaptation has been widely investigated in vision or language tasks, it remains unclear whether these methods are suitable for neural operators whose architectures and protected knowledge are fundamentally different. Neural operators need to preserve core-scale physical structures rather than semantic or visual features. We propose PhysGuard, a physics-preserving framework for accurate sim-to-real adaptation of neural operators. Specifically, PhysGuard uses the empirical Fisher Information Matrix computed on simulation data to identify physics-critical parameter directions, then restricts fine-tuning updates to directions that do not interfere with them. A layer-wise Gram-matrix formulation makes this efficient for models with millions of parameters, while an adaptive threshold automatically determines the protected subspace size. A spectral probe experiment shows that the dominant Fisher directions are strongly associated with low-frequency output structures. Experiments on benchmark across four neural operator architectures and different physical systems show that PhysGuard performs strongly on most evaluation metrics compared to baselines. The benefits are most evident under severe domain shift, where it reduces low-frequency error by up to 32% compared to standard fine-tuning while maintaining adaptability. Our code is available at https://github.com/Data-Driven-Computational-Geotechnics/PhysGuard.
ER  -

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