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

2026-06-15

AI Summary

This work addresses the performance degradation of neural operators under domain shift from simulation to real-world data, where standard fine-tuning often disrupts the physical structures encoded during pretraining. To mitigate this, the authors propose PhysGuard, a novel framework that introduces Fisher information–guided gradient projection for domain adaptation of neural operators. Specifically, empirical Fisher information identifies parameter directions critical to physical laws, and fine-tuning is constrained to their orthogonal complement to preserve these structures. The method employs layer-wise Gram matrix approximations for computational efficiency and incorporates an adaptive thresholding mechanism to automatically determine the dimensionality of the protected subspace. Experiments across four neural operator architectures and multiple physical systems demonstrate that PhysGuard reduces low-frequency error by up to 32% compared to standard fine-tuning under severe domain shifts, while maintaining strong adaptation capability.

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/ZhouChaunge/PhysGuard.

Problem

• sim-to-real gap
• neural operators
• physics-preserving adaptation
• domain shift
• fine-tuning

Innovation

• neural operators
• sim-to-real adaptation
• Fisher Information Matrix
• physics-preserving fine-tuning
• gradient projection