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

NeurIPS 2026 · Architectures and efficiency › Pruning and efficient tuning · approach: Low-rank compression and merging · 0 citations (OpenAlex)

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Proposes PhysGuard, which projects fine-tuning gradients away from the top empirical-Fisher directions computed on simulation data (via a Gram-matrix trick) to adapt neural operators sim-to-real while preserving low-frequency physics.

Problem

Neural operator PDE surrogates trained on simulations lose accuracy on real experimental data (sim-to-real gap), and standard fine-tuning can overwrite low-frequency physical structures learned in pretraining.

Approach

Compute the empirical Fisher Information Matrix on simulation data, use a Gram-matrix (N x N) eigendecomposition to find the top-k physics-critical parameter directions with an adaptive 90% cumulative-energy threshold, and project real-data fine-tuning gradients orthogonal to that subspace, with no auxiliary penalty terms.

Key results

• PhysGuard ranks first on 38 of 48 metric-architecture-scenario combinations on RealPDEBench.
• Reduces low-frequency error relative to pretrained by 31.4% (FNO), 27.4% (CNO), 21.0% (Transolver), and 16.0% (DeepONet).
• On Cylinder Flow with DeepONet, PhysGuard achieves over 50% relative R^2 improvement vs under 20% for DFT; reduces Low-f by 22-32% relative to DFT on FNO, CNO, DeepONet.

Surprising findings

• DFT raises Low-f error above the pretrained baseline for CNO on Cylinder Flow, even as RMSE improves.
• EWC performs close to DFT and rarely surpasses it by a large margin.

Limitations

• Relies on low-rank FIM spectrum; may be less effective for foundation-scale operators such as DPOT-S.
• Evaluated only on fluid-mechanics and combustion scenarios from RealPDEBench.
• Gains are small in low-shift scenarios such as Controlled Cylinder.

Experimental setup

Datasets: RealPDEBench

Benchmarks: RealPDEBench cylinder flow RealPDEBench controlled cylinder RealPDEBench turbulent combustion

Metrics: RMSE R^2 fRMSE Low-f error

Baselines: Direct Fine-Tuning (DFT) L2-SP EWC Pretrained

Builds on: Gradient Projection Memory (GPM) Elastic Weight Consolidation (EWC) L2-SP Fourier Neural Operator RealPDEBench

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