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Model-Agnostic Knowledge Guided Correction for Improved Neural Surrogate Rollout
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Proposes HyPER, a model-agnostic RL decision policy that selectively invokes a (possibly non-differentiable) physics simulator to correct neural surrogate rollout errors on PDE trajectories under a cost budget.
Problem
Neural surrogates for transient PDEs accumulate large rollout error when used autoregressively, especially with little training data, changing physical conditions, or noise; existing knowledge-guided fixes either slow-converge with physics losses or require differentiable simulators.
Approach
A REINFORCE-trained binary policy decides at each timestep whether to call the neural surrogate or the black-box simulator, with a reward combining per-step MSE, a random-policy baseline, and a penalty on the deviation from a target simulator-call fraction lambda; no simulator gradients are needed.
Key results
- On 2D Navier-Stokes, HyPER reduces cumulative MSE to 0.164 vs 0.311 for the best surrogate-only baseline (UNet-Multistep), about 68.30% average improvement, while invoking the simulator ~30% of the trajectory.
- Under changing boundary conditions, HyPER cuts cumulative MSE by 42.72% vs UNet and 45.61% vs FNO trained on the changed data.
- On subsurface flow, HyPER reduces cumulative MSE per timestep by 93.76% vs UNet-P and 97.52% vs FNO-P.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use HyPER simulator-guided RL correction instead of surrogate-only rollout | UNet on 2D Navier-Stokes · 2D Navier-Stokes | Cumulative MSE: 0.312 -> 0.164 | Helped |
| Use HyPER simulator-guided RL correction instead of surrogate-only rollout | UNet-P on changing-boundary Navier-Stokes · Changing Boundary | Cumulative MSE: 0.92 -> 0.527 | Helped |
| Use HyPER correction with pretrained UNet-P under unimodal noise | UNet-P · Unimodal noise σ²=1.0 | Cumulative MSE: 2.523 -> 1.291 | Helped |
| Use HyPER correction with pretrained UNet-P under unimodal noise | UNet-P · Unimodal noise σ²=0.75 | Cumulative MSE: 1.013 -> 0.8 | Helped |
| Use HyPER correction with pretrained UNet-P under unimodal noise | UNet-P · Unimodal noise σ²=0.5 | Cumulative MSE: 0.642 -> 0.49 | Helped |
| Use HyPER correction with pretrained UNet-P under unimodal noise | UNet-P · Unimodal noise σ²=0.25 | Cumulative MSE: 0.519 -> 0.26 | Helped |
| Use HyPER simulator-guided correction | UNet-P on subsurface flow · Subsurface flow | Cumulative MSE per timestep: 4.345 -> 0.271 | Helped |
| Learn the simulator-call policy with RL rather than choosing simulator-call timesteps uniformly at random at the same budget | HyPER on noise-free Navier-Stokes · Noise Free | Cumulative MSE: 0.186 -> 0.164 | Helped |
| Learn the simulator-call policy with RL rather than choosing simulator-call timesteps uniformly at random at the same budget | HyPER on changing-boundary Navier-Stokes · Changing Boundary | Cumulative MSE: 0.865 -> 0.527 | Helped |
| Train a multistep surrogate for 20-step autoregressive prediction instead of one-step prediction (ablation) | UNet · 2D Navier-Stokes | Cumulative MSE: 0.312 -> 0.311 | No clear effect |
Surprising findings
- Under noise-free conditions HyPER beats a random policy with the same simulator budget on only 57% of trajectories.
- UNet-Multistep has competitive cumulative MSE but produces smoothed predictions with poor high-frequency detail (spectral bias).
Limitations
- Policy trained with simple REINFORCE; sample efficiency acknowledged as a concern
- Noise experiments are contrived (noise injected into surrogate outputs at fixed timesteps)
- Evaluated only on two simulators/PDEs in 2D, with limited scale
Experimental setup
Datasets: 2D Navier-Stokes (generated with PhiFlow) 2D subsurface flow (generated with DPFEHM)
Benchmarks: 2D Navier-Stokes 2D Navier-Stokes changing boundary conditions 2D Navier-Stokes noisy inputs (unimodal and bimodal) 2D subsurface flow
Metrics: Final MSE Cumulative MSE Cumulative wins % wall-clock time / error per second
Baselines: UNet FNO UNet-Multistep MPP-ZS MPP PDE-Refiner Random Policy UNet-P FNO-P
Builds on: REINFORCE PDEArena Fourier Neural Operator PDE-Refiner Multiple Physics Pretraining
Closest papers by meaning
- Compute-optimal data scaling for neural surrogates via multi-fidelity training (NeurIPS 2026 · similarity 0.86)
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