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Derived Fields Preserve Fine-Scale Detail in Budgeted Neural Simulators

NeurIPS 2026 · Probabilistic and scientific modeling › Differential equations and PDEs · approach: Physics-informed operator learning · 0 citations (OpenAlex)

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Proposes Derived-Field Optimization (DerivOpt), which chooses which primitive and derived physical fields to carry and how to allocate bits across them under a fixed storage budget, showing gains already at input time across PDEBench forward families.

Problem

Neural PDE simulators with coarsen-quantize-decode state storage lose fine-scale detail when the carried state is constructed, before rollout learning begins; the choice of carried physical fields under a fixed storage budget is largely unexplored.

Approach

Treat the carried physical fields (primitive plus derived candidates such as vorticity) and the integer bit allocation across them as optimization variables, scored by a closed-form Bayesian posterior-covariance objective under a calibrated channel model, and select the best feasible design by exhaustive finite search.

Key results

• On canonical incompressible Navier-Stokes, DerivOpt raises detail-faithful horizon to 0.36-0.47 across four backbones versus 0.00-0.03 for Primitive, while lowering nRMSE in every backbone.
• Across all 252 aggregate configurations, DerivOpt attains mean nRMSE 0.074 versus 0.097 for Primitive and is best-count in 170 of 252 configurations.
• At input time on canonical NS, DerivOpt reduces fine-band error (fineRel(0)) by about 61% relative to Primitive and raises input pass rate from 0.030 to 0.840.

Surprising findings

• Rollout-side multiscale supervision (RolloutMulti) does not revive a detail-poor primitive state, staying at 0.01-0.05 detail horizon on canonical NS.
• Vorticity-only derived state is the first point where stable nonzero detail horizons appear, indicating the primitive input is the bottleneck rather than the predictor.

Limitations

• Candidate spaces are deliberately small and physics-interpretable rather than exhaustive.
• Selectors are family-specific closed-form scores and do not collapse to one universal theorem across PDE families.
• Scope limited to time-dependent 1D/2D forward PDEBench families; 3D and broader learned codecs left for future work.

Experimental setup

Datasets: PDEBench

Benchmarks: PDEBench

Metrics: nRMSE generalized detail-faithful horizon fineRel qfine eout pass rate at input

Baselines: Primitive BestSingleDerived DerivBase ArchMulti LatentAE-Hyper RolloutMulti

Builds on: PDEBench Fourier Neural Operator U-Net

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