Derived Fields Preserve Fine-Scale Detail in Budgeted Neural Simulators

TL;DR

This paper introduces Derived-Field Optimization (DerivOpt), a framework for selecting physical fields and allocating storage in neural simulators to enhance fine-scale fidelity under fixed budgets.

Contribution

It proposes a novel state-design framework that improves the fidelity of budgeted neural simulations by optimizing which physical fields to carry and how to allocate storage.

Findings

DerivOpt improves mean rollout nRMSE across PDEBench.

It provides a significant advantage in fine-scale detail preservation.

Gains are evident even before rollout learning begins.

Abstract

Fine-scale-faithful neural simulation under fixed storage budgets remains challenging. Many existing methods reduce high-frequency error by improving architectures, training objectives, or rollout strategies. However, under budgeted coarsen-quantize-decode pipelines, fine detail can already be lost when the carried state is constructed. In the canonical periodic incompressible Navier-Stokes setting, we show that primitive and derived fields undergo systematically different retained-band distortions under the same operator. Motivated by this observation, we formulate Derived-Field Optimization (DerivOpt), a general state-design framework that chooses which physical fields are carried and how storage budget is allocated across them under a calibrated channel model. Across the full time-dependent forward subset of PDEBench, DerivOpt not only improves pooled mean rollout nRMSE, but also delivers a decisive advantage in fine-scale fidelity over a broad set of strong baselines. More importantly, the gains are already visible at input time, before rollout learning begins. This indicates that the carried state is often the dominant bottleneck under tight storage budgets. These results suggest a broader conclusion: in budgeted neural simulation, carried-state design should be treated as a first-class design axis alongside architecture, loss, and rollout strategy.