[2603.29224] Derived Fields Preserve Fine-Scale Detail in Budgeted Neural Simulators

Computer Science > Machine Learning arXiv:2603.29224 (cs) [Submitted on 31 Mar 2026] Title:Derived Fields Preserve Fine-Scale Detail in Budgeted Neural Simulators Authors:Wenshuo Wang, Fan Zhang View a PDF of the paper titled Derived Fields Preserve Fine-Scale Detail in Budgeted Neural Simulators, by Wenshuo Wang and 1 other authors View PDF HTML (experimental) 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 o...