arXiv:2603.29224cs.LGcs.AI2026-03

通过优化携带场设计,提升受限存储下的神经模拟细节保真度。

Derived Fields Preserve Fine-Scale Detail in Budgeted Neural Simulators

  • 提出衍生场优化框架,动态选择并分配存储资源给物理场。
  • 在PDEBench上,滚动误差降低且细粒度保真度显著优于基线。
  • 优势在推理前就显现,说明状态设计是关键瓶颈。

在固定存储预算下保持细粒度保真的神经模拟仍具挑战。现有方法多通过改进架构、训练目标或滚动策略来减少高频误差,但在预算约束的粗化-量化-解码流程中,细粒度信息可能已在状态构建阶段丢失。在典型的周期性不可压缩纳维-斯托克斯设定中,我们发现原始场与衍生场在相同算子作用下表现出系统性不同的保留频带失真。受此启发,我们提出衍生场优化(DerivOpt),一个通用的状态设计框架,可在校准信道模型下决定携带哪些物理场及如何分配存储预算。在PDEBench完整时变前向子集上,DerivOpt不仅提升了整体平均滚动归一化均方误差(nRMSE),还在广泛基线上实现了细粒度保真度的决定性优势。更重要的是,性能提升早在输入阶段即可见,未依赖滚动学习。这表明,在严苛存储约束下,携带状态设计常为首要瓶颈。结果提示:在预算约束的神经模拟中,状态设计应与架构、损失函数和滚动策略并列作为核心设计维度。

原文摘要 · Abstract (English)

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.

神经模拟状态设计细粒度保真偏微分方程

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