Derived Fields Preserve Fine-Scale Detail in Budgeted Neural Simulators
Summary: arXiv:2603.29224v1 Announce Type: cross
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.
Key Findings
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.
Research Implications
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. The implications of this research extend to various fields where neural simulations are utilized, including computational fluid dynamics, climate modeling, and other areas that require accurate representation of physical phenomena.
Future Directions
Further research will focus on the optimization of derived fields in various simulation contexts and exploring how these techniques can be integrated with existing frameworks. By refining the principles of Derived-Field Optimization, we can enhance the efficiency and accuracy of neural simulations while adhering to storage constraints.
Conclusion
In conclusion, the formulation of Derived-Field Optimization presents a significant advancement in the field of neural simulations. By strategically designing the carried state, researchers can ensure that fine-scale details are preserved, leading to more accurate and reliable outcomes in simulations. The future of budgeted neural simulation is promising, with the potential for further innovations that will enhance our understanding and representation of complex physical systems.