Test-Time Accuracy-Cost Control in Neural Simulators via Recurrent-Depth

Classical numerical solvers let users spend more computation to obtain a more accurate result, while neural simulators generally have a fixed inference cost. Recurrent-Depth Simulator (RecurrSim) restores this control by repeatedly applying a simulator and exposing the number of recurrent iterations as a test-time parameter.

The framework is architecture-agnostic and does not require retraining for each compute budget. It produces physically faithful long-horizon simulations on several fluid-dynamics systems; on a 262,000-point compressible Navier–Stokes task, a 0.8-billion-parameter RecurrFNO outperforms 1.6-billion-parameter baselines while using 13.5% less training memory.

Tests with Vision Transformer and Universal Physics Transformer variants further show that recurrent depth can reduce accumulated error or parameter count across different simulator families while retaining an explicit accuracy–cost trade-off.

Paper: https://openreview.net/forum?id=U2j9ZNgHqw