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Time Without Timesteps: Simulating Coupled Dynamical Systems via Self-Consistency

arXiv · AI, language, vision and robotics · article · Sep 3, 2026 · UTC

Numerical simulation of dynamical systems is usually organized as a causal march through time: each state is computed from the previous one. We explore a different formulation for coupled systems. For each subsystem type we train a neural surrogate mapping a full driving trajectory and initial condition directly to a full output trajectory; following classical waveform relaxation, coupled systems are assembled by enforcing self-consistency among these trajectories: simulation becomes a fixed-point problem over complete trajectories rather than a stepwise rollout. On coupled van der Pol oscilla

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