Towards Infinitely Long Neural Simulations: Self-Refining Neural Surrogate Models for Dynamical Systems

• URL: http://arxiv.org/abs/2603.17750v1
• Date: Wed, 18 Mar 2026 14:14:40 GMT
• Title: Towards Infinitely Long Neural Simulations: Self-Refining Neural Surrogate Models for Dynamical Systems
• Abstract summary: Self-refining Neural Surrogate model (SNS) can be implemented as a standalone model or as a complementary model to existing neural surrogates.
• Score: 30.037248637148693
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Recent advances in autoregressive neural surrogate models have enabled orders-of-magnitude speedups in simulating dynamical systems. However, autoregressive models are generally prone to distribution drift: compounding errors in autoregressive rollouts that severely degrade generation quality over long time horizons. Existing work attempts to address this issue by implicitly leveraging the inherent trade-off between short-time accuracy and long-time consistency through hyperparameter tuning. In this work, we introduce a unifying mathematical framework that makes this tradeoff explicit, formalizing and generalizing hyperparameter-based strategies in existing approaches. Within this framework, we propose a robust, hyperparameter-free model implemented as a conditional diffusion model that balances short-time fidelity with long-time consistency by construction. Our model, Self-refining Neural Surrogate model (SNS), can be implemented as a standalone model that refines its own autoregressive outputs or as a complementary model to existing neural surrogates to ensure long-time consistency. We also demonstrate the numerical feasibility of SNS through high-fidelity simulations of complex dynamical systems over arbitrarily long time horizons.

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