解决神经仿真模型长期运行误差累积问题，实现无限时长精准模拟。
Towards Infinitely Long Neural Simulations: Self-Refining Neural Surrogate Models for Dynamical Systems
- 构建显式数学框架，明确短时精度与长时一致性权衡机制。
- 提出自修正神经代理模型，无需调参即可保持长期模拟稳定性。
- 可独立使用或融合现有模型，适用于复杂系统长期仿真任务。
自回归神经代理模型已实现动力系统模拟的数个数量级加速。然而，自回归模型普遍存在分布漂移问题：在逐步推理过程中误差累积，导致长时间模拟质量严重下降。现有方法通过超参数调优隐式利用短时准确性和长时一致性之间的权衡。本文提出一个统一的数学框架，使该权衡关系显式化，并推广了现有方法中的超参数策略。在此框架下，我们设计了一种无需调参的鲁棒模型——自修正神经代理模型（SNS），采用条件扩散模型实现，从结构上平衡短时保真度与长时一致性。SNS可作为独立模型自我修正自回归输出，也可作为互补模块嵌入现有神经代理模型以保障长期一致性。我们通过高保真复杂动力系统模拟，验证了SNS在任意长时域下的数值可行性。
原文摘要 · Abstract (English)
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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