用隐式单步法训练刚性神经微分方程，突破传统方法瓶颈。
Training Stiff Neural Ordinary Differential Equations with Implicit Single-Step Methods
- 采用隐式单步积分法解决刚性ODE的数值不稳定性问题。
- 在刚性系统上实现稳定训练，成功捕捉复杂动态行为。
- 适合需要高精度模拟的科学计算场景，如物理建模与生物系统。
刚性常微分方程（ODE）广泛存在于多个科学与工程领域，但现有神经ODE方法难以有效学习此类系统，成为限制其广泛应用的主要障碍。本文提出基于单步隐式格式的神经ODE训练方法，证明该方法可有效处理刚性动力学。该工作解决了当前神经ODE方法的关键缺陷，为神经ODE在更广泛科学问题中的应用铺平了道路。
原文摘要 · Abstract (English)
Stiff systems of ordinary differential equations (ODEs) are pervasive in many science and engineering fields, yet standard neural ODE approaches struggle to learn them. This limitation is the main barrier to the widespread adoption of neural ODEs. In this paper, we propose an approach based on single-step implicit schemes to enable neural ODEs to handle stiffness and demonstrate that our implicit neural ODE method can learn stiff dynamics. This work addresses a key limitation in current neural ODE methods, paving the way for their use in a wider range of scientific problems.
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