提出半隐式神经微分方程，提升刚性学习问题的稳定性和训练效率。
Semi-Implicit Neural Ordinary Differential Equations
- 利用动态可分解结构设计半隐式方法，增强数值稳定性。
- 在图分类与复杂动力系统学习中性能超越现有方法。
- 可训练传统显式与全隐式方法均无法处理的难解神经微分方程。
采用显式方法训练的经典神经微分方程在图学习和科学机器学习等刚性学习问题中受限于稳定性，影响效率与鲁棒性。本文提出一种半隐式神经微分方程方法，利用底层动力学的可分解结构。该方法在时间积分中实现更高稳定性与高效线性求解，带来显著计算优势。实验表明，其在图分类与复杂动力系统学习任务中优于现有方法。此外，该方法可训练传统显式与全隐式方法均不可行的挑战性神经微分方程。
原文摘要 · Abstract (English)
Classical neural ODEs trained with explicit methods are intrinsically limited by stability, crippling their efficiency and robustness for stiff learning problems that are common in graph learning and scientific machine learning. We present a semi-implicit neural ODE approach that exploits the partitionable structure of the underlying dynamics. Our technique leads to an implicit neural network with significant computational advantages over existing approaches because of enhanced stability and efficient linear solves during time integration. We show that our approach outperforms existing approaches on a variety of applications including graph classification and learning complex dynamical systems. We also demonstrate that our approach can train challenging neural ODEs where both explicit methods and fully implicit methods are intractable.
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