用于神经微分方程和通用微分方程鲁棒训练的课程多射击算法
Curriculum Multiple Shooting for Robust Training of Neural and Universal Differential Equations
AI总结：
提出课程多射击（CMS）训练策略，结合课程学习与多射击，在12个基准测试中加速稳定NODEs、UDEs等模型训练，性能优于现有方法。
AI中文摘要：
神经常微分方程（NODEs）和通用微分方程（UDEs）是从含噪声时间序列数据中学习可解释动力系统的灵活且受欢迎的框架，但训练这些模型仍具挑战性，且缺乏能稳健处理稀疏、含噪数据及部分观测模型的通用方法。为解决该问题，我们提出课程多射击（CMS），这是一种将课程学习与多射击相结合，用于将常微分方程（ODE）模型拟合到时间序列数据的通用训练策略。在涵盖模拟与真实数据、涉及NODEs、UDEs及机理ODE的12个基准测试中，CMS加速并稳定了训练收敛，优于现有最先进的训练策略，且在泛化能力方面跻身最优方法之列。最后，结合当代关于时间序列训练挑战成因的理论，我们探讨了CMS优异性能的可能解释。
英文摘要：
Neural ordinary differential equations (NODEs) and universal differential equations (UDEs) provide flexible and popular frameworks for learning interpretable dynamical systems from noisy time-series data. However, training these models remains challenging, and versatile methods that robustly handle sparse and noisy data as well as partially observed models are lacking. To address this, we introduce curriculum multiple shooting (CMS), a general-purpose training strategy for fitting ordinary differential equation (ODE) models to time-series data by integrating curriculum learning with multiple shooting. Across twelve benchmarks spanning simulated and real data, and covering NODEs, UDEs, and mechanistic ODEs, CMS accelerates and stabilises training convergence, outperforms state-of-the-art training strategies, and ranks among the best methods in generalisation. Finally, we discuss possible explanations for the strong performance of CMS in light of contemporary theories of what makes training on time-series challenging.
