Ensemble Kalman inversion (EKI) is a sequential Monte Carlo method used to solve inverse problems within a Bayesian framework. Unlike backpropagation, EKI is a gradient-free optimization method that only necessitates the evaluation of artificial neural networks in forward passes. In this study, we examine the effectiveness of EKI in training neural ordinary differential equations (neural ODEs) for system identification and control tasks. To apply EKI to optimal control problems, we formulate inverse problems that incorporate a Tikhonov-type regularization term. Our numerical results demonstrate that EKI is an efficient method for training neural ODEs in system identification and optimal control problems, with runtime and quality of solutions that are competitive with commonly used gradient-based optimizers.

翻译：集成卡尔曼反演（EKI）是一种在贝叶斯框架下解决逆问题的序贯蒙特卡洛方法。与反向传播不同，EKI是一种无梯度优化方法，仅需通过前向传播评估人工神经网络。本研究探讨了EKI在训练神经常微分方程（神经ODE）用于系统辨识和控制任务中的有效性。为了将EKI应用于最优控制问题，我们构建了带有吉洪诺夫型正则化项的逆问题。数值结果表明，EKI是一种高效训练神经ODE处理系统辨识与最优控制问题的方法，其运行时间和解的质量与常用基于梯度的优化器具有竞争力。