Training Neural ODEs Using Fully Discretized Simultaneous Optimization

TL;DR

This paper proposes a fully discretized collocation-based optimization method for training Neural ODEs, significantly reducing training time by simultaneously optimizing model parameters and discretization coefficients using nonlinear programming techniques.

Contribution

It introduces a novel fully discretized formulation and employs IPOPT for simultaneous optimization, along with an ADMM-based decomposition framework for efficient training.

Findings

Faster convergence compared to traditional Neural ODE training methods

Effective use of IPOPT for large-scale nonlinear optimization in Neural ODEs

Potential for scalable and efficient Neural ODE training pipelines

Abstract

Neural Ordinary Differential Equations (Neural ODEs) represent continuous-time dynamics with neural networks, offering advancements for modeling and control tasks. However, training Neural ODEs requires solving differential equations at each epoch, leading to high computational costs. This work investigates simultaneous optimization methods as a faster training alternative. In particular, we employ a collocation-based, fully discretized formulation and use IPOPT--a solver for large-scale nonlinear optimization--to simultaneously optimize collocation coefficients and neural network parameters. Using the Van der Pol Oscillator as a case study, we demonstrate faster convergence compared to traditional training methods. Furthermore, we introduce a decomposition framework utilizing Alternating Direction Method of Multipliers (ADMM) to effectively coordinate sub-models among data batches. Our results show significant potential for (collocation-based) simultaneous Neural ODE training pipelines.