Training Neural ODEs Using Fully Discretized Simultaneous Optimization
It addresses a computational bottleneck for researchers and practitioners using Neural ODEs, offering an incremental improvement in training efficiency.
This paper tackles the high computational cost of training Neural ODEs by proposing a fully discretized simultaneous optimization method using collocation and IPOPT, demonstrating faster convergence on the Van der Pol Oscillator case study.
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.