Differentiable Multiple Shooting Layers
This provides a more efficient drop-in replacement for Neural ODEs, benefiting researchers and practitioners in machine learning and control systems, though it is incremental as it builds on existing methods.
The authors tackled the computational inefficiency of neural ordinary differential equations (Neural ODEs) by introducing Multiple Shooting Layers (MSLs), which use parallelizable root-finding to reduce the number of function evaluations and wall-clock inference time, achieving speedups in tasks like optimal control and time series classification.
We detail a novel class of implicit neural models. Leveraging time-parallel methods for differential equations, Multiple Shooting Layers (MSLs) seek solutions of initial value problems via parallelizable root-finding algorithms. MSLs broadly serve as drop-in replacements for neural ordinary differential equations (Neural ODEs) with improved efficiency in number of function evaluations (NFEs) and wall-clock inference time. We develop the algorithmic framework of MSLs, analyzing the different choices of solution methods from a theoretical and computational perspective. MSLs are showcased in long horizon optimal control of ODEs and PDEs and as latent models for sequence generation. Finally, we investigate the speedups obtained through application of MSL inference in neural controlled differential equations (Neural CDEs) for time series classification of medical data.