A condensing approach to multiple shooting neural ordinary differential equation
This work addresses a stability issue in parameter estimation for NODEs, but it is incremental as it adapts an existing method to a specific context.
The paper tackles the challenge of incorporating equality constraints in multiple-shooting neural ordinary differential equations (MS-NODEs) by proposing a condensing-based approach, enabling training with first-order optimization methods like Adam.
Multiple-shooting is a parameter estimation approach for ordinary differential equations. In this approach, the trajectory is broken into small intervals, each of which can be integrated independently. Equality constraints are then applied to eliminate the shooting gap between the end of the previous trajectory and the start of the next trajectory. Unlike single-shooting, multiple-shooting is more stable, especially for highly oscillatory and long trajectories. In the context of neural ordinary differential equations, multiple-shooting is not widely used due to the challenge of incorporating general equality constraints. In this work, we propose a condensing-based approach to incorporate these shooting equality constraints while training a multiple-shooting neural ordinary differential equation (MS-NODE) using first-order optimization methods such as Adam.