Neural ODE training gains stability guarantees with concurrent learning
Neural ODEs Meet Concurrent Learning: Stable Online Learning with Lyapunov Guarantees
Machine Learning
Summary
Training neural ordinary differential equations (Neural ODEs) on streaming data usually lacks guarantees that learning will be stable. The authors show a hidden mathematical structure in the training process that lets them prove stability using a Lyapunov function, a common tool in control theory. They introduce a new method, NODE-CL, that combines online and stored data learning with strong stability guarantees and better performance under noisy measurements. Their tests on simulated robotics tasks demonstrate improved prediction accuracy compared to past methods, especially when sensor data is noisy.
What this means in practice
- •For robotics engineers: Improve the stability and accuracy of learned robot motion models in environments with noisy sensors.
- •For control system developers: Develop controllers that adapt neural dynamic models online with provable stability guarantees using NODE-CL.
Authors
Omkar Sudhir Patil
Abstract
Neural ODEs learn dynamics from trajectory losses, but their adjoint gradients lack the regressor-times-parameter-error structure on which Lyapunov analyses of online adaptation rest, so training on streaming data comes without stability guarantees. We show that this structure is in fact present: the adjoint gradient decomposes exactly into a positive semi-definite trajectory operator acting on the parameter error plus a nonlinear perturbation with explicit, horizon-dependent bounds. A quadratic Lyapunov function then certifies online Neural ODE training over sliding windows under computable gain and horizon conditions, and the same certificate extends to stored data: its drift branch recovers concurrent learning, and its trajectory branch yields NODE-CL, a stored-segment Gauss-Newton method built on batched forward sensitivities that needs no state-derivative estimates. On four DeepMind Control Suite domains, NODE-CL attains the lowest median prediction error on three under velocity measurement noise, where observer-based concurrent learning degrades by up to 8x; with clean measurements it is best on the pendulum and within a factor of 1.6 of the best stored-data baseline on the cartpole and reacher.