Distributional Gradient Matching for Learning Uncertain Neural Dynamics Models

TL;DR

This paper introduces a novel distributional gradient matching method for neural ODEs that estimates epistemic uncertainty directly in the state space, offering faster training and more accurate predictions than traditional methods.

Contribution

The paper presents a new approach for uncertainty estimation in neural ODEs that bypasses numerical integration, improving efficiency and accuracy in trajectory prediction.

Findings

Faster training compared to traditional methods

More accurate predictions of unseen trajectories

Significant improvements in neural ODE uncertainty estimation

Abstract

Differential equations in general and neural ODEs in particular are an essential technique in continuous-time system identification. While many deterministic learning algorithms have been designed based on numerical integration via the adjoint method, many downstream tasks such as active learning, exploration in reinforcement learning, robust control, or filtering require accurate estimates of predictive uncertainties. In this work, we propose a novel approach towards estimating epistemically uncertain neural ODEs, avoiding the numerical integration bottleneck. Instead of modeling uncertainty in the ODE parameters, we directly model uncertainties in the state space. Our algorithm - distributional gradient matching (DGM) - jointly trains a smoother and a dynamics model and matches their gradients via minimizing a Wasserstein loss. Our experiments show that, compared to traditional approximate inference methods based on numerical integration, our approach is faster to train, faster at predicting previously unseen trajectories, and in the context of neural ODEs, significantly more accurate.