Meta-Learning Nonlinear Dynamical Systems with Deep Kernels

Jacob Moss, Felix Opolka, Jeremy England, Pietro Lio

Primary Area: applications to physical sciences (physics, chemistry, biology, etc.)

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Keywords: latent force models, gaussian processes, meta-learning, dynamic model, differential equations

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TL;DR: We improve the scalability of inferring latent forces under nonlinear dynamics by learning multi-task deep kernels.

Abstract: Scientific processes are often modelled by sets of differential equations. As datasets grow, individually fitting these models and quantifying their uncertainties becomes a computationally challenging task. In this paper, we focus on improving the scalability of a particular class of stochastic dynamical model, called latent force models. These offer a balance between data-driven and mechanistic inference in dynamical systems, achieved by deriving a kernel function over a low-dimensional latent force. However, exact computation of posterior kernel terms is rarely tractable, requiring approximations for complex scenarios such as nonlinear dynamics. We overcome this issue by posing the problem as meta-learning the class of latent force models corresponding to a set of differential equations. By employing a deep kernel along with a sensible function embedding, we demonstrate the ability to extrapolate from simulations to real experimental datasets. Finally, we show how our model scales compared with other approximations.

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Submission Number: 7258