Approximate Latent Force Model Inference

TL;DR

This paper introduces a variational inference method for latent force models based on differential equations, enabling scalable and efficient inference for complex dynamical systems with intractable kernels.

Contribution

It proposes a novel variational approach and neural operator scaling technique to handle intractable kernels in latent force models, broadening their applicability.

Findings

Achieves competitive performance on various tasks.

Enables scalable inference for large datasets.

Handles intractable kernels effectively.

Abstract

Physically-inspired latent force models offer an interpretable alternative to purely data driven tools for inference in dynamical systems. They carry the structure of differential equations and the flexibility of Gaussian processes, yielding interpretable parameters and dynamics-imposed latent functions. However, the existing inference techniques associated with these models rely on the exact computation of posterior kernel terms which are seldom available in analytical form. Most applications relevant to practitioners, such as Hill equations or diffusion equations, are hence intractable. In this paper, we overcome these computational problems by proposing a variational solution to a general class of non-linear and parabolic partial differential equation latent force models. Further, we show that a neural operator approach can scale our model to thousands of instances, enabling fast, distributed computation. We demonstrate the efficacy and flexibility of our framework by achieving competitive performance on several tasks where the kernels are of varying degrees of tractability.