Approximate Latent Force Model Inference
This work addresses a computational bottleneck for practitioners using interpretable models in dynamical systems, such as in physics or engineering applications, by enabling inference in previously intractable cases like Hill or diffusion equations, though it is incremental as it builds on existing latent force models.
The paper tackles the computational intractability of inference in physically-inspired latent force models for dynamical systems, which rely on exact posterior kernel computations that are rarely analytically available, by proposing a variational solution for a general class of non-linear and parabolic PDE latent force models and scaling it with a neural operator to handle thousands of instances, achieving competitive performance on tasks with varying kernel tractability.
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.