Physics Informed Deep Kernel Learning
This work addresses data scarcity issues in deep kernel learning for applications requiring extrapolation, representing an incremental improvement by incorporating physics constraints into an existing framework.
The authors tackled the problem of deep kernel learning's performance being limited by scarce data, especially in extrapolation tasks, by proposing Physics Informed Deep Kernel Learning (PI-DKL) that integrates physics knowledge via differential equations, showing improved prediction accuracy and uncertainty quantification on synthetic and real-world datasets.
Deep kernel learning is a promising combination of deep neural networks and nonparametric function learning. However, as a data driven approach, the performance of deep kernel learning can still be restricted by scarce or insufficient data, especially in extrapolation tasks. To address these limitations, we propose Physics Informed Deep Kernel Learning (PI-DKL) that exploits physics knowledge represented by differential equations with latent sources. Specifically, we use the posterior function sample of the Gaussian process as the surrogate for the solution of the differential equation, and construct a generative component to integrate the equation in a principled Bayesian hybrid framework. For efficient and effective inference, we marginalize out the latent variables in the joint probability and derive a collapsed model evidence lower bound (ELBO), based on which we develop a stochastic model estimation algorithm. Our ELBO can be viewed as a nice, interpretable posterior regularization objective. On synthetic datasets and real-world applications, we show the advantage of our approach in both prediction accuracy and uncertainty quantification.