English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Physical modeling is critical for many modern science and engineeringapplications. From a data science or machine learning perspective, where moredomain-agnostic, data-driven models are pervasive, physical knowledge -- oftenexpressed as differential equations -- is valuable in that it is complementaryto data, and it can potentially help overcome issues such as data sparsity,noise, and inaccuracy. In this work, we propose a simple, yet powerful andgeneral framework -- AutoIP, for Automatically Incorporating Physics -- thatcan integrate all kinds of differential equations into Gaussian Processes (GPs)to enhance prediction accuracy and uncertainty quantification. These equationscan be linear or nonlinear, spatial, temporal, or spatio-temporal, complete orincomplete with unknown source terms, and so on. Based on kerneldifferentiation, we construct a GP prior to sample the values of the targetfunction, equation-related derivatives, and latent source functions, which areall jointly from a multivariate Gaussian distribution. The sampled values arefed to two likelihoods: one to fit the observations, and the other to conformto the equation. We use the whitening method to evade the strong dependencybetween the sampled function values and kernel parameters, and we develop astochastic variational learning algorithm. AutoIP shows improvement uponvanilla GPs in both simulation and several real-world applications, even usingrough, incomplete equations.

AutoIP: A United Framework to Integrate Physics into Gaussian Processes