Φ-DVAE: Physics-informed dynamical variational autoencoders for unstructured data assimilation

Alex Glyn-Davies, Connor Duffin, Ömer Deniz Akyildiz, Mark Girolami

Abstract: Highlights•Bayesian inference methodology for unstructured data assimilation.•Variational autoencoder embeds data to observations of latent differential equation.•Statistical FEM construction and parameter estimation account for misspecification.•Demonstrated on Lorenz-63, advection and Korteweg-de Vries differential equations.•Embedding physical prior knowledge produces data-efficient learning.