Bayesian learning of latent dynamics in computational physics
Organization:
Funded by: | Sectorplan Bèta en Techniek, under the focus area Mathematics of Computational Science |
Postdoc: |  |
Supervisors: | chair MIA:  Daily supervisor: |
Collaboration: |
Description:
Machine learning extracts insights from datasets and provides light-weighted predictions of the underlying system, but it is also limited by overfitting information in the given data. On the other hand, physics-based models offer better generalization but meanwhile suffer from demanding computational cost with classical numerical approximations, such as the finite element method.
In this project, we mainly aim to develop a framework for parametric time-dependent partial differential equations (PDEs) combining reduced-order modeling and Gaussian processes. Reduced-order modeling seeks a predominant low-dimensional representation of a high-dimensional physical system in a reduced latent space, yet without significantly compromising the solution accuracy. Gaussian processes will be utilized to enable the prediction over physical and geometrical parametrizations of initial conditions, boundary conditions and characteristics of the governing laws. Incorporated with Bayesian inference, a probabilistic framework will be formulated to facilitate constructed reduced systems with uncertainty quantification.