5 papers
An adjoint method for training data-driven reduced-order models
Donglin Liu, Francisco García Atienza, Mengwu Guo
Reduced-order modeling lies at the interface of numerical analysis and data-driven scientific computing, providing principled ways to compress high-fidelity simulations in science…
Physics-based deep kernel learning for parameter estimation in high dimensional PDEs
Weihao Yan, Christoph Brune, Mengwu Guo
Inferring parameters of high-dimensional partial differential equations (PDEs) poses significant computational and inferential challenges, primarily due to the curse of dimensional…
Towards scientific machine learning for granular material simulations -- challenges and opportunities
Marc Fransen, Andreas Fürst, Deepak Tunuguntla +21
Micro-scale mechanisms, such as inter-particle and particle-fluid interactions, govern the behaviour of granular systems. While particle-scale simulations provide detailed insights…
PDE-DKL: PDE-constrained deep kernel learning in high dimensionality
Weihao Yan, Christoph Brune, Mengwu Guo
Many physics-informed machine learning methods for PDE-based problems rely on Gaussian processes (GPs) or neural networks (NNs). However, both face limitations when data are scarce…
Sparsifying dimensionality reduction of PDE solution data with Bregman learning
Tjeerd Jan Heeringa, Christoph Brune, Mengwu Guo
Classical model reduction techniques project the governing equations onto a linear subspace of the original state space. More recent data-driven techniques use neural networks to e…