182 citations · 1.2k across the 59 of their papers we have counts for
6 papers · 2 filters
Learning Hidden Dynamics using Intelligent Automatic Differentiation
Kailai Xu, Dongzhuo Li, Eric Darve +1
Many engineering problems involve learning hidden dynamics from indirect observations, where the physical processes are described by systems of partial differential equations (PDE)…
Adversarial Numerical Analysis for Inverse Problems
Kailai Xu, Eric Darve
Many scientific and engineering applications are formulated as inverse problems associated with stochastic models. In such cases the unknown quantities are distributions. The appli…
Sparse Hierarchical Preconditioners Using Piecewise Smooth Approximations of Eigenvectors
Bazyli Klockiewicz, Eric Darve
When solving linear systems arising from PDE discretizations, iterative methods (such as Conjugate Gradient, GMRES, or MINRES) are often the only practical choice. To converge in a…
Learning Constitutive Relations from Indirect Observations Using Deep Neural Networks
Daniel Z. Huang, Kailai Xu, Charbel Farhat +1
We present a new approach for predictive modeling and its uncertainty quantification for mechanical systems, where coarse-grained models such as constitutive relations are derived…
The Neural Network Approach to Inverse Problems in Differential Equations
Kailai Xu, Eric Darve
We proposed a framework for solving inverse problems in differential equations based on neural networks and automatic differentiation. Neural networks are used to approximate hidde…
An Algebraic Sparsified Nested Dissection Algorithm Using Low-Rank Approximations
Léopold Cambier, Chao Chen, Erik G Boman +3
We propose a new algorithm for the fast solution of large, sparse, symmetric positive-definite linear systems, spaND -- sparsified Nested Dissection. It is based on nested dissecti…