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A Learning-Based Optimal Uncertainty Quantification Method and Its Application to Ballistic Impact Problems
Xingsheng Sun, Burigede Liu
This paper concerns the study of optimal (supremum and infimum) uncertainty bounds for systems where the input (or prior) probability measure is only partially/imperfectly known (e…
Learning macroscopic internal variables and history dependence from microscopic models
Burigede Liu, Eric Ocegueda, Margaret Trautner +2
This paper concerns the study of history dependent phenomena in heterogeneous materials in a two-scale setting where the material is specified at a fine microscopic scale of hetero…
Fourier Neural Operator with Learned Deformations for PDEs on General Geometries
Zongyi Li, Daniel Zhengyu Huang, Burigede Liu +1
Deep learning surrogate models have shown promise in solving partial differential equations (PDEs). Among them, the Fourier neural operator (FNO) achieves good accuracy, and is sig…
Learning Markovian Homogenized Models in Viscoelasticity
Kaushik Bhattacharya, Burigede Liu, Andrew M. Stuart +1
Fully resolving dynamics of materials with rapidly-varying features involves expensive fine-scale computations which need to be conducted on macroscopic scales. The theory of homog…