1.1k citations · 1.8k across the 9 of their papers we have counts for
12 papers
Learning Memory and Material Dependent Constitutive Laws
Kaushik Bhattacharya, Lianghao Cao, George Stepaniants +2
We propose and study a neural operator framework for learning memory- and material microstructure-dependent constitutive laws for heterogeneous materials. We work in the two-scale…
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…
Neural Operator: Learning Maps Between Function Spaces
Nikola Kovachki, Zongyi Li, Burigede Liu +4
The classical development of neural networks has primarily focused on learning mappings between finite dimensional Euclidean spaces or finite sets. We propose a generalization of n…
Learning Dissipative Dynamics in Chaotic Systems
Zongyi Li, Miguel Liu-Schiaffini, Nikola Kovachki +5
Chaotic systems are notoriously challenging to predict because of their sensitivity to perturbations and errors due to time stepping. Despite this unpredictable behavior, for many…
Multiscale modeling of materials: Computing, data science,uncertainty and goal-oriented optimization
Nikola Kovachki, Burigede Liu, Xingsheng Sun +4
The recent decades have seen various attempts at accelerating the process of developing materials targeted towards specific applications. The performance required for a particular…
A learning-based multiscale method and its application to inelastic impact problems
Burigede Liu, Nikola Kovachki, Zongyi Li +4
The macroscopic properties of materials that we observe and exploit in engineering application result from complex interactions between physics at multiple length and time scales:…