1.1k citations · 1.8k across the 9 of their papers we have counts for
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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:…