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Physics-Informed Neural Operator for Learning Partial Differential Equations
Zongyi Li, Hongkai Zheng, Nikola Kovachki +5
In this paper, we propose physics-informed neural operators (PINO) that combine training data and physics constraints to learn the solution operator of a given family of parametric…
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…
Concurrent goal-oriented materials-by-design
Xingsheng Sun, Burigede Liu, Kaushik Bhattacharya +1
The development of new materials and structures for extreme conditions including impact remains a continuing challenge despite steady advances. Design is currently accomplished usi…
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:…
Hierarchical multiscale quantification of material uncertainty
Burigede Liu, Xingsheng Sun, Kaushik Bhattacharya +1
The macroscopic behavior of many materials is complex and the end result of mechanisms that operate across a broad range of disparate scales. An imperfect knowledge of material beh…