1.1k citations · 1.7k across the 16 of their papers we have counts for
18 papers
Neural operators solve inverse problems for constitutive model discovery
Moritz Flaschel, Burigede Liu, Ellen Kuhl
Characterizing the mechanical response of materials traditionally requires solving optimization problems in which model parameters are calibrated or trained to minimize the discrep…
A Quantum Spectral Method for Non-Periodic Boundary Value Problems
Eky Febrianto, Yiren Wang, Burigede Liu +2
Quantum computing holds the promise of solving computational mechanics problems in polylogarithmic time, meaning computational time scales as , where i…
A Learning-based Domain Decomposition Method
Rui Wu, Nikola Kovachki, Burigede Liu
Recent developments in mechanical, aerospace, and structural engineering have driven a growing need for efficient ways to model and analyse structures at much larger and more compl…
Towards Quantum Computational Mechanics
Burigede Liu, Michael Ortiz, Fehmi Cirak
The advent of quantum computers, operating on entirely different physical principles and abstractions from those of classical digital computers, sets forth a new computing paradigm…
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…
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…
Fourier Neural Operator for Parametric Partial Differential Equations
Zongyi Li, Nikola Kovachki, Kamyar Azizzadenesheli +4
The classical development of neural networks has primarily focused on learning mappings between finite-dimensional Euclidean spaces. Recently, this has been generalized to neural o…
Multipole Graph Neural Operator for Parametric Partial Differential Equations
Zongyi Li, Nikola Kovachki, Kamyar Azizzadenesheli +4
One of the main challenges in using deep learning-based methods for simulating physical systems and solving partial differential equations (PDEs) is formulating physics-based data…
Neural Operator: Graph Kernel Network for Partial Differential Equations
Zongyi Li, Nikola Kovachki, Kamyar Azizzadenesheli +4
The classical development of neural networks has been primarily for mappings between a finite-dimensional Euclidean space and a set of classes, or between two finite-dimensional Eu…