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02/24/2023
Elliptic PDE learning is provably data-efficient
PDE learning is an emerging field that combines physics and machine lear...
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11/22/2022
Bifurcation analysis of a two-dimensional magnetic Rayleigh-Bénard problem
We perform bifurcation analysis of a two-dimensional magnetic Rayleigh-B...
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11/06/2022
Principled interpolation of Green's functions learned from data
We present a data-driven approach to mathematically model physical syste...
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10/28/2022
Data-driven discovery of Green's functions
Discovering hidden partial differential equations (PDEs) and operators f...
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04/27/2022
Learning Green's functions associated with parabolic partial differential equations
Given input-output pairs from a parabolic partial differential equation ...
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01/27/2022
Optimal control of Hopf bifurcations
We introduce a numerical technique for controlling the location and stab...
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05/31/2021
Control of bifurcation structures using shape optimization
Many problems in engineering can be understood as controlling the bifurc...
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05/27/2021
A generalization of the randomized singular value decomposition
The randomized singular value decomposition (SVD) is a popular and effec...
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05/01/2021
Data-driven discovery of physical laws with human-understandable deep learning
There is an opportunity for deep learning to revolutionize science and t...
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03/30/2021
An optimal complexity spectral method for Navier–Stokes simulations in the ball
We develop a spectral method for solving the incompressible generalized ...
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02/21/2021
Bifurcation analysis of two-dimensional Rayleigh–Bénard convection using deflation
We perform a bifurcation analysis of the steady state solutions of Rayle...
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02/04/2021
Accurate numerical simulation of electrodiffusion and water movement in brain tissue
Mathematical modelling of ionic electrodiffusion and water movement is e...
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01/31/2021
Learning elliptic partial differential equations with randomized linear algebra
Given input-output pairs of an elliptic partial differential equation (P...
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04/04/2020
Rational neural networks
We consider neural networks with rational activation functions. The choi...
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10/31/2019