3.4k citations · 27.2k across the 213 of their papers we have counts for
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Physics-informed neural networks for inverse problems in nano-optics and metamaterials
Yuyao Chen, Lu Lu, George Em Karniadakis +1
In this paper we employ the emerging paradigm of physics-informed neural networks (PINNs) for the solution of representative inverse scattering problems in photonic metamaterials a…
Multiscale modeling meets machine learning: What can we learn?
Grace C. Y. Peng, Mark Alber, Adrian Buganza Tepole +9
Machine learning is increasingly recognized as a promising technology in the biological, biomedical, and behavioral sciences. There can be no argument that this technique is incred…
Highly-scalable, physics-informed GANs for learning solutions of stochastic PDEs
Liu Yang, Sean Treichler, Thorsten Kurth +8
Uncertainty quantification for forward and inverse problems is a central challenge across physical and biomedical disciplines. We address this challenge for the problem of modeling…
Integrating Machine Learning and Multiscale Modeling: Perspectives, Challenges, and Opportunities in the Biological, Biomedical, and Behavioral Sciences
Mark Alber, Adrian Buganza Tepole, William Cannon +8
Fueled by breakthrough technology developments, the biological, biomedical, and behavioral sciences are now collecting more data than ever before. There is a critical need for time…
Learning and Meta-Learning of Stochastic Advection-Diffusion-Reaction Systems from Sparse Measurements
Xiaoli Chen, Jinqiao Duan, George Em Karniadakis
Physics-informed neural networks (PINNs) were recently proposed in [1] as an alternative way to solve partial differential equations (PDEs). A neural network (NN) represents the so…
DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators
Lu Lu, Pengzhan Jin, George Em Karniadakis
While it is widely known that neural networks are universal approximators of continuous functions, a less known and perhaps more powerful result is that a neural network with a sin…