1.1k citations · 7.2k across the 70 of their papers we have counts for
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On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks
Sifan Wang, Hanwen Wang, Paris Perdikaris
Physics-informed neural networks (PINNs) are demonstrating remarkable promise in integrating physical models with gappy and noisy observational data, but they still struggle in cas…
Learning Unknown Physics of non-Newtonian Fluids
Brandon Reyes, Amanda A. Howard, Paris Perdikaris +1
We extend the physics-informed neural network (PINN) method to learn viscosity models of two non-Newtonian systems (polymer melts and suspensions of particles) using only velocity…
When and why PINNs fail to train: A neural tangent kernel perspective
Sifan Wang, Xinling Yu, Paris Perdikaris
Physics-informed neural networks (PINNs) have lately received great attention thanks to their flexibility in tackling a wide range of forward and inverse problems involving partial…
Deep learning of free boundary and Stefan problems
Sifan Wang, Paris Perdikaris
Free boundary problems appear naturally in numerous areas of mathematics, science and engineering. These problems present a great computational challenge because they necessitate n…
Bayesian differential programming for robust systems identification under uncertainty
Yibo Yang, Mohamed Aziz Bhouri, Paris Perdikaris
This paper presents a machine learning framework for Bayesian systems identification from noisy, sparse and irregular observations of nonlinear dynamical systems. The proposed meth…
Exact artificial boundary conditions of 1D semi-discretized peridynamics
Songsong Ji, Gang Pang, Jiwei Zhang +2
The peridynamic theory reformulates the equations of continuum mechanics in terms of integro-differential equations instead of partial differential equations. It is not trivial to…
Understanding and mitigating gradient pathologies in physics-informed neural networks
Sifan Wang, Yujun Teng, Paris Perdikaris
The widespread use of neural networks across different scientific domains often involves constraining them to satisfy certain symmetries, conservation laws, or other domain knowled…