106 citations · 136 across the 9 of their papers we have counts for
9 papers
Error-in-variables modelling for operator learning
Ravi G. Patel, Indu Manickam, Myoungkyu Lee +1
Deep operator learning has emerged as a promising tool for reduced-order modelling and PDE model discovery. Leveraging the expressive power of deep neural networks, especially in h…
Reduced Basis Approximations of Parameterized Dynamical Partial Differential Equations via Neural Networks
Peter Sentz, Kristian Beckwith, Eric C. Cyr +2
Projection-based reduced order models are effective at approximating parameter-dependent differential equations that are parametrically separable. When parametric separability is n…
Partition of unity networks: deep hp-approximation
Kookjin Lee, Nathaniel A. Trask, Ravi G. Patel +2
Approximation theorists have established best-in-class optimal approximation rates of deep neural networks by utilizing their ability to simultaneously emulate partitions of unity…
Thermodynamically consistent physics-informed neural networks for hyperbolic systems
Ravi G. Patel, Indu Manickam, Nathaniel A. Trask +4
Physics-informed neural network architectures have emerged as a powerful tool for developing flexible PDE solvers which easily assimilate data, but face challenges related to the P…
A physics-informed operator regression framework for extracting data-driven continuum models
Ravi G. Patel, Nathaniel A. Trask, Mitchell A. Wood +1
The application of deep learning toward discovery of data-driven models requires careful application of inductive biases to obtain a description of physics which is both accurate a…
A block coordinate descent optimizer for classification problems exploiting convexity
Ravi G. Patel, Nathaniel A. Trask, Mamikon A. Gulian +1
Second-order optimizers hold intriguing potential for deep learning, but suffer from increased cost and sensitivity to the non-convexity of the loss surface as compared to gradient…
Robust Training and Initialization of Deep Neural Networks: An Adaptive Basis Viewpoint
Eric C. Cyr, Mamikon A. Gulian, Ravi G. Patel +2
Motivated by the gap between theoretical optimal approximation rates of deep neural networks (DNNs) and the accuracy realized in practice, we seek to improve the training of DNNs.…
GMLS-Nets: A framework for learning from unstructured data
Nathaniel Trask, Ravi G. Patel, Ben J. Gross +1
Data fields sampled on irregularly spaced points arise in many applications in the sciences and engineering. For regular grids, Convolutional Neural Networks (CNNs) have been succe…
Nonlinear integro-differential operator regression with neural networks
Ravi G. Patel, Olivier Desjardins
This note introduces a regression technique for finding a class of nonlinear integro-differential operators from data. The method parametrizes the spatial operator with neural netw…