106 citations · 136 across the 9 of their papers we have counts for
6 papers · 1 filter
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…
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…
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…