17 citations · 24 across the 4 of their papers we have counts for
6 papers
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…
Asymptotically compatible reproducing kernel collocation and meshfree integration for the peridynamic Navier equation
Yu Leng, Xiaochuan Tian, Nathaniel A. Trask +1
In this work, we study the reproducing kernel (RK) collocation method for the peridynamic Navier equation. We first apply a linear RK approximation on both displacements and dilata…
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.…