Search Results for author:
Found 8 papers, 2 papers with code
Uncertainty Quantification of Graph Convolution Neural Network Models of Evolving Processes
In this work we present comparisons of the parametric uncertainty quantification of neural networks modeling complex spatial-temporal processes with Hamiltonian Monte Carlo and Stein variational gradient descent and its projected variant.
Error-in-variables modelling for operator learning
We propose error-in-variables (EiV) models for two operator regression methods, MOR-Physics and DeepONet, and demonstrate that these new models reduce bias in the presence of noisy independent variables for a variety of operator learning problems.
Partition of unity networks: deep hp-approximation
Approximation theorists have established best-in-class optimal approximation rates of deep neural networks by utilizing their ability to simultaneously emulate partitions of unity and monomials.
A physics-informed operator regression framework for extracting data-driven continuum models
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 and robust.
A block coordinate descent optimizer for classification problems exploiting convexity
By alternating between a second-order method to find globally optimal parameters for the linear layer and gradient descent to train the hidden layers, we ensure an optimal fit of the adaptive basis to data throughout training.
Robust Training and Initialization of Deep Neural Networks: An Adaptive Basis Viewpoint
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
Data fields sampled on irregularly spaced points arise in many applications in the sciences and engineering.
Nonlinear integro-differential operator regression with neural networks
The method parametrizes the spatial operator with neural networks and Fourier transforms such that it can fit a class of nonlinear operators without needing a library of a priori selected operators.
