5 citations · 8 across the 5 of their papers we have counts for
7 papers
Deep learning and multi-level featurization of graph representations of microstructural data
Reese Jones, Cosmin Safta, Ari Frankel
Many material response functions depend strongly on microstructure, such as inhomogeneities in phase or orientation. Homogenization presents the task of predicting the mean respons…
Gaussian Process Regression constrained by Boundary Value Problems
Mamikon Gulian, Ari Frankel, Laura Swiler
We develop a framework for Gaussian processes regression constrained by boundary value problems. The framework may be applied to infer the solution of a well-posed boundary value p…
A Survey of Constrained Gaussian Process Regression: Approaches and Implementation Challenges
Laura Swiler, Mamikon Gulian, Ari Frankel +2
Gaussian process regression is a popular Bayesian framework for surrogate modeling of expensive data sources. As part of a broader effort in scientific machine learning, many recen…
Tensor Basis Gaussian Process Models of Hyperelastic Materials
Ari Frankel, Reese Jones, Laura Swiler
In this work, we develop Gaussian process regression (GPR) models of hyperelastic material behavior. First, we consider the direct approach of modeling the components of the Cauchy…
Prediction of the evolution of the stress field of polycrystals undergoing elastic-plastic deformation with a hybrid neural network model
Ari Frankel, Kousuke Tachida, Reese Jones
Crystal plasticity theory is often employed to predict the mesoscopic states of polycrystalline metals, and is well-known to be costly to simulate. Using a neural network with conv…
Solution of the Generalized Linear Boltzmann Equation for Transport in Multidimensional Stochastic Media
Ari Frankel
The generalized linear Boltzmann equation (GLBE) is a recently developed framework based on non-classical transport theory for modeling the expected value of particle flux in an ar…