34 citations · 91 across the 15 of their papers we have counts for
4 papers · 1 filter
Time-dependent stochastic basis adaptation for uncertainty quantification
Ramakrishna Tipireddy, Panos Stinis, Alexandre M. Tartakovsky
We extend stochastic basis adaptation and spatial domain decomposition methods to solve time varying stochastic partial differential equations (SPDEs) with a large number of input…
An efficient epistemic uncertainty quantification algorithm for a class of stochastic models: A post-processing and domain decomposition framework
Mahadevan Ganesh, Stuart C Hawkins, Alexandre Tartakovsky +1
Partial differential equations (PDEs) are fundamental for theoretically describing numerous physical processes that are based on some input fields in spatial configurations. Unders…
Inverse Modeling of Viscoelasticity Materials using Physics Constrained Learning
Kailai Xu, Alexandre M. Tartakovsky, Jeff Burghardt +1
We propose a novel approach to model viscoelasticity materials using neural networks, which capture rate-dependent and nonlinear constitutive relations. However, inputs and outputs…
Gaussian Process Regression and Conditional Polynomial Chaos for Parameter Estimation
Jing Li, Alexandre M Tartakovsky
We present a new approach for constructing a data-driven surrogate model and using it for Bayesian parameter estimation in partial differential equation (PDE) models. We first use…