315 citations · 502 across the 7 of their papers we have counts for
8 papers
Generative diffusion learning for parametric partial differential equations
Ting Wang, Petr Plechac, Jaroslaw Knap
We develop a class of data-driven generative models that approximate the solution operator for parameter-dependent partial differential equations (PDE). We propose a novel probabil…
Stochastic Deep-Ritz for Parametric Uncertainty Quantification
Ting Wang, Jaroslaw Knap
Scientific machine learning has become an increasingly important tool in materials science and engineering. It is particularly well suited to tackle material problems involving man…
A surrogate model for studying random field energy release rates in 2D brittle fractures
Luis Blanco-Cocom, Marcos A. Capistrán, Jaroslaw Knap +1
This article proposes a weighted-variational model as an approximated surrogate model to lessen numerical complexity and lower the execution times of brittle fracture simulations.…
Stochastic Gradient Descent for Semilinear Elliptic Equations with Uncertainties
Ting Wang, Jaroslaw Knap
Randomness is ubiquitous in modern engineering. The uncertainty is often modeled as random coefficients in the differential equations that describe the underlying physics. In this…
Accelerated scale bridging with sparsely approximated Gaussian learning
Ting Wang, Kenneth W. Leiter, Petr Plechac +1
Multiscale modeling is a systematic approach to describe the behavior of complex systems by coupling models from different scales. The approach has been demonstrated to be very eff…
Higher-order adaptive finite-element methods for Kohn-Sham density functional theory
Phani Motamarri, Michael R Nowak, Kenneth Leiter +2
We present an efficient computational approach to perform real-space electronic structure calculations using an adaptive higher-order finite-element discretization of Kohn-Sham den…
Higher-order adaptive finite-element methods for orbital-free density functional theory
Phani Motamarri, Mrinal Iyer, Jaroslaw Knap +1
In the present work, we investigate the computational efficiency afforded by higher-order finite-element discretization of the saddle-point formulation of orbital-free density func…
An Analysis of the Quasicontinuum Method
J. Knap, M. Ortiz
The aim of this paper is to present a streamlined and fully three-dimensional version of the quasicontinuum (QC) theory of Tadmor et al. and to analyze its accuracy and convergence…