209 citations · 596 across the 42 of their papers we have counts for
8 papers · 1 filter
Control of fractional diffusion problems via dynamic programming equations
Alessandro Alla, Marta D'Elia, Christian Glusa +1
We explore the approximation of feedback control of integro-differential equations containing a fractional Laplacian term. To obtain feedback control for the state variable of this…
Bayesian Nonlocal Operator Regression (BNOR): A Data-Driven Learning Framework of Nonlocal Models with Uncertainty Quantification
Yiming Fan, Marta D'Elia, Yue Yu +2
We consider the problem of modeling heterogeneous materials where micro-scale dynamics and interactions affect global behavior. In the presence of heterogeneities in material micro…
Probabilistic partition of unity networks for high-dimensional regression problems
Tiffany Fan, Nathaniel Trask, Marta D'Elia +1
We explore the probabilistic partition of unity network (PPOU-Net) model in the context of high-dimensional regression problems and propose a general framework focusing on adaptive…
Nonlocal Machine Learning of Micro-Structural Defect Evolutions in Crystalline Materials
Eduardo Augusto Barros de Moraes, Marta D'Elia, Mohsen Zayernouri
The presence and evolution of defects that appear in the manufacturing process play a vital role in the failure mechanisms of engineering materials. In particular, the collective b…
An asymptotically compatible coupling formulation for nonlocal interface problems with jumps
Christian Glusa, Marta D'Elia, Giacomo Capodaglio +2
We introduce a mathematically rigorous formulation for a nonlocal interface problem with jumps and propose an asymptotically compatible finite element discretization for the weak f…
Efficient optimization-based quadrature for variational discretization of nonlocal problems
Marco Pasetto, Zhaoxiang Shen, Marta D'Elia +3
Casting nonlocal problems in variational form and discretizing them with the finite element (FE) method facilitates the use of nonlocal vector calculus to prove well-posedeness, co…
Machine-learning of nonlocal kernels for anomalous subsurface transport from breakthrough curves
Xiao Xu, Marta D'Elia, Christian Glusa +1
Anomalous behavior is ubiquitous in subsurface solute transport due to the presence of high degrees of heterogeneity at different scales in the media. Although fractional models ha…
Nonlocal Kernel Network (NKN): a Stable and Resolution-Independent Deep Neural Network
Huaiqian You, Yue Yu, Marta D'Elia +2
Neural operators have recently become popular tools for designing solution maps between function spaces in the form of neural networks. Differently from classical scientific machin…