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math.NA2026
Global Sensitivity Analysis of Spatial Sets: Finite-Element-Based Estimation and the Role of Observation Windows
Farbod Chamanian, Chiara Piazzola, Elisabeth Ullmann
In this work we consider numerical models with random input parameters, where the model output is a spatially distributed random field. We carry out a statistical sensitivity analy…
math.NA2025
Neural Network Localized Orthogonal Decomposition for Numerical Homogenization of Diffusion Operators with Random Coefficients
Fabian Kröpfl, Daniel Peterseim, Elisabeth Ullmann
This paper presents a neural network--enhanced surrogate modeling approach for diffusion problems with spatially varying random field coefficients. The method builds on numerical h…
math.NA2024
Uncertainty quantification analysis of bifurcations of the Allen--Cahn equation with random coefficients
Christian Kuehn, Chiara Piazzola, Elisabeth Ullmann
In this work we consider the Allen--Cahn equation, a prototypical model problem in nonlinear dynamics that exhibits bifurcations corresponding to variations of a deterministic bifu…