24 July 2025 , Thursday, 14:15, in seminar room J2.138
Title:
Uncertainty quantification analysis of bifurcations of PDEs with random coefficients
Abstract:
In this talk we address the forward uncertainty quantification analysis of random dynamical systems exhibiting bifurcations.
In particular, we focus on the Allen–Cahn equation, a prototypical model problem in nonlinear dynamics that exhibits bifurcations corresponding to variations of a deterministic bifurcation parameter. Going beyond the state-of-the-art, we introduce a random coefficient in the linear reaction part of the equation, thereby accounting for random, spatially-heterogeneous effects. Thus, we show that the bifurcation points and bifurcation curves are random objects and propose a surrogate modeling strategy employing the generalized polynomial chaos expansion based on sparse-grids to efficiently approximate the statistical properties of the random bifurcation points and bifurcation curves. Finally, we present numerical examples where we combine the popular software package Continuation Core and Toolboxes (COCO) for numerical continuation and the Sparse Grids Matlab Kit for the sparse-grid-based polynomial chaos expansion.