[Dottorcomp] Seminari di Matematica Applicata, 09/07/2025, Chiara Piazzola

[Lorenzo Tamellini]

Seminari di Matematica Applicata, Dipartimento di Matematica "F. Casorati"
e Istituto CNR IMATI "E. Magenes" di Pavia.

*Mercoledì 9 Luglio* 2025, alle *ore 15 precise*, presso la *sala
conferenze del CNR-IMATI* di Pavia

*Chiara Piazzola (Technische Universität München, Germania)*

terrà un seminario dal titolo:
*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.

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https://matematica.unipv.it/ricerca/cicli-di-seminari/seminari-di-matematica-applicata/