Time-Evolving Stochastic Manifolds

Informazioni relative al progetto

StochMan

ID dell’accordo di sovvenzione: 101088589

DOI

10.3030/101088589

Data della firma CE 3 Aprile 2023

Data di avvio 1 Settembre 2023

Data di completamento 31 Agosto 2028

Finanziato da

• European Research Council (ERC)

Costo totale

€ 1 997 651,00

Contributo UE

€ 1 997 651,00

Coordinato da

CHALMERS TEKNISKA HOGSKOLA AB
Sweden

Periodic Reporting for period 1 - StochMan (Time-Evolving Stochastic Manifolds)

Periodo di rendicontazione: 2023-09-01 al 2026-02-28

Sintesi del contesto e degli obiettivi generali del progetto

Uncertainty is all around us and caused, for example, by the nature of a problem as in quantum mechanics, the lack of our precise knowledge as in porous media, or inaccuracies in measurements as in experiments with imperfect equipment. While traditionally and due to the lack of computing power, science and technology relied on deterministic models, recent developments allow to include randomness. This trend requires efficient simulation methods for models with uncertainty. In space-time problems such as moving biological cells and the surface of the ocean, the randomness could be modeled by a stochastic process given explicitly or described implicitly by stochastic partial differential equations. Fast and accurate methods for sampling the stochastic processes are the key when computing statistical quantities of the advanced models.

The main contribution of the ERC-funded StochMan project is the development of a theoretical framework for evolving stochastic manifolds and their efficient simulation with analyzed algorithms. Special emphasis is paid to the situation when the evolving stochastic manifold is a moving surface disturbed by external forces and described by stochastic partial differential equations.

Lavoro eseguito dall’inizio del progetto fino alla fine del periodo coperto dalla relazione e principali risultati finora ottenuti

The project has developed efficient approximation methods for stochastic partial differential equations on surfaces that are a cornerstone for uncertainty quantification for spatio-temporal models with pre-described roughness or smoothness. The methods allow for random surfaces and their time evolution. Besides mathematically proven properties, the developed algorithms are ready to be used in applications.

Progressi oltre lo stato dell’arte e potenziale impatto previsto (incluso l’impatto socioeconomico e le implicazioni sociali più ampie del progetto fino ad ora)

Based on many small pieces of the puzzle, the main goal is to develop the mathematical foundations of stochastic manifolds and their approximation. The project bridges mathematical theory with algorithms that are ready for use in applications that suffer under uncertainty and require its simulation.

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