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GSPTexp

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Model Reduction for Complex Systems with Exponential Nonlinearity via Geometric...

Model Reduction for Complex Systems with Exponential Nonlinearity via Geometric Singular Perturbation Theory "Important aspects of nonlinear complex systems like the Earth's climate, gene regulatory networks or the global telecommunication network can be modelled mathematically by systems of ordinary differential equations. However, the... ver más

01/04/2026

TU WIEN

199K€

Presupuesto del proyecto: 199K€

Líder del proyecto

TECHNISCHE UNIVERSITAET WIEN No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

Fecha límite participación Sin fecha límite de participación.

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Financiación concedida El organismo HORIZON EUROPE notifico la concesión del proyecto el día 2023-05-05

HORIZON-MSCA-2022-PF-01-01: MSCA Postdoctoral Fellowships 2022 Expected Outcome:

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3 Participantes

TU WIEN

199.44K€ | Lider

UNIVERSITE DE MONTPELLIER

N.D. | Participante

TECHNICAL UNIVERSITY OF DENM...

N.D. | Participante

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Duración del proyecto: 34 meses Fecha Inicio: 2023-05-05
Fecha Fin: 2026-04-01

Líder del proyecto

TECHNISCHE UNIVERSITAET WIEN No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

Presupuesto del proyecto 199K€

Fecha límite de participación Sin fecha límite de participación.

Descripción del proyecto "Important aspects of nonlinear complex systems like the Earth's climate, gene regulatory networks or the global telecommunication network can be modelled mathematically by systems of ordinary differential equations. However, the dynamics of such systems can rarely be understood by direct numerical simulation due to significant problems including high dimensionality, strong nonlinearity and processes occurring over a wide range of timescales. This leads to the necessity of model reduction, i.e. the identification of reliable methods for discarding unnecessary details to obtain a simpler 'reduced system', whilst preserving the salient dynamical features of the original system. Existing approaches to model reduction rely on a combination of methods which (i) exploit multi-scale structure in order to decompose the problem into lower dimensional subsystems, and (ii) reduce nonlinearity by replacing highly nonlinear terms by piecewise-smooth (PWS) approximations. Despite substantial progress in particular applications, a sound mathematical basis is often lacking and existing methodologies sometimes lead to qualitatively different results. This project addresses a number of limitations to existing model reduction techniques, by developing a mathematical formalism which we call ""GSPTexp"". We begin by building upon recent developments in Geometric Singular Perturbation Theory, with the aim to formalise recently identified connections between PWS systems and multi-scale systems with exponential nonlinearities. Via multiple novel adaptations of a geometric method known as blow-up, the GSPTexp formalism will be developed and used as a mathematically sound method for model reduction of (i) classical model problems from combustion and (ii) gene regulatory networks. Finally, in an ambitious interdisciplinary collaboration with systems biologists, we aim to couple GSPTexp with emerging techniques based on tropical geometry to study and simplify (iii) biochemical networks."

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