FluCo

European Research Council and European Union Horizon Europe acknowledgement

Fluctuations in continuum and conservative stochastic partial differential equations

Fluctuations occur throughout complex systems: as thermal fluctuations in physical models, algorithmic randomness in machine learning and unresolved small-scale variability in climate dynamics. Although the microscopic details differ, many such systems exhibit common large-scale structures. FluCo seeks mathematical principles that explain this universality by deriving and analysing scaling limits that retain both the effective mean behaviour and the fluctuations around it.

The project focuses on conservative stochastic partial differential equations as universal fluctuating continuum models. These equations preserve quantities such as mass and arise naturally as mesoscopic descriptions between microscopic particle systems and deterministic macroscopic PDEs. Their analysis brings together singular SPDEs, strongly nonlinear and degenerate PDEs, kinetic formulations, supercriticality, interacting particle systems and random dynamical systems.

Scientific programme

FluCo is organized around three central challenges:

  1. Well-posedness: establishing robust solution theories for singular conservative SPDEs.
  2. Singular limits: understanding scaling limits for supercritical conservative SPDEs.
  3. Stochastic dynamics: developing a long-time and qualitative theory for conservative SPDEs.

These questions support a wider programme on regularity, non-equilibrium large deviations, numerical approximation and stochastic models of learning. The broader aim is to uncover structures that remain meaningful across different physical and computational systems despite their many parameters and interactions.

Project facts

ProgrammeHorizon Europe — European Research Council (ERC) Main Programme
CallERC Consolidator Grants 2022 (ERC-2022-COG)
Grant agreement101088488
DOI10.3030/101088488
Period1 November 2023–31 October 2028
Host institutionTechnische Universität Berlin
Principal investigatorBenjamin Gess

SAiS team

Benjamin Gess
Javier Castro
Shanshan Hu
Sarah Geiss
Johannes Müller
Adrian Martini

Research areas

Nonlinear PDEs
SPDEs
Stochastic Dynamics
Numerics
Machine Learning
Non-equilibrium Statistical Mechanics and Fluctuating Hydrodynamics
Stochastic Fluid Dynamics

Official sources

CORDIS project record
FluCo project website

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