4 papers
Well-posedness for a regularised inertial Dean-Kawasaki model for slender particles in several space dimensions
Federico Cornalba, Tony Shardlow, Johannes Zimmer
A stochastic PDE, describing mesoscopic fluctuations in systems of weakly interacting inertial particles of finite volume, is proposed and analysed in any finite dimension $d\in\ma…
A deep surrogate approach to efficient Bayesian inversion in PDE and integral equation models
Teo Deveney, Eike Mueller, Tony Shardlow
We investigate a deep learning approach to efficiently perform Bayesian inference in partial differential equation (PDE) and integral equation models over potentially high-dimensio…
From weakly interacting particles to a regularised Dean--Kawasaki model
Federico Cornalba, Tony Shardlow, Johannes Zimmer
The evolution of finitely many particles obeying Langevin dynamics is described by Dean-Kawasaki equations, a class of stochastic equations featuring a non-Lipschitz multiplicative…
A regularised Dean-Kawasaki model: derivation and analysis
Federico Cornalba, Tony Shardlow, Johannes Zimmer
The Dean-Kawasaki model consists of a nonlinear stochastic partial differential equation featuring a conservative, multiplicative, stochastic term with non-Lipschitz coefficient, a…