Data-driven methods for partial differential equations

Session

Invited talks 7

Mar 4, 2026, 9:45 AM

Karlsruhe Institute of Technology

Conveners

Invited talks 7

• Mathias Trabs (KIT)

3. On gradient stability in nonlinear PDE models and inference in interacting particle systems

Aurélien Castre (University of Cambridge, DPMMS)

3/4/26, 9:45 AM

Invited talk

We consider general parameter to solution maps $\theta \mapsto \mathcal G(\theta)$ of non-linear partial differential equations and describe an approach based on a Banach space version of the implicit function theorem to verify the gradient stability condition of Nickl & Wang (JEMS 2024) for the underlying non-linear inverse problem, providing also injectivity estimates and corresponding...

9. Learning stochastic reduced order models from data

Melina Freitag (University of Potsdam)

Invited talk

We propose a non-intrusive model order reduction technique for stochastic differential equations with additive Gaussian noise. The method extends the operator inference framework and focuses on inferring reduced-order drift and diffusion coefficients by formulating and solving suitable least-squares problems based on observational data. Various subspace constructions based on the available...