This seminar is organized by the Scientific Computing group of CWI Amsterdam. The focus is on the application of Machine Learning (ML) and Uncertainty Quantification in scientific computing. Topics of interest include, among others:

- combination of data-driven models and (multi scale) simulations
- new ML architectures suited for scientific computing or UQ,
- incorporation of (physical) constraints into data-driven models,
- efficient (online) learning strategies,
- using ML for dimension reduction / creating surrogates,
- inverse problems using ML surrogates,

and any other topic in which some form of ML and/or UQ is used to enhance (existing) scientific computing methodologies. All applications are welcome, be it financial, physical, biological or otherwise.

For more information, or if you'd like to attend one of the talks, please contact Wouter Edeling of the SC group.

## Schedule upcoming talks

### May

**22 May 2023 11h00 CET**: *Sagy Ephrati (U. Twente)*: Data-driven stochastic forcing for uncertainty quantification and subgrid-scale modeling in geophysical fluid dynamics

Stochasticity has been employed systematically in geophysical fluid dynamics (GFD) to model uncertainty. Geophysical flows are typically dominated by advection effects and contain a family of conserved quantities, of which energy and enstrophy are considered most important. Stochastic advection by Lie transport (SALT), which is a data-driven enstrophy-preserving transport noise, can be used to quantify uncertainty in these models. The first part of the presentation illustrates how SALT can be used efficiently to quantify uncertainty due to unresolved dynamics. However, this approach seems insufficient in the presence of discretization error. To counteract the effects of coarsening, we apply a simple data-driven stochastic subgrid-scale parametrization inspired by data assimilation algorithms. In the second part of the presentation, we show that the proposed parametrization recovers measured reference kinetic energy spectra in coarse numerical simulations.

### June

**6 June 2023 11h00 CET**: Olga Mula (Eindhoven): Optimal State and Parameter Estimation Algorithms and Applications to Biomedical Problems

In this talk, I will present an overview of recent works aiming at solving inverse problems (state and parameter estimation) by combining optimally measurement observations and parametrized PDE models. After defining a notion of optimal performance in terms of the smallest possible reconstruction error that any reconstruction algorithm can achieve, I will present practical numerical algorithms based on nonlinear reduced models for which we can prove that they can deliver a performance close to optimal. The proposed concepts may be viewed as exploring alternatives to Bayesian inversion in favor of more deterministic notions of accuracy quantification. I will illustrate the performance of the approach on simple benchmark examples and we will also discuss applications of the methodology to biomedical problems

which are challenging due to shape variability.