We are a research group of applied mathematicians striving to develop a coherent mathematical and algorithmic framework that optimally combines the strengths of complex physics-based models with the (often vast) data sets which are now routinely available in many fields of engineering, science and technology. The main challenges that we face are:

• the high dimensionality of the involved mathematical objects,
• the heterogenous nature and the noise of the available data,
• the underlying optimization problems is often neither convex nor smooth.

Developing a coherent mathematical and algorithmic framework optimally combining the strengths of complex physics-based models with (often vast) data sets.

In many fields of science and engineering, decisions are based on the outcomes of models that estimate/predict the state of a physical system or some of its relevant properties. One can distinguish two main families of such predictive models:

• Data-Driven models that are learnt from possibly noisy observation measurements,
• Physics-Based models which are usually expressed in the form of a Partial Differential Equations. The PDE formulations rely on first physical principles, and are usually solved by Computational Science methods.

Both approaches yield valuable yet incomplete descriptions of the true state since, in general, the phenomenon is too complex to be perfectly captured by either strategy.

Current fields of research:

• Approximation and Learning: model reduction, neural networks, tensor methods
• Inverse Problems and Data Assimilation: optimal reconstruction schemes, sensor placement
• Numerical Optimal Transport
• Numerical Analysis of PDEs: numerical solution of kinetic models, a posteriori error estimation, domain decomposition
• Applications: haemodynamics, pollution, epidemiology, nuclear engineering