Research
We combine rigorous numerical analysis with scientific computing and machine learning. A common thread in our work is the question of how to obtain accurate predictions at a fraction of the computational cost of full-order simulations.
Atmospheric and ocean flows
We develop finite volume and finite element solvers for mesoscale atmospheric flows and for quasi-geostrophic ocean models, including filter stabilization and Large Eddy Simulation techniques that keep under-resolved simulations accurate. To make these simulations fast enough for many-query and real-time applications, we build reduced order models and other surrogate models – from filter-stabilized POD models to data-driven approaches based on randomized POD, convolutional autoencoders with reservoir computing, and super-resolution – that deliver accurate predictions at a fraction of the computational cost.
Reduced-order and data-driven modeling
Reduced-order models (ROMs) have emerged as the methodology of choice to reduce the computational burden when traditional simulations have to be carried out for several parameter values, as in the case of uncertainty quantification, optimal control, and inverse problems. ROMs replace expensive simulations by compact surrogates that can be evaluated in seconds. We work on projection-based methods (POD–Galerkin, reduced basis), purely data-driven approaches (dynamic mode decomposition, autoencoders, reservoir computing) and hybrid strategies that combine both.
Multiphysics problems
Many problems in civil and environmental engineering involve several physical processes that act on each other, e.g., a flow deforms a structure, which in turn changes the flow. Capturing these interactions is essential for reliable predictions, but coupling the models raises serious challenges in accuracy, stability and computational cost. We design robust algorithms for coupled problems: fluid–structure interaction, two-phase and surface flows, and gravity-driven granular-fluid mixtures such as landslides and submarine avalanches. Special attention goes to splitting schemes, preconditioning, and systematic benchmarking and validation against experiments.
Collective behavior dynamics
Unlike particles in a fluid, people make decisions, react to each other and to their surroundings, and the data to describe them are often scarce and noisy. Building mathematical models that explain how individual choices give rise to collective patterns, and calibrating them against observations, is a challenge we take on in two settings: crowd and crime dynamics. We develop microscopic, kinetic, and macroscopic models, with applications that include evacuation planning and the design of safe public spaces.