Credible High-Fidelity and Data-Driven Models

Development of numerical tools to assess and control the credibility of simulations. This embraces four underlying ideas: controlling the numerical accuracy (Verification); enhancing the quality of the approximation (Adaptivity); monitoring the pertinence of the model (Validation); accounting for the aleatoric nature of the analysed systems (Uncertainty Quantification).

Development of next-generation simulation tools designed to tackle complex physical problems of industrial relevance, with both accuracy and reliability. Methodologies span from low-order face-centred finite volume (FCFV) schemes, known for their robustness against mesh distortion, to high-order, degree-adaptive hybridisable discontinuous Galerkin (HDG) methods, which deliver precision and efficiency even on coarse or unstructured meshes. This research line also includes the treatment of high-fidelity geometries, where boundaries and interfaces are exactly described using NURBS, enabling simulations to remain accurate regardless of geometric complexity.

Development of intrusive and non-intrusive physics-based reduced order models (ROMs) tailored for parametric partial differential equations. The goal is to create efficient, accurate, and interpretable surrogate models that preserve the underlying physics while enabling rapid simulations across parameter spaces. The research line integrates several numerical strategies with built-in error control, including: proper generalised decomposition (PGD) for real-time, separated-variable approximation, proper orthogonal decomposition (POD) and kernel POD (kPOD) for projection-based reduction, neural networks (NN) surrogates for learning nonlinear parametric dependencies, and multi-fidelity methods that combine simulations at varying resolutions and accuracies to optimise computational costs. This line bridges model reduction and scientific machine learning, delivering robust tools for design, control, optimisation, and uncertainty quantification in computational science and engineering.

Development of numerical tools to construct engineering models from data and observations, instead of using physical or analytical models. The proposed methodologies pertain the direct data-driven design (D4) framework, including: structured low-rank approximation (SLA), direct and indirect data-driven control, behavioral approach to system theory, and reinforcement learning (RL). Moreover, this line aims to bridge physical models (and their approximations) with data-driven models. The goal is to improve physical models using data from sensors and observations and to enhance interpretability and explainability of data via physical knowledge by means of data assimilation, Bayesian model updating, physics-based data augmentation, and Markov chain Monte Carlo approaches. This research line specifically targets robust methodologies, with a focus on noisy data, disturbances, and model uncertainty.

Development of open-source solutions implementing frontier numerical tools suitable for industrial practice and sustainable development. Relevant software includes simulation solvers for systems involving fluid, solid, electromagnetics, and multi-physics phenomena, and surrogate applications for digital twinning in many-queries scenarios (e.g., design, shape and topology optimization, control, monitoring, inverse analysis, uncertainty quantification,…).