Streamlining mathematical models for real-time simulations.
As powerful as they may be, numerical computation algorithms can require significant time to simulate highly complex phenomena. However, in many cases, real-time simulation is required—for example, during surgical procedures. To turn this need into a concrete possibility, the scientific community relies on Model Order Reduction (MOR) techniques: mathematical tools that streamline models, making calculations much faster while preserving a good degree of accuracy. Research Topic 2 (RT2) explores the application of MOR in the field of computational fluid dynamics, a crucial discipline for simulating industrial, physiological, and environmental phenomena. Since every simplification inevitably introduces approximations—and thus small margins of error—RT2 draws on the science of uncertainty quantification to estimate, manage, and reduce uncertainties in the results.
A collection of techniques to streamline mathematical models, based on the principle of keeping only the most relevant parameters within them.
Computational fluid dynamics
The branch of physics that studies and simulates how fluids move and interact—with other objects or with each other—through numerical computation algorithms.
Uncertainty quantification
Mathematical discipline dedicated to studying and estimating uncertainties in simulations and mathematical models.
Tasks and outputs
Research Topic 2 is organized into four tasks, each corresponding to a different step in the research workflow, from the review of current techniques to the design and development of real-time ROM applications.
Each scientific output of Research Topic 2 is associated with a particular task and with a milestone that situates it within the iNEST project, either along the project timeline (2022, 2023, 2024, 2025) or within specific project activities (e.g., those involving Young Researcher Grants).
1 – ROM review
Task RT2.1 is focused on the review of current reduced-order models and uncertainty quantification techniques.
Sparse Identification of Bifurcating CFD Phenomena
Tomada, L., Khamlich, M., Pichi, F., & Rozza, G. (2025). Sparse Identification for bifurcating phenomena in Computational Fluid Dynamics. Computers & Fluids, 302, 106841. https://doi.org/10.1016/j.compfluid.2025.106841
SISSA
Young Researchers
Journal paper
2 – Real-time design
Task RT2.2 revolves around the design of one or more real-time applications, using both full and reduced-order models.
Generative Models for Constrained Shape Deformation
Padula, G., Romor, F., Stabile, G., & Rozza, G. (2024). Generative models for the deformation of industrial shapes with linear geometric constraints: Model order and parameter space reductions. Computer Methods in Applied Mechanics and Engineering, 423.
SISSA
2023
Journal paper
Deep Kalman Filtering for Partially Unknown Systems
Chinellato, E., Marcuzzi, F. (2024). State Estimation of Partially Unknown Dynamical Systems with a Deep Kalman Filter. Computational Science – ICCS 2024, Lecture Notes in Computer Science, International Conference on Computational Science (ICCS) 2024. https://dx.doi.org/10.1007/978-3-031-63775-9_22
University of Padua
2023
Conference paper
Optimal Transport-Driven Deep Learning for Model Reduction
Khamlich, M., Pichi, F., & Rozza, G. (2025). Optimal Transport-Inspired Deep Learning Framework for Slow-Decaying Kolmogorov n-Width Problems: Exploiting Sinkhorn Loss and Wasserstein Kernel. SIAM Journal on Scientific Computing, C235–C264. https://doi.org/10.1137/23M1604680
SISSA
2024
Journal paper
Graph Networks for Resolution-Invariant Operator Learning
Morrison, O. M., Pichi, F., & Hesthaven, J. S. (2024). GFN: A graph feedforward network for resolution-invariant reduced operator learning in multifidelity applications. Computer Methods in Applied Mechanics and Engineering, 432, 117458. https://doi.org/10.1016/j.cma.2024.117458
SISSA
2024
Journal paper
Space-Dependent Aggregation for Non-Intrusive ROMs
Ivagnes, A., Tonicello, N., Cinnella, P., & Rozza, G. (2024). Enhancing non-intrusive reduced-order models with space-dependent aggregation methods. Acta Mechanica, 1-30.
SISSA
2024
Journal paper
Certified Greedy Methods for Bifurcating PDEs
Pichi, F., & Strazzullo, M. (2025). Deflation-based certified greedy algorithm and adaptivity for bifurcating nonlinear PDEs. Communications in Nonlinear Science and Numerical Simulation, 149, 108941. https://doi.org/10.1016/j.cnsns.2025.108941
SISSA
2025
Journal paper
3 – ROM development
Task RT2.3 is the development step, in which the problem is analyzed and both a full and a reduced-order model are created. The two kinds of models are compared, especially in terms of errors.
Accuracy and Efficiency of Reduced Order Models
Siena, P., Africa, P. C., Girfoglio, M., & Rozza, G. (2024). On the accuracy and efficiency of reduced order models: Towards real-world applications. In F. Chouly, S. P. A. Bordas, R. Becker, & P. Omnes (Eds.), Error control, adaptive discretizations, and applications, Part 2 (Vol. 59, pp. 245–288). Elsevier.
SISSA
2023
Book contribution
Reduced Order Control of Cardiovascular Flows
Rathore, S., Africa, P. C., Ballarin, F., Pichi, F., Girfoglio, M., & Rozza, G. (2025). Projection-based reduced order modelling for unsteady parametrized optimal control problems in 3D cardiovascular flows. Computer Methods and Programs in Biomedicine, 269, 108813. https://doi.org/10.1016/j.cmpb.2025.108813
SISSA
2024
Journal paper
Mesh-Informed ROMs for Aneurysm Risk Prediction
D’Inverno, G. A., Moradizadeh, S., Salavatidezfouli, S., Africa, P. C., & Rozza, G. (2025). Mesh-informed Reduced Order Models for aneurysm rupture risk prediction. Journal of Computational and Applied Mathematics, 116727.
SISSA
2024
Journal paper
Data-Driven Implicit LES with Spectral Difference Methods
Clinco, N., Tonicello, N., & Rozza, G. (2025). A data-driven study on Implicit LES using a spectral difference method. Journal of Computational Physics, 114302.
SISSA
2024
Journal paper
Reduced Order Modeling: Intrusive and Non-Intrusive Review
Padula, G., Girfoglio, M., & Rozza, G. (2024). A brief review of reduced order models using intrusive and non‐intrusive techniques. Proceedings in Applied Mathematics.
SISSA
2024
Conference paper
Hybrid ROMs for Hemodynamic Boundary Conditions
Siena, P., Africa, P. C., Girfoglio, M., & Rozza, G. (2025). A hybrid reduced order model to enforce outflow pressure boundary conditions in computational hemodynamics. Biomechanics and Modeling in Mechanobiology.
SISSA
2025
Journal paper
Transport-Based Interpolation for Nonlinear Reduced Models
Khamlich, M., Pichi, F., Girfoglio, M., Quaini, A., & Rozza, G. (2025). Optimal transport-based displacement interpolation with data augmentation for reduced order modeling of nonlinear dynamical systems. Journal of Computational Physics, 531, 113938. https://doi.org/10.1016/j.jcp.2025.113938
SISSA
Young Researchers
Journal paper
4 – UQ and deployment
Task RT2.4 aims at deploying the ROM application and establishing a suited approach for uncertainty quantification.
Coordination
Research Topic 2 is led by the International School for Advanced Studies (SISSA). The University of Padua (UniPD) and the National Institute of Oceanography and Experimental Geophysics (OGS) are also involved in RT2.
