Mathematical models: simulating reality with equations and algorithms.
Digital Twins are designed to replicate complex systems, which are difficult to observe and predict. These include urban traffic flows, living organisms’ physiological responses, and the turbulent behavior of air around airplanes. To understand and simulate such phenomena, scientists rely on mathematical models: they translate these phenomena into mathematical language and solve equations to understand how they will evolve. This task becomes much easier and faster thanks to numerical computation algorithms, which can instantly perform thousands of operations. Research Topic 1 (RT1) of Spoke 9 aims to refine these mathematical and computational tools to build increasingly accurate models and more efficient algorithms. In doing so, RT1 seeks to lay a solid framework for developing efficient Digital Twins, capable of faithfully and dynamically mirroring the complexity of their real-world counterparts.
A collection of interconnected elements whose interactions yield global behaviors and properties beyond the understanding of individual components alone.
Mathematical model
Set of equations encapsulating the physical laws governing a given system: solving these equations corresponds to determining the evolution of the system.
Numerical computation algorithm
A set of step-by-step instructions enabling a computer to solve a certain problem using only numbers and logical-mathematical operations.
Tasks and outputs
Research Topic 1 is organized into four tasks, each corresponding to a different step in the research workflow, from methodological foundations to applications, data analysis, and tool development.
Each scientific output of Research Topic 1 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 – State of art
Task RT1.1 aims at analyzing current methods for modeling complex systems, with a focus on data-driven approaches and uncertainty management.
Supervisory Control of Data-Aware Business Processes
Bresolin, D., Zavatteri, M. (2023). Supervisory control of business processes with resources, parallel and mutually exclusive branches, loops, and uncertainty. Inf. Syst. 119: 102288
University of Padua
2023
Journal paper
Reducing Disjunctive Complexity in Temporal Planning
Raffaele, A., Zavatteri, M. (2023). Reducing the number of disjuncts in dtps. Information and Computation, 293:105048.
University of Padua
2023
Repairing Unsound Data-Aware Process Models
Zavatteri, M., Bresolin, D., de Leoni, M. (2024). Repair of unsound data-aware process models. In: Business Process Management Workshops, pages 383–395. Springer.
University of padua
2023
High-Order Diffuse-Interface Methods for Two-Phase Flows
Tonicello, N., & Ihme, M. (2024). A high-order diffused-interface approach for two-phase compressible flow simulations using a discontinuous Galerkin framework. Journal of Computational Physics, 508, 112983.
SISSA
2024
Journal paper
Over-Parameterized Randomized Graph Networks
Donghi, G., Pasa, L., Oneto, L., Gallicchio, C., Micheli, A., Anguita, A., Sperduti, A., Navarin, N. (2024). Investigating over-parameterized randomized graph networks, Neurocomputing, 606, 128281. https://doi.org/10.1016/j.neucom.2024.128281
University of Padua
2024
Journal paper
Certified Neural Network Synthesis
Zavatteri, M., Bresolin, D., Navarin, N. (2024). Automated synthesis of certified neural networks. In: ECAI 2024 – 27th European Conference on Artificial Intelligence, volume 392 of Frontiers in Artificial Intelligence and Applications, pages 1341–1348. IOS Press.
University of Padua
2024
Certified Neural Networks: Early Results
Zavatteri, M., Bresolin, D., Navarin, N. (2024). Automated synthesis of certified neural networks: Initial results and open research lines. In: Porello, D., Vinci, C., and Zavatteri, M., editors, Short Paper Proceedings of the 6th International Workshop on Artificial Intelligence and Formal Verification, Logic, Automata, and Synthesis, OVERLAY 2024, Bolzano, Italy, November 28-29, 2024, volume 3904 of CEUR Workshop Proceedings, pages 77–82. CEUR-WS.org.
University of Padua
2024
Soundness and Repair of Data-Aware Process Models
Zavatteri, M., Bresolin, D., de Leoni, M. (2025). Data-aware process models: from soundness checking to repair. Data & Knowledge Engineering, 155:102377.
University of Padua
2025
Spectral Difference Methods for Diffuse-Interface Models
Tonicello, N., Lodato, G., & Ihme, M. (2025). Extension of a spectral difference method for the diffused-interface five-equation model. Computers & Fluids, 106880.
SISSA
2025
Journal paper
Neural Interpolation for Nonlinear Model Reduction
Hirsch, M., Pichi, F., & Hesthaven, J. S. (2025). Neural Empirical Interpolation Method for Nonlinear Model Reduction. SIAM Journal on Scientific Computing, C1264–C1293. https://doi.org/10.1137/24M1681434
SISSA
Young Researchers
Journal paper
2 – Application design
Task RT1.2 consists of developing and studying selected applications in mathematical analysis and mathematical physics, supported by appropriate data sources.
deal.II 9.6: Advanced Finite Element Computing
Africa, P. C. et al. (2024). The deal.II library, Version 9.6. Journal of Numerical Mathematics, 32(4), 369-380.
SISSA
2023
Journal paper
Preconditioning Double Saddle-Point Systems
Balani Bakrani F. et al (2024). Some preconditioning techniques for a class of double saddle point problems. Numerical Linear Algebra with Applications 31(4):e2551. https://doi.org/10.1002/nla.2551
University of Trieste
2023
Journal paper
Deep Kalman Filters for State and Parameter Estimation
Chinellato, E., Marcuzzi, F. (2025). State, parameters and hidden dynamics estimation with the Deep Kalman Filter: Regularization strategies. Journal of Computational Science. https://dx.doi.org/10.1016/j.jocs.2025.102569
University of Padua
2023
Journal paper
Feed-Forward Schemes for Augmented Kalman Filters
Marcuzzi, F. (2024). A Numerical Feed-Forward Scheme for the Augmented Kalman Filter. Lecture Notes in Computer Science, 24th International Conference on Computational Science, ICCS 2024. https://dx.doi.org/10.1007/978-3-031-63778-0_10
University of Padua
2023
Conference paper
Parallel-in-Time Solvers for Runge-Kutta Discretizations
Leveque, S. et al. (2024). Parallel-in-Time Solver for the All-at-Once Runge–Kutta Discretization, 45(4), 1902-1928. https://doi.org/10.1137/23M1567862
University of Trieste
2024
Journal paper
Physics-Aware Hit Detection in Audio Mixtures
Chinellato, E., Marcuzzi, F. (2025). Hit detection in audio mixtures by means of a physics-aware Deep-NMF algorithm. Mechanical Systems and Signal Processing. https://dx.doi.org/10.1016/j.ymssp.2024.112162
University of Padua
2024
Journal paper
Block Preconditioners for PDE-Constrained Optimization
Bergamaschi, L. et al. (2025). Spectral analysis of block preconditioners for double saddle-point linear systems with application to PDE-constrained optimization. Computational Optimization and Applications 91, 423–455. https://doi.org/10.1007/s10589-024-00623-2
University of Trieste
2025
Journal paper
3 – Data analysis
Task RT1.3 pertains to building data workflows and analysis pipelines to study the selected problems.
Physics-Aware Soft Sensors for Embedded Digital Twins
Chinellato, E., Marcuzzi, F., Pierobon, S. (2024). Physics-Aware Soft Sensors for Embedded Digital Twins. Lecture Notes in Networks and Systems, 9th International Congress on Information and Communication Technology, ICICT 2024. https://dx.doi.org/10.1007/978-981-97-3559-4_34
University of Padua
2023
Conference paper
Real-Time Audio Source Separation on IoT Devices
Chinellato, E., Marcuzzi, F., Martin, P. (2024). Real-Time Generation of a Targeted Clean Audio Sequence from Source Separation of Noisy Environmental Mixtures Using a Deep Nonnegative Matrix Factorization on IOT Devices. ICT for Intelligent Systems. ICTIS 2024. Smart Innovation, Systems and Technologies, SMart Innovation, Systems and Technologies, ICT for Intelligent Systems. ICTIS 2024. https://dx.doi.org/10.1007/978-981-97-5810-4_23
University of Padua
2024
Conference paper
4 – Model deployment
Task RT1.4 has the goal of developing and deploying tools for data analysis and mathematical modeling of complex systems.
A Benchmark for Cardiac Elastodynamics
Aróstica, R. et al. (2025). A software benchmark for cardiac elastodynamics. Computer Methods in Applied Mechanics and Engineering, 435, 117485.
SISSA
2024
Journal paper
Data-Driven Optimization of Sediment Transport Models
Dehghan-Souraki, D., López-Gómez, D., Bladé-Castellet, E., Larese, A., Sanz-Ramos, M. (2024). Optimizing sediment transport models by using the Monte Carlo simulation and deep neural network (DNN): A case study of the Riba-Roja reservoir. Environmental Modelling & Software, 175, 105979.
University of Padua
2024
Journal paper
3D Multiphysics Modeling of Reservoir Thermal Stratification
Dehghan-Souraki, D., Goñi, U. C., Martínez, R. Z., Bladé i Castellet, E., & Larese, A. (2025). Three-Dimensional Finite Element Modeling of Thermal Stratification in the Riba-Roja Reservoir Confluence: A Fluid–Thermal Multiphysics Approach. Water, 17(5), 674. https://doi.org/10.3390/w17050674
University of Padua
2025
Journal paper
Stabilized MPM for Incompressible Hyperelastic Materials
Moreno-Martinez, L. Wüchner, R., Larese, A. (2025). A mixed stabilized MPM formulation for incompressible hyperelastic materials using Variational Subgrid-Scales. Computer Methods in Applied Mechanics and Engineering, 435, 117621.
University of Padua
2025
Journal paper
Coordination
Research Topic 1 is led by the University of Padua. The International School for Advanced Studies (SISSA) and the University of Trieste (UniTS) are also involved in RT1.
