Publications

2025

1. Using Physics-Informed neural networks for solving Navier-Stokes equations in fluid dynamic complex scenarios

   Tommaso Botarelli, Marco Fanfani, Paolo Nesi, and 1 more author

   Engineering Applications of Artificial Intelligence, 2025

   Abs DOI

   Navier-Stokes equations used to model fluid dynamic processes are fundamental to address several real-world problems related to energy production, aerospace applications, automotive design, industrial process, etc. However, since in most cases they do not admit any analytical solution, numerical simulations are required in industrial contexts to assess fluid dynamic behaviors in specific setups. Computational Fluid Dynamics (CFD) methods, like those using finite volume or element approaches, are exploited to find Navier-Stokes solutions and carry out simulations. However, such methods require expensive hardware resources, relevant computational times, and manual efforts for the definition of dense meshes on which equations are evaluated iteratively for each time step of the simulation. Physics-Informed Neural Networks (PINNs), which are deep neural networks where physical laws are directly embedded into the training process, offer a promising approach for solving Navier-Stokes equations, thus alleviating hardware and time requirements. PINNs bypass some CFD limitations by using neural networks to produce solutions based on governing equations, thus reducing the need for large datasets, dense meshing, and iterative estimation over time. This paper evaluates the application of PINNs in near real-world scenarios, while considering various geometries. The study focuses on the achieved accuracy, by comparing PINN estimates with CFD solutions obtained via OpenFOAM, and the required training times; this includes evaluating different neural network architectures, activation functions, and numbers of sampling points. Additionally, several training strategies such as fine-tuning, multi-resolution learning, and parametrized training are proposed to enhance efficiency and obtain speed up. Results demonstrate that PINNs can achieve comparable accuracy to CFD methods (with a velocity magnitude mean absolute error inferior to 10−2) and significantly reduce computational costs. Our findings demonstrated that with appropriate training techniques PINNs can be effectively used in industrial applications requiring rapid and accurate fluid dynamic simulations, thus paving the way for their broader adoption in practical engineering problems.

2024

1. A Compositional Approach to Coordinated Software Rejuvenation of Component-Based Systems

   Leonardo Paroli, Tommaso Botarelli, Laura Carnevali, and 1 more author

   In 2024 IEEE 35th International Symposium on Software Reliability Engineering (ISSRE), Oct 2024

   Abs DOI

   In component-based software systems, micro-rejuvenation of individual components can be performed to limit the number of more time-consuming system macro-rejuvenations, requiring appropriate selection of rejuvenation times to actually reduce the system unavailability. We present a novel coordinated approach to micro-rejuvenation of software components, aimed at minimizing the system cumulative unavailability over time.Specifically, each component is periodically rejuvenated, and, if it fails, rejuvenation is scheduled after repair. To limit concurrent component rejuvenations, an efficient calculus is defined to derive the optimal rejuvenation offset of each component, based on the condition of system unavailability expressed as a static fault tree with AND and OR gates. An efficient compositional approach is also provided to derive the system unavailability, by leveraging numerical analysis of a stochastic model with underlying Markov regenerative process. The solution accuracy is exploited to analyze how components loose synchronization over time due to random rejuvenation and repair times, enabling the definition of a macro-rejuvenation policy. Experiments performed on several randomly and manually generated models show feasibility and effectiveness of the approach, enabling further extensions.