publications

2024

1. Nature Sci. Rep.

   Generative adversarial reduced order modelling

   Dario Coscia, Nicola Demo, and Gianluigi Rozza

   Scientific Reports, 2024

   Abs Bib HTML

   In this work, we present GAROM, a new approach for reduced order modeling (ROM) based on generative adversarial networks (GANs). GANs attempt to learn to generate data with the same statistics of the underlying distribution of a dataset, using two neural networks, namely discriminator and generator. While widely applied in many areas of deep learning, little research is done on their application for ROM, i.e. approximating a high-fidelity model with a simpler one. In this work, we combine the GAN and ROM framework, introducing a data-driven generative adversarial model able to learn solutions to parametric differential equations. In the presented methodology, the discriminator is modeled as an autoencoder, extracting relevant features of the input, and a conditioning mechanism is applied to the generator and discriminator networks specifying the differential equation parameters. We show how to apply our methodology for inference, provide experimental evidence of the model generalization, and perform a convergence study of the method.

   @article{coscia2023generative,
     author = {Coscia, Dario and Demo, Nicola and Rozza, Gianluigi},
     da = {2024/02/15},
     date-added = {2024-02-19 10:48:01 +0100},
     date-modified = {2024-02-19 10:48:45 +0100},
     doi = {10.1038/s41598-024-54067-z},
     id = {Coscia2024},
     isbn = {2045-2322},
     journal = {Scientific Reports},
     number = {1},
     pages = {3826},
     rating = {5},
     read = {1},
     title = {Generative adversarial reduced order modelling},
     ty = {JOUR},
     url = {https://doi.org/10.1038/s41598-024-54067-z},
     volume = {14},
     year = {2024}
   }

2. ICLR

   PINA: a PyTorch Framework for Solving Differential Equations by Deep Learning for Research and Production Environments

   Dario Coscia, Nicola Demo, and Gianluigi Rozza

   In ICLR 2024 Workshop on AI4DifferentialEquations In Science, 2024

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   We present a versatile software designed for solving differential equations employing neural networks. The package is called PINA, an open-source Python library built upon the robust foundations of PyTorch and Lightning. It allows end-users to formulate their problem and craft their models to effortlessly compute solutions of PDEs by Physics Informed Neural Networks and Neural Operators. The modular structure of PINA permits it to adapt for user specifics, thus offering the freedom to select the most suitable learning techniques for their particular problem domain. Furthermore, by leveraging the capabilities of the Lightning package, PINA adapts to various hardware setups, including GPUs and TPUs. This adaptability positions PINA as an ideal candidate for the transition of these methodologies into production and industrial pipelines, where computational efficiency and scalability are of paramount importance.

2023

1. Comput. Mech.

   A continuous convolutional trainable filter for modelling unstructured data

   Dario Coscia, Laura Meneghetti, Nicola Demo, and 2 more authors

   Computational Mechanics, 2023

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   Convolutional Neural Network (CNN) is one of the most important architectures in deep learning. The fundamental building block of a CNN is a trainable filter, represented as a discrete grid, used to perform convolution on discrete input data. In this work, we propose a continuous version of a trainable convolutional filter able to work also with unstructured data. This new framework allows exploring CNNs beyond discrete domains, enlarging the usage of this important learning technique for many more complex problems. Our experiments show that the continuous filter can achieve a level of accuracy comparable to the state-of-the-art discrete filter, and that it can be used in current deep learning architectures as a building block to solve problems with unstructured domains as well.

   @article{coscia2023continuous,
     title = {A continuous convolutional trainable filter for modelling unstructured data},
     author = {Coscia, Dario and Meneghetti, Laura and Demo, Nicola and Stabile, Giovanni and Rozza, Gianluigi},
     journal = {Computational Mechanics},
     pages = {1--13},
     year = {2023},
     publisher = {Springer},
   }

2. JOSS

   Physics-Informed Neural networks for Advanced modeling

   Dario Coscia, Anna Ivagnes, Nicola Demo, and 1 more author

   Journal of Open Source Software, 2023

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   PINA is an open-source Python library providing an intuitive interface for solving differential equations using PINNs, NOs or both together. Based on PyTorch and PyTorchLightning, PINA offers a simple and intuitive way to formalize a specific (differential) problem and solve it using neural networks . The approximated solution of a differential equation can be implemented using PINA in a few lines of code thanks to the intuitive and user-friendly interface.

   @article{coscia2023physics,
     title = {Physics-Informed Neural networks for Advanced modeling},
     author = {Coscia, Dario and Ivagnes, Anna and Demo, Nicola and Rozza, Gianluigi},
     journal = {Journal of Open Source Software},
     volume = {8},
     number = {87},
     pages = {5352},
     year = {2023},
   }