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Surrogate Models for Parametric PDEs via Graph-Informed Neural Networks

Susanna Olivero

Surrogate Models for Parametric PDEs via Graph-Informed Neural Networks.

Rel. Francesco Della Santa, Maria Strazzullo. Politecnico di Torino, Corso di laurea magistrale in Data Science And Engineering, 2024

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Abstract:

This thesis focuses on training surrogate models based on Deep Learning (DL) to predict the solutions of parametric Partial Differential Equation (PDE) problems. In particular, the PDE problems we consider have most of their parameters used to characterize the boundary conditions, not only the physical properties embedded in the differential equations. The scenarios examined involve two types of problems, one purely diffusion-based and one involving both diffusion and convection. Several kinds of DL models are taken into account, including a novel spatial-based graph network called Graph-Informed Neural Network (GINN). Error statistics are computed to understand how the models' predictions are affected by the model architecture, the amount of training data, the hyperparameters of the network, and the physical parameters of the problem. The experiments demonstrate the effectiveness of the GINNs as surrogate models for parametric PDEs, also compared to more traditional DL models.

Relators: Francesco Della Santa, Maria Strazzullo
Academic year: 2024/25
Publication type: Electronic
Number of Pages: 101
Subjects:
Corso di laurea: Corso di laurea magistrale in Data Science And Engineering
Classe di laurea: New organization > Master science > LM-32 - COMPUTER SYSTEMS ENGINEERING
Aziende collaboratrici: UNSPECIFIED
URI: http://webthesis.biblio.polito.it/id/eprint/33102
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