From the 1 of 56 linked papers with an AI index.
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Trainable Spline Representations for Physics-Informed Learning
Giovanni Canali, Nicola Demo, Gianluigi Rozza
This work introduces Physics-Informed Splines (PI-Splines), a structured spline-based architecture for physics-informed learning. Instead of representing the solution of a differen…
Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs
Lorenzo Tomada, Federico Pichi, Gianluigi Rozza
Graph Neural Networks (GNNs) are emerging as powerful tools for nonlinear Model Order Reduction (MOR) of time-dependent parameterized Partial Differential Equations (PDEs). However…
Revisiting Deep Information Propagation: Fractal Frontier and Finite-size Effects
Giuseppe Alessio D'Inverno, Zhiyuan Hu, Leo Davy +3
Information propagation characterizes how input correlations evolve across layers in deep neural networks. This framework has been well studied using mean-field theory, which assum…
BARNN: A Bayesian Autoregressive and Recurrent Neural Network
Dario Coscia, Max Welling, Nicola Demo +1
Autoregressive and recurrent networks have achieved remarkable progress across various fields, from weather forecasting to molecular generation and Large Language Models. Despite t…
Generative Adversarial Reduced Order Modelling
Dario Coscia, Nicola Demo, Gianluigi Rozza
In this work, we present GAROM, a new approach for reduced order modelling (ROM) based on generative adversarial networks (GANs). GANs have the potential to learn data distribution…