Related papers: Generalized energy and gradient flow via graph fra…

In this work, we propose an end-to-end graph network that learns forward and inverse models of particle-based physics using interpretable inductive biases. Physics-informed neural networks are often engineered to solve specific problems…

The prediction of physicochemical properties from molecular structures is a crucial task for artificial intelligence aided molecular design. A growing number of Graph Neural Networks (GNNs) have been proposed to address this challenge.…

This paper aims at revisiting Graph Convolutional Neural Networks by bridging the gap between spectral and spatial design of graph convolutions. We theoretically demonstrate some equivalence of the graph convolution process regardless it is…

Machine learning frameworks such as graph neural networks typically rely on a given, fixed graph to exploit relational inductive biases and thus effectively learn from network data. However, when said graphs are (partially) unobserved,…

Recent advances at the intersection of control theory, neuroscience, and machine learning have revealed novel mechanisms by which dynamical systems perform computation. These advances encompass a wide range of conceptual, mathematical, and…

In this paper we introduce a general abstract formulation of a variational thermomechanical model, by means of a unified derivation via a generalization of the principle of virtual powers for all the variables of the system, including the…

Gradient-based learning in multi-layer neural networks displays a number of striking features. In particular, the decrease rate of empirical risk is non-monotone even after averaging over large batches. Long plateaus in which one observes…

Here we present the entropic dynamics formalism for networks. That is, a framework for the dynamics of graphs meant to represent a network derived from the principle of maximum entropy and the rate of transition is obtained taking into…

While physics conveys knowledge of nature built from an interplay between observations and theory, it has been considered less importantly in deep neural networks. Especially, there are few works leveraging physics behaviors when the…

Lots of learning tasks require dealing with graph data which contains rich relation information among elements. Modeling physics systems, learning molecular fingerprints, predicting protein interface, and classifying diseases demand a model…

We study evolution equations on metric graphs with reservoirs, that is graphs where a one-dimensional interval is associated to each edge and, in addition, the vertices are able to store and exchange mass with these intervals. Focusing on…

We present a graph theory-based method to characterise flow defects and structural shifts in condensed matter. We explore the connection between dynamical properties, particularly the recently introduced concept of ''softness'', and…

We propose a dynamical neural network model with a hierarchical and modular structure. The network architecture can be derived by minimizing an energy function that is originally designed based on two kinds of neurons with quite different…

Effective information analysis generally boils down to properly identifying the structure or geometry of the data, which is often represented by a graph. In some applications, this structure may be partly determined by design constraints or…

Feature selection (FS) plays an important role in machine learning, which extracts important features and accelerates the learning process. In this paper, we propose a deep FS method that simultaneously conducts feature selection and…

We explore the use of graph neural networks (GNNs) to model spatial processes in which there is no a priori graphical structure. Similar to finite element analysis, we assign nodes of a GNN to spatial locations and use a computational…

Graph Neural Networks (GNNs) are powerful tools for addressing learning problems on graph structures, with a wide range of applications in molecular biology and social networks. However, the theoretical foundations underlying their…

Graph convolutional networks (GCNs) are \emph{discriminative models} that directly model the class posterior $p(y|\mathbf{x})$ for semi-supervised classification of graph data. While being effective, as a representation learning approach,…

Recent works have shown that physics-inspired architectures allow the training of deep graph neural networks (GNNs) without oversmoothing. The role of these physics is unclear, however, with successful examples of both reversible (e.g.,…

In this paper we present a unifying geometric and compositional framework for modeling complex physical network dynamics as port-Hamiltonian systems on open graphs. Basic idea is to associate with the incidence matrix of the graph a Dirac…