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In certain situations, neural networks are trained upon data that obey underlying symmetries. However, the predictions do not respect the symmetries exactly unless embedded in the network structure. In this work, we introduce architectures…
Hamiltonian neural networks (HNNs) are state-of-the-art models that regress the vector field of a dynamical system under the learning bias of Hamilton's equations. A recent observation is that embedding a bias regarding the additive…
We introduce a method for training exactly conservative physics-informed neural networks and physics-informed deep operator networks for dynamical systems. The method employs a projection-based technique that maps a candidate solution…
Performing machine learning on structured data is complicated by the fact that such data does not have vectorial form. Therefore, multiple approaches have emerged to construct vectorial representations of structured data, from kernel and…
Improving the interpretability of deep neural networks has recently gained increased attention, especially when the power of deep learning is leveraged to solve problems in physics. Interpretability helps us understand a model's ability to…
Models for image representation learning are typically designed for either recognition or generation. Various forms of contrastive learning help models learn to convert images to embeddings that are useful for classification, detection, and…
Patterns stored within pre-trained deep neural networks compose large and powerful descriptive languages that can be used for many different purposes. Typically, deep network representations are implemented within vector embedding spaces,…
We train embodied neural networks to plan and navigate unseen complex 3D environments, emphasising real-world deployment. Rather than requiring prior knowledge of the agent or environment, the planner learns to model the state transitions…
This work begins by establishing a mathematical formalization between different geometrical interpretations of Neural Networks, providing a first contribution. From this starting point, a new interpretation is explored, using the idea of…
Graph embeddings have emerged as a powerful tool for representing complex network structures in a low-dimensional space, enabling the use of efficient methods that employ the metric structure in the embedding space as a proxy for the…
Gaussian process regression is increasingly applied for learning unknown dynamical systems. In particular, the implicit quantification of the uncertainty of the learned model makes it a promising approach for safety-critical applications.…
Network embedding has attracted an increasing attention over the past few years. As an effective approach to solve graph mining problems, network embedding aims to learn a low-dimensional feature vector representation for each node of a…
A class of neural networks that gained particular interest in the last years are neural ordinary differential equations (neural ODEs). We study input-output relations of neural ODEs using dynamical systems theory and prove several results…
Neural network architectures have been extensively employed in the fair representation learning setting, where the objective is to learn a new representation for a given vector which is independent of sensitive information. Various…
We investigate the use of discrete and continuous versions of physics-informed neural network methods for learning unknown dynamics or constitutive relations of a dynamical system. For the case of unknown dynamics, we represent all the…
This paper is a summary of the theory of discrete embeddings introduced in [5]. A discrete embedding is an algebraic procedure associating a numerical scheme to a given ordinary differential equation. Lagrangian systems possess a…
Neural operators, which emerge as implicit solution operators of hidden governing equations, have recently become popular tools for learning responses of complex real-world physical systems. Nevertheless, the majority of neural operator…
We propose a learning framework to find the representation of a robot's kinematic structure and motion embedding spaces using graph neural networks (GNN). Finding a compact and low-dimensional embedding space for complex phenomena is a key…
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…
Deep neural networks come in many sizes and architectures. The choice of architecture, in conjunction with the dataset and learning algorithm, is commonly understood to affect the learned neural representations. Yet, recent results have…