相关论文: Deep Neural Networks with Symplectic Preservation …
Toward a deeper understanding on the inner work of deep neural networks, we investigate CNN (convolutional neural network) using DCN (deconvolutional network) and randomization technique, and gain new insights for the intrinsic property of…
Recently, Hamiltonian neural networks (HNN) have been introduced to incorporate prior physical knowledge when learning the dynamical equations of Hamiltonian systems. Hereby, the symplectic system structure is preserved despite the…
In this paper we propose a Deep Learning architecture to approximate diffeomorphisms diffeotopic to the identity. We consider a control system of the form $\dot x = \sum_{i=1}^lF_i(x)u_i$, with linear dependence in the controls, and we use…
Implicit representations are widely used for object reconstruction due to their efficiency and flexibility. In 2021, a novel structure named neural implicit map has been invented for incremental reconstruction. A neural implicit map…
A data-driven framework is developed to represent chaotic dynamics on an inertial manifold (IM), and applied to solutions of the Kuramoto-Sivashinsky equation. A hybrid method combining linear and nonlinear (neural-network) dimension…
We introduce an architecture based on deep hierarchical decompositions to learn effective representations of large graphs. Our framework extends classic R-decompositions used in kernel methods, enabling nested part-of-part relations. Unlike…
This research addresses the challenge of characterizing the complexity and unpredictability of basins within various dynamical systems. The main focus is on demonstrating the efficiency of convolutional neural networks (CNNs) in this field.…
In this work we study the properties of deep neural networks (DNN) with random weights. We formally prove that these networks perform a distance-preserving embedding of the data. Based on this we then draw conclusions on the size of the…
Neural networks have greatly boosted performance in computer vision by learning powerful representations of input data. The drawback of end-to-end training for maximal overall performance are black-box models whose hidden representations…
This paper explores the use of deep neural networks for semiparametric estimation of economic models of maximizing behavior in production or discrete choice. We argue that certain deep networks are particularly well suited as a…
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…
While Hamiltonian mechanics provides a powerful inductive bias for neural networks modeling dynamical systems, Hamiltonian Neural Networks and their variants often fail to capture complex temporal dynamics spanning multiple timescales. This…
This research uses deep learning to estimate the topology of manifolds represented by sparse, unordered point cloud scenes in 3D. A new labelled dataset was synthesised to train neural networks and evaluate their ability to estimate the…
Although deep neural networks have shown well-performance in various tasks, the poor interpretability of the models is always criticized. In the paper, we propose a new interpretable neural network method, by embedding neurons into the…
In this work, we propose and explore Deep Graph Value Network (DeepGV) as a promising method to work around sample complexity in deep reinforcement-learning agents using a message-passing mechanism. The main idea is that the agent should be…
A framework for identifying nonlinear port-Hamiltonian systems using input-state-output data is introduced. The framework utilizes neural networks' universal approximation capacity to effectively represent complex dynamics in a structured…
In this paper, we present SIMAP, a novel layer integrated into deep learning models, aimed at enhancing the interpretability of the output. The SIMAP layer is an enhanced version of Simplicial-Map Neural Networks (SMNNs), an explainable…
Neural networks are a central technique in machine learning. Recent years have seen a wave of interest in applying neural networks to physical systems for which the governing dynamics are known and expressed through differential equations.…
We propose a message passing neural network architecture designed to be equivariant to column and row permutations of a matrix. We illustrate its advantages over traditional architectures like multi-layer perceptrons (MLPs), convolutional…
Recent years have witnessed an increased interest in the application of persistent homology, a topological tool for data analysis, to machine learning problems. Persistent homology is known for its ability to numerically characterize the…