Related papers: A multiscale neural network based on hierarchical …

Artificial Neuronal Networks are models widely used for many scientific tasks. One of the well-known field of application is the approximation of high-dimensional problems via Deep Learning. In the present paper we investigate the Deep…

The simulation of quantum many-body systems poses a significant challenge in physics due to the exponential scaling of Hilbert space with the number of particles. Traditional methods often struggle with large system sizes and frustrated…

This paper introduces a novel method for eigenvalue computation using a distributed cooperative neural network framework. Unlike traditional techniques that face scalability challenges in large systems, our decentralized algorithm enables…

We introduce bio-inspired artificial neural networks consisting of neurons that are additionally characterized by spatial positions. To simulate properties of biological systems we add the costs penalizing long connections and the proximity…

The discretization of non-local operators, e.g., solution operators of partial differential equations or integral operators, leads to large densely populated matrices. $\mathcal{H}^2$-matrices take advantage of local low-rank structures in…

This paper explores learned-context neural networks. It is a multi-task learning architecture based on a fully shared neural network and an augmented input vector containing trainable task parameters. The architecture is interesting due to…

Deeper convolutional neural networks provide more capacity to approximate complex mapping functions. However, increasing network depth imposes difficulties on training and increases model complexity. This paper presents a new nonlinear…

In this paper, based on the combination of finite element mesh and neural network, a novel type of neural network element space and corresponding machine learning method are designed for solving partial differential equations. The…

We present a deep semi-nonnegative matrix factorization method for identifying subject-specific functional networks (FNs) at multiple spatial scales with a hierarchical organization from resting state fMRI data. Our method is built upon a…

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…

Hyperspectral imaging can help better understand the characteristics of different materials, compared with traditional image systems. However, only high-resolution multispectral (HrMS) and low-resolution hyperspectral (LrHS) images can…

The use of deep neural network (DNN) models as surrogates for linear and nonlinear structural dynamical systems is explored. The goal is to develop DNN based surrogates to predict structural response, i.e., displacements and accelerations,…

This work introduces a new framework integrating port-Hamiltonian systems (PHS) and neural network architectures. This framework bridges the gap between deterministic and stochastic modeling of complex dynamical systems. We introduce new…

The coincidence similarity index, based on a combination of the Jaccard and overlap similarity indices, has noticeable properties in comparing and classifying data, including enhanced selectivity and sensitivity, intrinsic normalization,…

We present Hierarchical Residual Networks (HiResNets), deep convolutional neural networks with long-range residual connections between layers at different hierarchical levels. HiResNets draw inspiration on the organization of the mammalian…

A new deep-learning neural network architecture based on high-order weak approximation algorithms for stochastic differential equations (SDEs) is proposed. The architecture enables the efficient learning of martingales by deep learning…

We present a global algorithm for training multilayer neural networks in this Letter. The algorithm is focused on controlling the local fields of neurons induced by the input of samples by random adaptations of the synaptic weights. Unlike…

In this paper, we present a new kind of learning implementation to recognize the patterns using the concept of Mirroring Neural Network (MNN) which can extract information from distinct sensory input patterns and perform pattern recognition…

In this paper, the class of random irregular block-hierarchical networks is defined and algorithms for generation and calculation of network properties are described. The algorithms presented for this class of networks are more efficient…

This paper introduces a new approach to reconstruct cosmological functions using artificial neural networks based on observational measurements with minimal theoretical and statistical assumptions. By using neural networks, we can generate…