Related papers: Pattern Formation in Quantum Hierarchical Cellular…

The steady incompressible Navier--Stokes equations pose significant computational challenges due to their nonlinear convective terms and pressure--velocity coupling. Physics-informed neural networks (PINNs) provide a mesh-free framework for…

Neural networks (NN) have achieved state-of-the-art performance in various applications. Unfortunately in applications where training data is insufficient, they are often prone to overfitting. One effective way to alleviate this problem is…

In this work we apply deep neural networks to find the non-equilibrium steady state solution to correlated open quantum many-body systems. Motivated by the ongoing search to find more powerful representations of (mixed) quantum states, we…

Starting from the hypothesis that both physics, in particular space-time and the physical vacuum, and the corresponding mathematics are discrete on the Planck scale we develop a certain framework in form of a class of ' cellular networks'…

Despite the prevalent view that quantum mechanics is irrelevant to macroscopic biological systems because of inherent noise and decoherence, this paper demonstrates that the electrical noise (Brownian motion) in neuron membranes gives rise…

We introduce a distributed quantum-classical framework that synergizes photonic quantum neural networks (QNNs) with matrix-product-state (MPS) mapping to achieve parameter-efficient training of classical neural networks. By leveraging…

Convolutional Neural Networks (CNNs) have been successfully applied to many computer vision tasks, such as image classification. By performing linear combinations and element-wise nonlinear operations, these networks can be thought of as…

Neural Quantum States (NQS) are a class of variational wave functions parametrized by neural networks (NNs) to study quantum many-body systems. In this work, we propose \texttt{SineKAN}, a NQS \textit{ansatz} based on Kolmogorov-Arnold…

We develop a randomized Newton's method for solving differential equations, based on a fully connected neural network discretization. In particular, the randomized Newton's method randomly chooses equations from the overdetermined nonlinear…

Convolutional Neural Network (CNN) is a popular model in computer vision and has the advantage of making good use of the correlation information of data. However, CNN is challenging to learn efficiently if the given dimension of data or…

The training of neural networks (NNs) is a computationally intensive task requiring significant time and resources. This paper presents a novel approach to NN training using Adiabatic Quantum Computing (AQC), a paradigm that leverages the…

Quantum computing promises to provide machine learning with computational advantages. However, noisy intermediate-scale quantum (NISQ) devices pose engineering challenges to realizing quantum machine learning (QML) advantages. Recently, a…

Gradient descent methods have long been the de facto standard for training deep neural networks. Millions of training samples are fed into models with billions of parameters, which are slowly updated over hundreds of epochs. Recently, it's…

Solving the Schr\"{o}dinger equation for interacting many-body quantum systems faces computational challenges due to exponential scaling with system size. This complexity limits the study of important phenomena in materials science and…

We introduce a new class of deep neural networks (DNNs) with multilayered tree-like architectures. The architectures are codified using numbers from the ring of integers of non-Archimdean local fields. These rings have a natural…

Motivated by the geometric advantages of quaternions in representing rotations and postures, we propose a quaternion-valued supervised learning Hopfield-structured neural network (QSHNN) with a fully connected structure inspired by the…

Quantum neuromorphic computing (QNC) is a sub-field of quantum machine learning (QML) that capitalizes on inherent system dynamics. As a result, QNC can run on contemporary, noisy quantum hardware and is poised to realize challenging…

Machine-learning-based variational Monte Carlo simulations are a promising approach for targeting quantum many-body ground states, especially in two dimensions and in cases where the ground state is known to have a non-trivial sign…

In this work we approach the Schr\"odinger equation in quantum wells with arbitrary potentials, using the machine learning technique. Two neural networks with different architectures are proposed and trained using a set of potentials,…

We advance our approach of analyzing the dynamics of interacting complex systems with the nonlinear dynamics of interacting nonlinear elements. We replace the widely used lattice-like connection topology of cellular neural networks (CNN) by…