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With the evolution of numerical methods, we are now aiming at not only qualitative understanding but also quantitative prediction and design of quantum many-body phenomena. As a novel numerical approach, machine learning techniques have…
Analyzing quantum many-body problems and elucidating the entangled structure of quantum states is a significant challenge common to a wide range of fields. Recently, a novel approach using machine learning was introduced to address this…
This study presents a general alternative scheme of the procedure and necessary conditions for solving the $n$-body problem. The presented solution is not a solution of the classical problem, where the initial conditions of positions and…
Artificial neural networks (ANNs) have been broadly utilized to analyze various data and solve different domain problems. However, neural networks (NNs) have been considered a black box operation for years because their underlying…
Euler's three-body problem is the problem of solving for the motion of a particle moving in a Newtonian potential generated by two point sources fixed in space. This system is integrable in the Liouville sense. We consider the Euler problem…
We investigate the use of Physics-Informed Neural Networks (PINNs) for solving the wave equation. Whilst PINNs have been successfully applied across many physical systems, the wave equation presents unique challenges due to the multi-scale,…
In this paper, we introduce a numerical method based on Artificial Neural Networks (ANNs) for the analysis of black hole solutions to the Einstein-axion-dilaton system in a high dimensional parabolic class. Leveraging a profile root-finding…
Current Deep Learning approaches have been very successful using convolutional neural networks (CNN) trained on large graphical processing units (GPU)-based computers. Three limitations of this approach are: 1) they are based on a simple…
The nature of abstract reasoning is a matter of debate. Modern artificial neural network (ANN) models, like large language models, demonstrate impressive success when tested on abstract reasoning problems. However, it has been argued that…
Deep Neural Networks (DNNs) which are trained end-to-end have been successfully applied to solve complex problems that we have not been able to solve in past decades. Autonomous driving is one of the most complex problems which is yet to be…
In this paper, we propose a novel deep convolutional neural network (CNN)-based algorithm for solving ill-posed inverse problems. Regularized iterative algorithms have emerged as the standard approach to ill-posed inverse problems in the…
Deep learning has solved a problem that as little as five years ago was thought by many to be intractable - the automatic recognition of patterns in data; and it can do so with accuracy that often surpasses human beings. It has solved…
Since the earliest proposals for artificial neural network (ANN) models of the mind and brain, critics have pointed out key weaknesses in these models compared to human cognitive abilities. Here we review recent work that uses metalearning…
One of the oldest problems in physics is that of calculating the motion of $N$ particles under a specified mutual force: the $N$-body problem. Much is known about this problem if the specified force is non-relativistic gravity, and…
The manpower scheduling problem is a kind of critical combinational optimization problem. Researching solutions to scheduling problems can improve the efficiency of companies, hospitals, and other work units. This paper proposes a new model…
The full three-body problem, on the motion of three celestial bodies under their mutual gravitational attraction, is one of the oldest unsolved problems in classical mechanics. The main difficulty comes from the presence of unstable and…
The Newtonian n-Body Problem is modified assuming positive inertial masses but different sign for the interacting force which is assumed with the possibility of two different signs for the gravitational masses, according to the prescription…
A solvable many-body problem in the plane is exhibited. It is characterized by rotation-invariant Newtonian (``acceleration equal force'') equations of motion, featuring one-body (``external'') and pair (``interparticle'') forces. The…
Human motion modelling is a classical problem at the intersection of graphics and computer vision, with applications spanning human-computer interaction, motion synthesis, and motion prediction for virtual and augmented reality. Following…
While quantum computing provides an exponential advantage in solving system of linear equations, there is little work to solve system of nonlinear equations with quantum computing. We propose quantum Newton's method (QNM) for solving…