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Studying physics-informed neural networks (PINNs) for modeling partial differential equations to solve the acoustic wave field has produced promising results for simple geometries in two-dimensional domains. One option is to compute the…
We present a quantum computing formulation to address a challenging problem in the development of probabilistic learning on manifolds (PLoM). It involves solving the spectral problem of the high-dimensional Fokker-Planck (FKP) operator,…
Partial differential equations and variational problems can be solved with physics informed neural networks (PINNs). The unknown field is approximated with neural networks. Minimizing the residuals of the static Maxwell equation at…
In classical physics, there is a basic principle, namely "A particle cannot be located at the position of another one on the same time". Which consequences can be derived if this principle is transferred into quantum physics? For doing…
We introduce physics informed neural networks -- neural networks that are trained to solve supervised learning tasks while respecting any given law of physics described by general nonlinear partial differential equations. In this two part…
Initial value problems -- a system of ordinary differential equations and corresponding initial conditions -- can be used to describe many physical phenomena including those arise in classical mechanics. We have developed a novel approach…
Some recent results concerning a particle confined in a one-dimensional box with moving walls are briefly reviewed. By exploiting the same techniques used for the 1D problem, we investigate the behavior of a quantum particle confined in a…
Over the past years, machine learning has emerged as a powerful computational tool to tackle complex problems over a broad range of scientific disciplines. In particular, artificial neural networks have been successfully deployed to…
We introduce physics informed neural networks -- neural networks that are trained to solve supervised learning tasks while respecting any given law of physics described by general nonlinear partial differential equations. In this second…
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,…
Physics-Informed Neural Networks (PINNs) have emerged as a promising approach for solving partial differential equations (PDEs) by embedding the governing physics into the loss function associated with a deep neural network. In this work, a…
Solving the intricate quantum behavior of interacting particles is key to unlocking the mysteries of condensed matter, but capturing their complex correlations across different scales remains a monumental challenge. We introduce a neural…
Quantum dynamics of a particle confined in a box with time-dependent wall is revisited by considering some unexplored aspects of the problem. In particular, the case of dynamical confinement in a time-dependent box in the presence of purely…
In this thesis, we investigate whether quantum algorithms can be used in the field of machine learning for both long and near term quantum computers. We will first recall the fundamentals of machine learning and quantum computing and then…
We use the discrete approach to solve the Schr\"odinger as well as the Bloch equations for a free particle and the quantum gas of free particles embedded in an infinite quantum well with the finite width. We obtain the expressions of energy…
A classical computer simulating Schrodinger dynamics of a quantum system requires resources which scale exponentially with the size of the system, and is regarded as inefficient for such purposes. However, a quantum computer made up of a…
We propose a physics-informed quantum algorithm to solve nonlinear and multidimensional differential equations (DEs) in a quantum latent space. We suggest a strategy for building quantum models as state overlaps, where exponentially large…
Quantum algorithms are able to solve particular problems exponentially faster than conventional algorithms, when implemented on a quantum computer. However, all demonstrations to date have required already knowing the answer to construct…
This paper proposes a new framework using physics-informed neural networks (PINNs) to simulate complex structural systems that consist of single and double beams based on Euler-Bernoulli and Timoshenko theory, where the double beams are…
Quantum Physics-Informed Neural Networks (QPINNs) integrate quantum computing and machine learning to impose physical biases on the output of a quantum neural network, aiming to either solve or discover differential equations. The approach…