Related papers: A deep neural network approach to solve the Dirac …
We extend a previously successful discussion of the constrained Schr\"{o}dinger system through the Dirac--Bergmann algorithm to the case of the Dirac field. In order to follow the analogy, first we discuss the classical Dirac field as a…
Exact solutions of the Dirac equation, a system of four partial differential equations, are rare. The vast majority of them are for highly symmetric stationary systems. Moreover, only a handful of solutions for time dependent dynamics…
We propose a neural network-based algorithm for solving forward and inverse problems for partial differential equations in unsupervised fashion. The solution is approximated by a deep neural network which is the minimizer of a cost…
Scientific machine learning has become an increasingly important tool in materials science and engineering. It is particularly well suited to tackle material problems involving many variables or to allow rapid construction of surrogates of…
Quantum theory has been remarkably successful in providing an understanding of physical systems at foundational scales. Solving the Schr\"odinger equation provides full knowledge of all dynamical quantities of the physical system. However…
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,…
The integration of deep neural networks with the Variational Monte Carlo (VMC) method has marked a significant advancement in solving the Schr\"odinger equation. In this work, we enforce spin symmetry in the neural network-based VMC…
This paper deals with an inverse nodal problem for the Dirac differential operator with the discontinuity conditions inside the interval. We obtain a new approach for asymptotic expressions of the solutions and prove that the coefficients…
Variational data assimilation and machine-learning based super-resolution are two alternative approaches to state estimation in turbulent flows. The former is an optimisation problem featuring a time series of coarse observations, the…
We propose a general framework for solving statistical mechanics of systems with finite size. The approach extends the celebrated variational mean-field approaches using autoregressive neural networks, which support direct sampling and…
Physical motion models offer interpretable predictions for the motion of vehicles. However, some model parameters, such as those related to aero- and hydrodynamics, are expensive to measure and are often only roughly approximated reducing…
An approximation method, namely, the Extended Wronskian Determinant Approach, is suggested to study the one-dimensional Dirac equation. An integral equation which can be solved by iterative procedure to find the wave functions is…
Landing an unmanned aerial vehicle (UAV) on a ground marker is an open problem despite the effort of the research community. Previous attempts mostly focused on the analysis of hand-crafted geometric features and the use of external sensors…
Neural network approaches to approximate the ground state of quantum hamiltonians require the numerical solution of a highly nonlinear optimization problem. We introduce a statistical learning approach that makes the optimization trivial by…
Neural algorithmic reasoning aims to capture computations with neural networks by training models to imitate the execution of classical algorithms. While common architectures are expressive enough to contain the correct model in the weight…
We provide an alternative approach to relativistic dynamics based on the Feshbach projection technique. Instead of directly studying the Dirac equation, we derive a two-component equation for the upper spinor. This approach allows one to…
We propose a machine learning method to solve Schrodinger equations for a Hamiltonian that consists of an unperturbed Hamiltonian and a perturbation. We focus on the cases where the unperturbed Hamiltonian can be solved analytically or…
A variation of Dirac equation based on SO(2,1) group is suggested for treating low dimensional systems in the three dimensional x,y,t space. Non-unitary representations are developed in an analogous way to those used in the ordinary Dirac…
This paper introduces a deep learning system based on a quantum neural network for the binary classification of points of a specific geometric pattern (Two-Moons Classification problem) on a plane. We believe that the use of hybrid deep…
We develop a novel deep learning method for uncertainty quantification in stochastic partial differential equations based on Bayesian neural network (BNN) and Hamiltonian Monte Carlo (HMC). A BNN efficiently learns the posterior…