Physics-constrained 3D Convolutional Neural Networks for Electrodynamics

• URL: http://arxiv.org/abs/2301.13715v1
• Date: Tue, 31 Jan 2023 15:51:28 GMT
• Title: Physics-constrained 3D Convolutional Neural Networks for Electrodynamics
• Authors: Alexander Scheinker and Reeju Pokharel
• Abstract summary: We create a 3D convolutional PCNN to map time-varying current and charge densities J(r,t) and p(r,t) to vector and scalar potentials A(r,t) and V(r,t) We generate electromagnetic fields according to Maxwell's equations: B=curl(A), E=-div(V)-dA/dt.
• Score: 77.34726150561087
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present a physics-constrained neural network (PCNN) approach to solving Maxwell's equations for the electromagnetic fields of intense relativistic charged particle beams. We create a 3D convolutional PCNN to map time-varying current and charge densities J(r,t) and p(r,t) to vector and scalar potentials A(r,t) and V(r,t) from which we generate electromagnetic fields according to Maxwell's equations: B=curl(A), E=-div(V)-dA/dt. Our PCNNs satisfy hard constraints, such as div(B)=0, by construction. Soft constraints push A and V towards satisfying the Lorenz gauge.

Related papers

• Physics-informed neural networks viewpoint for solving the Dyson-Schwinger equations of quantum electrodynamics [0.0]
  We employ physics-informed neural networks to solve fundamental Dyson-Schwinger integral equations in quantum electrodynamics. Our approach uses neural networks to approximate the fermion wave function renormalization, dynamical mass function, and photon propagator.
  arXiv  Detail & Related papers  (2024-11-04T15:36:17Z)
• Constructing Berry-Maxwell equations with Lorentz invariance and Gauss' law of Weyl monopoles in 4D energy-momentum space [0.0]
  We present the construction of a reciprocal electromagnetic field by extending the Berry curvatures into 4D energy-momentum space. We find that the physical reality of this reciprocal electromagnetic field is rooted in the fundamental principles of special relativity and Gauss's law of Weyl monopoles.
  arXiv  Detail & Related papers  (2023-07-30T05:37:50Z)
• Speed Limits for Deep Learning [67.69149326107103]
  Recent advancement in thermodynamics allows bounding the speed at which one can go from the initial weight distribution to the final distribution of the fully trained network. We provide analytical expressions for these speed limits for linear and linearizable neural networks. Remarkably, given some plausible scaling assumptions on the NTK spectra and spectral decomposition of the labels -- learning is optimal in a scaling sense.
  arXiv  Detail & Related papers  (2023-07-27T06:59:46Z)
• Predicting Angular-Momentum Waves Based on Yang-Mills Equations [0.0]
  Yang-Mills (YM) theory incorporates Maxwell's equations unifying electromagnetism. The angular-momentum waves are hopefully realized in the experiments through the oscillations of spin angular momentum.
  arXiv  Detail & Related papers  (2023-04-25T07:50:20Z)
• Physics Informed RNN-DCT Networks for Time-Dependent Partial Differential Equations [62.81701992551728]
  We present a physics-informed framework for solving time-dependent partial differential equations. Our model utilizes discrete cosine transforms to encode spatial and recurrent neural networks. We show experimental results on the Taylor-Green vortex solution to the Navier-Stokes equations.
  arXiv  Detail & Related papers  (2022-02-24T20:46:52Z)
• Ab-Initio Potential Energy Surfaces by Pairing GNNs with Neural Wave Functions [2.61072980439312]
  In this work, we combine a Graph Neural Network (GNN) with a neural wave function to simultaneously solve the Schr"odinger equation for multiple geometries via VMC. Compared to existing state-of-the-art networks, our Potential Energy Surface Network (PESNet) speeds up training for multiple geometries by up to 40 times while matching or surpassing their accuracy.
  arXiv  Detail & Related papers  (2021-10-11T07:58:31Z)
• Simultaneous boundary shape estimation and velocity field de-noising in Magnetic Resonance Velocimetry using Physics-informed Neural Networks [70.7321040534471]
  Magnetic resonance velocimetry (MRV) is a non-invasive technique widely used in medicine and engineering to measure the velocity field of a fluid. Previous studies have required the shape of the boundary (for example, a blood vessel) to be known a priori. We present a physics-informed neural network that instead uses the noisy MRV data alone to infer the most likely boundary shape and de-noised velocity field.
  arXiv  Detail & Related papers  (2021-07-16T12:56:09Z)
• Deep learning in physics: a study of dielectric quasi-cubic particles in a uniform electric field [4.947248396489835]
  We show how an a priori knowledge can be incorporated into neural networks to achieve efficient learning. We study how the electric potential inside and outside a quasi-cubic particle evolves through a sequence of shapes from a sphere to a cube. The present work's objective is two-fold, first to show how an a priori knowledge can be incorporated into neural networks to achieve efficient learning.
  arXiv  Detail & Related papers  (2021-05-11T10:40:03Z)
• Conditional physics informed neural networks [85.48030573849712]
  We introduce conditional PINNs (physics informed neural networks) for estimating the solution of classes of eigenvalue problems. We show that a single deep neural network can learn the solution of partial differential equations for an entire class of problems.
  arXiv  Detail & Related papers  (2021-04-06T18:29:14Z)
• General quantum-mechanical solution for twisted electrons in a uniform magnetic field [68.8204255655161]
  A theory of twisted (and other structured) paraxial electrons in a uniform magnetic field is developed. The observable effect of a different behavior of relativistic Laguerre-Gauss beams with opposite directions of the orbital angular momentum penetrating from the free space into a magnetic field is predicted.
  arXiv  Detail & Related papers  (2020-05-13T16:35:10Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.