mlsanityData to 14 Oct 2026

Physics-constrained 3D Convolutional Neural Networks for Electrodynamics

arXiv 2301.13715 ↗First posted 31 Jan 2023physics.acc-ph stat.MLcited by 3

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Abstract (arXiv)

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.

Key facts. Cited by 3 papers in the map (data through 14 Oct 2026). Builds on 9 of its 68 references that are in the map. First posted on arXiv 31 Jan 2023.

Builds on

9 of 68 references.

References · 9

  1. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 2,018
  2. 2021Learning the solution operator of parametric partial differential equations with physics-informed DeepOnetscited by 540
  3. 2022On the influence of over-parameterization in manifold based surrogates and deep neural operatorscited by 29
  4. 2021Metasurface-Enabled On-Chip Multiplexed Diffractive Neural Networks in the Visiblecited by 18
  5. 2020Adaptive 3D convolutional neural network-based reconstruction method for 3D coherent diffraction imagingcited by 8
  6. 2020Physics-Based Deep Neural Networks for Beam Dynamics in Charged Particle Acceleratorscited by 7
  7. 2021High-fidelity Prediction of Megapixel Longitudinal Phase-space Images of Electron Beams using Encoder-Decoder Neural Networkscited by 7
  8. 2021Adaptive Machine Learning for Time-Varying Systems: Low Dimensional Latent Space Tuningcited by 3
  9. 2022Mixed Diagnostics for Longitudinal Properties of Electron Bunches in a Free-Electron Lasercited by 1

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 1; 2025: 0; 2026: 2.

3 papers.

  1. 2024A conditional latent autoregressive recurrent model for generation and forecasting of beam dynamics in particle acceleratorscited by 8
  2. 2026Bidirectional Autoregressive Latent Diffusion for Forward and Inverse Magnetohydrodynamicscited by 1
  3. 2026Fast Reconstruction of Exact Maxwell Dynamics from Sparse Datacited by 0