3D Magnetic Field Reconstruction and Mapping with Physics-Informed Neural Networks

• URL: http://arxiv.org/abs/2605.25640v1
• Date: Mon, 25 May 2026 09:42:27 GMT
• Title: 3D Magnetic Field Reconstruction and Mapping with Physics-Informed Neural Networks
• Abstract summary: This study proposes an advanced Physics-Informed Neural Network framework for high-precision 3D magnetic field mapping.<n>The proposed PINN integrates Maxwell's equations directly into the loss function, enforcing divergence-free and curl-free conditions.<n> validation using simulated data achieves a reconstruction accuracy of $10-4$, a tenfold improvement over existing PINN benchmarks.
• Score: 11.823793229327954
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Accurate reconstruction of magnetic fields in inaccessible regions is vital for many high-precision experiments in physics. Traditional methods, such as spherical harmonic expansion, often suffer from truncation errors that limit their precision. This study proposes an advanced Physics-Informed Neural Network (PINN) framework for high-precision 3D magnetic field mapping. Unlike conventional data-driven models, the proposed PINN integrates Maxwell's equations directly into the loss function, enforcing divergence-free and curl-free conditions across the entire domain. A key innovation is the inclusion of explicit physics-residual losses at measurement locations, ensuring rigorous physical consistency beyond random collocation sampling. Validation using simulated data achieves a reconstruction accuracy of $10^{-4}$, a tenfold improvement over existing PINN benchmarks. Furthermore, experimental validation using a custom coil assembly demonstrates robust reconstruction with sub-percent relative accuracy, reaching the $10^{-3}$ level under ambient conditions. This AI-driven methodology provides a robust, high-precision solution for field monitoring and measurement in complex experimental environments where direct sensor placement is restricted.

Related papers

• Neural Field Thermal Tomography: A Differentiable Physics Framework for Non-Destructive Evaluation [3.697746606429496]
  We propose a differentiable physics framework for the quantitative 3D reconstruction of material properties from transient surface temperature measurements.<n>NeFTY parameterizes the 3D diffusivity field as a continuous neural field optimized through a rigorous numerical solver.<n>Our approach enforces thermodynamic laws as hard constraints while maintaining the memory efficiency required for high-resolution 3D tomography.
  arXiv  Detail & Related papers  (2026-03-11T17:59:42Z)
• Surrogate models for nuclear fusion with parametric Shallow Recurrent Decoder Networks: applications to magnetohydrodynamics [0.0]
  This work investigates a data-driven framework for MHD state reconstruction.<n>SHRED is a neural network architecture designed to recover the full-temporal state from sparse time-series measurements.<n>Results show that SHRED accurately reconstructs the full MHD state even for magnetic field intensities not included in the training set.
  arXiv  Detail & Related papers  (2026-03-11T11:43:39Z)
• Physics Aware Neural Networks: Denoising for Magnetic Navigation [3.624059602945058]
  Airborne systems face a key challenge in extracting geomagnetic field data: the aircraft itself induces magnetic noise.<n>We propose a framework based on two physics-based constraints: divergence-free vector field and E(3)equivariance.<n>Experiments show that embedding these constraints significantly improves predictive accuracy and physical plausibility, outperforming classical deep learning approaches.
  arXiv  Detail & Related papers  (2026-02-14T09:23:57Z)
• Physics-Informed Neural Networks with Architectural Physics Embedding for Large-Scale Wave Field Reconstruction [8.953088273349499]
  Physics-informed neural networks (PINNs) integrate physical principles into machine learning models.<n>PINNs embed physical principles only in loss functions, leading to slow convergence, optimization instability, and spectral bias.<n>This work introduces architecture physics embedded (PE)-PINN, which integrates additional physical guidance directly into the neural network architecture.
  arXiv  Detail & Related papers  (2026-02-13T04:28:23Z)
• Deep Deterministic Nonlinear ICA via Total Correlation Minimization with Matrix-Based Entropy Functional [41.05541240448253]
  Blind source separation, particularly through independent component analysis (ICA), is widely utilized across various signal processing domains.<n>We present deep deterministic nonlinear independent component analysis (DDICA), a novel deep neural network-based framework designed to address these limitations.<n>We validated DDICA across a range of applications, including simulated signal mixtures, hyperspectral image unmixing, modeling of primary visual receptive fields, and resting-state functional magnetic resonance imaging (fMRI) data analysis.
  arXiv  Detail & Related papers  (2025-12-31T19:44:19Z)
• NeuralSSD: A Neural Solver for Signed Distance Surface Reconstruction [34.55776349064238]
  Implicit method is preferred due to its ability to accurately represent shapes and its robustness in handling topological changes.<n>We propose a novel energy equation that balances the reliability of point cloud information.<n>We introduce a new convolutional network that learns three-dimensional information to achieve superior optimization results.
  arXiv  Detail & Related papers  (2025-11-18T09:20:15Z)
• FNIN: A Fourier Neural Operator-based Numerical Integration Network for Surface-form-gradients [31.570033378168574]
  Surface-from-gradients (SfG) aims to recover a three-dimensional (3D) surface from its gradients.<n>Traditional methods encounter challenges in achieving high accuracy and handling high-resolution inputs.<n>We propose a Fourier neural operator-based Numerical Integration Network (FNIN) within a two-stage optimization framework.
  arXiv  Detail & Related papers  (2025-01-21T04:11:04Z)
• Deterministic and statistical calibration of constitutive models from full-field data with parametric physics-informed neural networks [36.136619420474766]
  parametric physics-informed neural networks (PINNs) for model calibration from full-field displacement data are investigated.<n>Due to the fast evaluation of PINNs, calibration can be performed in near real-time.
  arXiv  Detail & Related papers  (2024-05-28T16:02:11Z)
• Physics-informed neural networks for gravity currents reconstruction from limited data [0.0]
  The present work investigates the use of physics-informed neural networks (PINNs) for the 3D reconstruction of unsteady gravity currents from limited data. In the PINN context, the flow fields are reconstructed by training a neural network whose objective function penalizes the mismatch between the network predictions and the observed data.
  arXiv  Detail & Related papers  (2022-11-03T11:27:29Z)
• Physics-enhanced deep surrogates for partial differential equations [30.731686639510517]
  We present a "physics-enhanced deep-surrogate" ("PEDS") approach towards developing fast surrogate models for complex physical systems. Specifically, a combination of a low-fidelity, explainable physics simulator and a neural network generator is proposed, which is trained end-to-end to globally match the output of an expensive high-fidelity numerical solver.
  arXiv  Detail & Related papers  (2021-11-10T18:43:18Z)
• 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)

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.