Electromagnetic field reconstruction is crucial in many applications, including antenna diagnostics, electromagnetic interference analysis, and system modeling. This paper presents a deep learning-based approach for Far-Field to Near-Field (FF-NF) transformation using Convolutional Neural Networks (CNNs). The goal is to reconstruct near-field distributions from the far-field data of an antenna without relying on explicit analytical transformations. The CNNs are trained on paired far-field and near-field data and evaluated using mean squared error (MSE). The best model achieves a training error of 0.0199 and a test error of 0.3898. Moreover, visual comparisons between the predicted and true near-field distributions demonstrate the model's effectiveness in capturing complex electromagnetic field behavior, highlighting the potential of deep learning in electromagnetic field reconstruction.

We propose a 3D U-Net model to predict the spatial distribution of electromagnetic fields inside a radio-frequency (RF) coil with a subject present, using the phase, amplitude, and position of the coils, along with the density, permittivity, and conductivity of the surrounding medium as inputs. To improve accuracy, we introduce a physics-augmented variant, U-Net Phys, which incorporates Gauss's law of magnetism into the loss function using finite differences. We train our models on electromagnetic field simulations from CST Studio Suite for an eight-channel dipole array RF coil at 7T MRI. Experimental results show that U-Net Phys significantly outperforms the standard U-Net, particularly in predicting fields within the subject, demonstrating the advantage of integrating physical constraints into deep learning-based field prediction.

Cryo-electron microscopy (cryo-EM) is an imaging modality that provides unique insights into the dynamics of proteins and other building blocks of life. The algorithmic challenge of jointly estimating the poses, 3D structure, and conformational heterogeneity of a biomolecule from millions of noisy and randomly oriented 2D projections in a computationally efficient manner, however, remains unsolved. Our method, cryoFIRE, performs ab initio heterogeneous reconstruction with unknown poses in an amortized framework, thereby avoiding the computationally expensive step of pose search while enabling the analysis of conformational heterogeneity. Poses and conformation are jointly estimated by an encoder while a physics-based decoder aggregates the images into an implicit neural representation of the conformational space. We show that our method can provide one order of magnitude speedup on datasets containing millions of images without any loss of accuracy. We validate that the joint estimation of poses and conformations can be amortized over the size of the dataset. For the first time, we prove that an amortized method can extract interpretable dynamic information from experimental datasets.

Electromagnetic (EM) imaging is widely applied in sensing for security, biomedicine, geophysics, and various industries. It is an ill-posed inverse problem whose solution is usually computationally expensive. Machine learning (ML) techniques and especially deep learning (DL) show potential in fast and accurate imaging. However, the high performance of purely data-driven approaches relies on constructing a training set that is statistically consistent with practical scenarios, which is often not possible in EM imaging tasks. Consequently, generalizability becomes a major concern. On the other hand, physical principles underlie EM phenomena and provide baselines for current imaging techniques. To benefit from prior knowledge in big data and the theoretical constraint of physical laws, physics embedded ML methods for EM imaging have become the focus of a large body of recent work. This article surveys various schemes to incorporate physics in learning-based EM imaging. We first introduce background on EM imaging and basic formulations of the inverse problem. We then focus on three types of strategies combining physics and ML for linear and nonlinear imaging and discuss their advantages and limitations. Finally, we conclude with open challenges and possible ways forward in this fast-developing field. Our aim is to facilitate the study of intelligent EM imaging methods that will be efficient, interpretable and controllable.