Research

Our research focuses on computational electromagnetic imaging (CEMI). We use electromagnetic waves to detect the unknown real world by constructing highly efficient mathematical models to simulate wave propagation and developing advanced inverse algorithms to reliably and rapidly reconstruct images from recorded electromagnetic signals. Our primary areas of study heavily rely on numerical computation, optimization algorithms, probability and statistics, antenna array theory, machine learning, and geophysical exploration methods.

Our current research initiatives at CEMI are concentrated on several cutting-edge thrusts:

The development of sophisticated forward and inverse models adapting to complex electromagnetic scattering scenarios.
The deep fusion of physics-based models of electromagnetic scattering with artificial neural networks.
The optimization of antenna array layout in electromagnetic inversion problems.
The application of state-of-the-art technologies to subsurface imaging and the exploration of deep Earth resources.

Electromagnetic Scattering And Inverse Scattering in Complex Environments

Electromagnetic scattering refers to the physical process in which an incident wave interacts with specific targets immersed inside an ambient medium, leading to changes of the wave's propagation direction, amplitude, phase, and polarization, as recorded by sensors. Inverse scattering, typically characterized by purely mathematical models, is the reverse process used to retrieve the target parameters from the sensor data. Both electromagnetic scattering and inverse scattering have extensive applications in the design of artificial materials, microwave imaging, subsurface detection, geophysical exploration, etc.

The real world is complicated. The electromagnetic scattering and inverse scattering usually occur in an environment filled with diverse media and multiple targets. On the one hand, the ambient medium is not necessarily homogeneous or isotropic. For example, in near-surface electromagnetic detection, the ambient medium is frequently modeled as planarly stratified. Additionally, in certain contexts, irregular topography can substantially influence scattered electromagnetic field data, necessitating its inclusion in the stratification model. In space exploration using radio waves, the ionosphere is considered a spherically stratified and anisotropic medium due to gravitational and geomagnetic influences. On the other hand, the targets immersed inside the ambient medium that scatter the incident wave often possess complex shapes and also exhibit notable inhomogeneity and anisotropy. For example, anisotropy at the subwavelength scale and macroscopic periodicity are commonly utilized in the design of artificial materials to manipulate electromagnetic wave propagation through and reflection from certain targets. In light of these considerations, we are pursuing the following research directions:

Electromagnetic Full-Wave Inversion Based on Physics-Driven Artificial Neural Networks

Electromagnetic full-wave inversion essentially maps the measured field dataset to the scatterer model parameter set. However, the inherent nonlinear relationship between the field data and model parameters necessitates iterative processes during inversion, leading to significant computational demands. The use of artificial neural networks can significantly reduce the computational costs by learning and storing the partial or complete nonlinear relationship between the field data and scatterer model parameters during the offline training phase, thus enabling instantaneous inversion during the online prediction phase. Typically, the neural network is trained using the big data from the field data space, model parameter space, or mapping space. As a result, the neural network operates as a purely data-driven black box, ignoring the domain knowledge of electromagnetic scattering hidden behind the training data, which complicates its interpretability and predictability.

A physics-driven artificial neural network incorporates established domain knowledge into its architecture or training process. This incorporation not only enhances the network's interpretability and predictability but also reduces the amount of training data and associated costs. For example, Green's functions, which are explicitly known in the integral equations that describe electromagnetic scattering, can be directly embedded into the network. This embedding not only makes the network structure more consistent with the scattering physical mechanism but also avoids redundant learning during training. Utilizing the differential operators of a neural network to represent the differential relationship between two physical variables in the Helmholtz equation is equivalent to mandatorily imposing known prior information in the training. Regularizing the network’s loss function with known scattering equations, such as integral equations or the Helmholtz equation, can expedite training convergence and enhance the network's adaptability. In light of these considerations, we are pursuing the following research directions:

Optimizing Antenna Array Layout for Optimized Inversion Performance

The configuration of a transceiver array is widely acknowledged as a crucial factor affecting the outcomes of electromagnetic tomography. It is well-established that lateral resolution is significantly influenced by the array aperture size, while radial resolution is primarily determined by the signal bandwidth. However, other factors, such as antenna polarization, radiation pattern, and interaction with the ambient medium, also play substantial roles in the reconstruction of unknown targets. Therefore, it is essential to explore the optimal antenna array layout to achieve maximum reconstruction resolution in specific electromagnetic detection scenarios.

Within the framework of integral equations and using Born approximation for weak scattering, a linear correlation is established between the Fourier spectra of the scattered electromagnetic fields measured at the receiver array and the reconstructable spectra of the unknown targets. When the array aperture size is reduced, a "lowpass" effect occurs in the lateral direction of the scatterer reconstructable spectra. In contrast, the radial direction of the reconstructable spectra exhibits complex variations, often showing "bandpass," "bandstop," or even "allpass" characteristics as the array aperture size diminishes. This complexity stems from the antenna radiation coupling with the background layer interface or the mutual coupling between two orthogonal directions in 3-D electromagnetic scattering. These investigations are limited to ideal electromagnetic inversion scenarios. In practical electromagnetic detection contexts, the ambient medium may have rough surfaces or display inhomogeneity, and the unknown targets may present high dielectric contrasts relative to the ambient medium. Such conditions can disrupt the linear correlation between the scattered field spectra and the scatterer reconstructable spectra. Additionally, traditional Green's functions for infinitesimal dipoles are not applicable to practical antennas, such as Vivaldi or horn antennas, which may also interfere with the linear correlation. In light of these challenges, we are pursuing the following research directions:

Subsurface Electromagnetic Imaging And Deep Earth Resource Exploration

Electromagnetic wave propagation displays unique characteristics across different frequency ranges. In the high-frequency band, where the wavelength is considerably smaller than the relevant scale, the electromagnetic field exhibits pronounced oscillations, highlighting wave phenomena. In these situations, targets can significantly alter the wave's direction, polarization, amplitude, and phase through mechanisms such as reflection, penetration, diffraction, interference, and scattering. Subsurface electromagnetic detection utilizes these changes in wave parameters to infer target characteristics. For example, reverse time migration creates target images by correlating incident and reflected waves at the temporal point corresponding to the target's spatial position. The linear sampling method generates subsurface target images by converting near-field electromagnetic data, recorded at the receiver array, into far-field spherically symmetric waves emitted by a hypothetical focal source within the imaging domain. A more rigorous approach, full-wave inversion, can simultaneously derive subsurface target images and dielectric parameters by strictly solving the electromagnetic scattering equations.

In the low-frequency band, where the wavelength far exceeds the scale of interest, the system's behavior changes significantly. The electromagnetic field exhibits a distinct diffusive phenomenon. Under these conditions, the skin depth increases significantly, and the electromagnetic field is often used to explore anomalies, such as metallic orebodies, buried in the deep-Earth region. However, due to the loss of the wave property and the weak variations in field amplitude and phase caused by these anomalies, conventional imaging techniques, like reverse time migration and linear sampling, become ineffective. As a result, the distribution of the underground resistivity is typically retrieved through full-wave inversion, based on either an integral-equation forward solver or a differential-equation forward solver with absorbing boundary conditions.