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

It is well-known that the configuration of a transceiver array directly influences the results of electromagnetic tomography. The common sense is that the lateral resolution heavily depends on the array aperture size while the radial one is mainly determined by the signal bandwidth. However, other factors such as antenna polarization, its radiation diagram, and coupling with the ambient medium also have non-negligible effects on the reconstruction of unknown targets. Therefore, it is of great importance to explore the most optimized antenna array layout to achieve the maximum reconstruction resolution in a certain electromagnetic detection scenario.

In the framework of integral equations, with Born approximation for weak scattering, the Fourier spectra of the scattered electromagnetic fields sampled at the receiver array and the reconstructable spectra of the unknown targets are linearly correlated. Reducing the array aperture size results in the “lowpass” phenomenon of the scatterer reconstructable spectra in the lateral direction. By contrast, in the radial direction, the variations of the reconstructable spectra are complicated. They usually show “bandpass”, “bandstop” or even “allpass” with the decrease of the array aperture size due to the antenna radiation coupling with the background layer interface or the mutual coupling between two orthogonal directions in the 3-D electromagnetic scattering. These studies are only for ideal electromagnetic inversion. In a practical electromagnetic detection scenario, the ambient medium may have rough surfaces or even show inhomogeneity and the unknown targets can have high dielectric contrasts with respect to the ambient medium. They will directly lead to the failure of the linear correlation between the scattered field spectra and the scatterer reconstructable spectra. Moreover, the traditional Green’s functions for infinitesimal dipoles are invalid for practical antennas, e.g. Vivaldi or horn ones, which also may disrupt the linear correlation. Regarding these issues, we are working on following research directions:

Subsurface Electromagnetic Imaging And Deep Earth Resource Exploration

Electromagnetic wave propagation has obviously different characteristics in different frequency regimes. In the high-frequency band, when the wavelength is much less than the concerned scale, the electromagnetic field shows high oscillation, and thus, the wave phenomenon dominates. In this situation, the targets can dramatically alter the wave direction, polarization, amplitude, phase, etc. via reflection, penetration, diffraction, interference, scattering, etc. The subsurface electromagnetic detection utilizes these wave parameter changes to infer the target parameters. For example, the reverse time migration obtains the target images by correlating the incident wave and the reflected wave in the timestamp of the target space position. The linear sampling method obtains the subsurface target images by converting the near-field electromagnetic field data recorded at the receiver array into the far-field spherically symmetric wave radiated by the fictitious focal source in the imaging domain. A more rigorous method, the full-wave inversion, can simultaneously obtain the subsurface target images and dielectric parameters by strictly solving the electromagnetic scattering equations.

In the low-frequency band, when the wavelength is much larger than the concerned scale, it is a completely different story. The electromagnetic field exhibits an obvious diffusive phenomenon. In this situation, the skin depth becomes large and the electromagnetic field is always used to explore the anomalies e.g. metallic orebodies, buried in the deep Earth region. Meanwhile, due to the loss of the wave property and the weak changes of the field amplitude and phase caused by the anomalies, ordinary imaging methods such as reverse time migration and linear sampling fail. The distribution of the underground resistivity is usually retrieved by full-wave inversion based on either the integral-equation forward solver or the differential-equation forward solver with absorbing boundary conditions.