Deep learning and Tucker decomposition-based fast simulators for low-frequency electromagnetic analyses - Jia, Xiaofan (Nanyang Technological University, 2024)
Electromagnetic (EM) simulators become indispensable for innovation and design in many engineering disciplines using EM fields and waves. These simulators are mature, yet substantial research is needed to further accelerate them and make them thoroughly useful for analysis and design. For example, for the analyses of biomedical procedures, EM simulators require significant computation time. Medical practitioners and researchers need ultra-fast EM simulators for real-time visualization of the fields and currents induced on the patients/subjects during biomedical procedures. Such visualization helps to better assess the current/field delivery to the targetted regions. Furthermore, for the designs of semiconductor devices and integrated circuits, magneto-quasi-static (MQS) simulators are extensively used for extracting the parameters of the interconnects. During iterative design explorations, designers and engineers need ultra-fast simulators to shorten the design cycle, requiring repetitive parameter extraction. To this end, ultra-fast EM simulators are called for many practical applications today. To fill this gap, this Ph.D. thesis proposes three ultra-fast EM simulators accelerated via non-traditional acceleration techniques, including deep learning and tensor decomposition techniques. These simulators are developed to be used for biomedical analysis as well as inductance extraction of the integrated circuits, as alluded to below. First, a deep learning-accelerated EM simulator, called DeeptDCS, is proposed for (near) real-time visualization of current density induced during transcranial direct current stimulation (tDCS). TDCS is a non-invasive brain stimulation technique used to excite brain regions for therapeutic effects or cognitive enhancement. To rapidly evaluate tDCS-induced current density in near real time, the developed DeeptDCS simulator takes the volume conductor models (VCMs) of head tissues as inputs and outputs the 3-D current density distribution across the entire head. The electrode configurations are also incorporated into VCMs without increasing the number of input channels; this enables the straightforward incorporation of the features of electrodes (e.g., thickness, shape, size, and position) in the training and testing of the proposed simulator. The computation time required by one execution of the proposed simulator DeeptDCS is around milliseconds and at least two orders of magnitude less than that required by one execution of the popular physics-based open-source simulator SimNIBS. Numerical results demonstrate the accuracy, efficiency, and applicability of DeeptDCS for near real-time estimation of current density induced on any provided VCM during tDCS procedures. Second, a deep learning-accelerated inductance extractor, called DeepHenry, is proposed for computing the partial-inductances of the interconnects. DeepHenry takes a physics-based skin depth map and a geometry identifier of the interconnects as inputs and provides the current density distribution on the interconnects as the output. The predicted currents are then used to compute the self-resistances, self-inductances, and mutual-inductances of the interconnects. During the training of the deep learning algorithm in DeepHenry, a specifically designed loss function is used to ensure the accurate modeling of the currents on the structure as well as ports. It is demonstrated that the computation time required by one execution of the proposed DeepHenry is around two and three orders of magnitude less than that required by one execution of the popular physics-based open-source simulator VoxHenry on CPU and GPU, respectively. The accuracy, efficiency, and generalization ability of DeepHenry are demonstrated via partial inductance extraction of the interconnects with and without a ground plane, including straight single interconnects, interconnects with sharp bends, parallel interconnects, and multiple conductor crossover buses. Finally, an EM simulator accelerated by tensor decompositions, particularly interpolative decomposition and Tucker decomposition, called ID Tucker, is proposed for the inductance extraction of voxelized interconnects. In particular, the proposed scheme partitions the systems matrix into blocks and distinguishes the admissible and inadmissible blocks. While interactions between basis functions within inadmissible blocks are accounted for by the conventional fast Fourier transform (FFT) acceleration scheme, the interactions between basis functions within admissible blocks are handled by the ID Tucker acceleration scheme. In specific, ID Tucker is used to compress the admissible blocks after converting them to six-dimensional (6-D) arrays. The admissible block matrix-vector multiplication (MVM) is performed via tensor-vector multiplication (TVM), where the tensor is stored in ID Tucker-compressed format. The proposed ID Tucker-FFT-accelerated EM simulator requires 1-2 order(s) of magnitude less computation time and memory compared to an open-source MQS VoxHenry simulator for the inductance extraction of the parallel straight interconnects and parallel square coils. In conclusion, this PhD thesis proposes three EM simulators accelerated by nontraditional techniques, namely deep learning and tensor decomposition techniques. Such simulators offer orders of magnitude of reduction in the computation time requirements of open-source simulators for low-frequency EM analyses. It is important to note that while the ID Tucker-FFT-accelerated simulator is physics-based and applicable to any configuration and voxelized geometry, deep learning-accelerated simulators are data-driven and restricted to the applications considered during data generation. Having said that, they still show a remarkable generalization capability, as shown in the numerical tests on these simulators.