3-D Steady Heat Conduction Solver via Deep Learning
Authors: Yinpeng Wang; Jianmei Zhou; Qiang Ren; Yaoyao Li; Donglin Su
Conventional numerical heat conduction solvers are exceedingly computationally expensive and memory demanding. Recent advances in deep learning have witnessed its extensive application in computational physics field. Compared to traditional methods, deep learning framework emerges superior computational efficiency, providing a substitution for speeding up the calculation. In this paper, we propose an innovate deep learning framework to predict the 3D temperature field in a cubic region filled with random objects of various geometries and materials. The framework is capable of resolving both passive and active heat conduction problems. After being fully trained, it can achieve similar precision to the finite element method (FEM), while the calculation speed is accelerated by two orders of magnitude. Furthermore, the deep learning model has demonstrated robust generalization ability in predicting the temperature distribution of the cases with real-world objects not existing in the data set. We believe that the framework paves the way for solving complex heat conduction problems in engineering, as well as inverse problems in the future.
Space-time Adaptive Processing Concept for Calculation Speed Improvement In Multi-Region/FDTD Method
Authors: Kei Asahi ; Takuji Arima ; Akihisa Uematsu ; Toshiyuki Nishibori ; Toru Uno
Nowadays, the demand for large-scale electromagnetic simulations has been generally increasing, and the FDTD method is one of the effective electromagnetic simulation methods. The MR (Multi-Region) / FDTD method allows the calculation of free space between the antenna and the objects to be omitted from the simulation model. This method utilizes the equivalence theorem to connect the multiple regions. One of the limitations of the MR/FDTD method is a high time complexity when it involves large-scale simulations. Thus, in this communication, we propose a space-time adaptive processing concept to optimize the computation time of the MR/FDTD method. In the proposed method, a quadtree structure is utilized for adaptive processing. We confirmed the effectiveness of the proposed method using numerical simulations.
Reverse-Time Migration by Combining Laplacian Filtering with Wavefield Decomposition for High-Resolution Subsurface Imaging
Authors: Xinrong Mao ; Yuanguo Zhou ; Fei Lei ; Lushun Zhao ; Kirill Zeyde
Reverse-time migration (RTM) is considered to be one of the most accurate migration methods, especially for imaging geologically complex structures. Howeverthe conventional RTM using cross-correlation imaging condition is subject to strong migration artifacts. Recent researches on electromagnetic wavefield decomposition exhibit that the method can greatly suppresses the internal reflection noise, however, it is still subject to residual noise. To further eliminate the low-frequency noise to obtain high-resolution subsurface image, a novel electromagnetic imaging scheme by combining a Laplacian filtering with wavefield decomposition is presented, and the pseudospectral time-domain (PSTD) method is introduced to solve the time-dependent partial differential equations efficiently. In this work, we apply the Laplacian filtering on each wavefield snapshot in space domain to sharpen the field distribution. The filtered wavefields are further decomposed into downgoing and upgoing components for final imaging. Numerical experiments show that the proposed method balances the amplitudes of reflectors, and exhibits higher resolution compared to the conventional RTM.
Potential-Based Time Domain Integral Equations Free from Interior Resonances
Authors: Thomas Edgar Roth ; Weng Cho Chew
Potential-based integral equations are being explored to develop numerical methods that avoid low-frequency breakdown issues so that they can analyze multiscale structures that are becoming increasingly important in electromagnetic engineering. This work continues the development of potential-based time domain integral equations by presenting three new formulations in the Lorenz gauge that do not support interior resonances. These modifications allow the methods to be applied to deeply multiscale structures of practical importance that contain significantly subwavelength- and wavelength-sized geometric features. Appropriate marching-on-in-time discretization schemes are developed for each formulation that fully conform to the temporal Sobolev space properties of the integral equations. It is shown that following this approach leads to a discrete system with improved stability properties. Further, it is demonstrated that this new system can produce accurate results over broad bandwidths and analyze deeply multiscale systems that previous potential-based time domain integral equations could not.
CNN for Compressibility to Permittivity Mapping for Combined Ultrasound-Microwave Breast Imaging
Authors: Pedram Mojabi ; Max Hughson ; Vahab Khoshdel ; Ian Jeffrey ; Joe Lovetri
Combined ultrasound-microwave breast imaging requires a mechanism to guide one imaging modality using the other. To this end, a convolutional neural network (CNN) is proposed for the mapping of ultrasound property images to dielectric property images for combined ultrasound-microwave breast imaging applications. In this approach, higher resolution ultrasound images are obtained by inverting the ultrasound scattered pressure data using a linearized inverse scattering algorithm. The reconstructed Born-based ultrasound compressibility images are then used to predict dielectric images for the same breast phantoms. These predicted dielectric images can then be used to guide microwave imaging reconstruction to achieve higher accuracy images. To this end, a CNN is trained based on the input of the reconstructed quantitative ultrasonic compressibility and the output of the true quantitative dielectric properties corresponding to the same numerical phantom. Several numerical MRI-derived breast phantoms are used to train and test this CNN. The predicted dielectric properties are tested using different numerical MRI-derived breast phantoms and the predicted profiles show promising results. The predicted dielectric properties are also used as the initial guess prior for the microwave inversion algorithm which leads to the enhancement of the reconstruction of dielectric properties as compared to the blind microwave inversion.