Wei Tang

Bio: Wei Tang is an academic researcher from Tsinghua University. The author has contributed to research in topics: Deep learning & Solver. The author has an hindex of 3, co-authored 3 publications receiving 92 citations.

Study on a Poisson's Equation Solver Based On Deep Learning Technique

Abstract: In this work, we investigated the feasibility of applying deep learning techniques to solve Poisson's equation. A deep convolutional neural network is set up to predict the distribution of electric potential in 2D or 3D cases. With proper training data generated from a finite difference solver, the strong approximation capability of the deep convolutional neural network allows it to make correct prediction given information of the source and distribution of permittivity. With applications of L2 regularization, numerical experiments show that the predication error of 2D cases can reach below 1.5\% and the predication of 3D cases can reach below 3\%, with a significant reduction in CPU time compared with the traditional solver based on finite difference methods.

Study on a Fast Solver for Poisson’s Equation Based on Deep Learning Technique

Abstract: Fast and efficient computational electromagnetic simulation is a long-standing challenge. In this article, we propose a data-driven model to solve Poisson’s equation that leverages the learning capacity of deep learning techniques. A deep convolutional neural network (ConvNet) is trained to predict the electric potential with different excitations and permittivity distribution in 2-D and 3-D models. With a careful design of cost function and proper training data generated from finite-difference solvers, the proposed network enables a reliable simulation with significant speedup and fairly good accuracy. Numerical experiments show that the same ConvNet architecture is effective for both 2-D and 3-D models, and the average relative prediction error of the proposed ConvNet model is less than 3% in both 2-D and 3-D simulations with a significant reduction in computation time compared to the finite-difference solver. This article shows that deep neural networks have a good learning capacity for numerical simulations. This could help us to build some fast solvers for some computational electromagnetic problems.

Study on a Poisson's equation solver based on deep learning technique

Abstract: In this work, we investigated the feasibility of applying deep learning techniques to solve 2D Poisson's equation. A deep convolutional neural network is set up to predict the distribution of electric potential in 2D. With training data generated from a finite difference solver, the strong approximation capability of the deep convolutional neural network allows it to make correct prediction given information of the source and distribution of permittivity. Numerical experiments show that the predication error can reach below one percent, with a significant reduction in CPU time compared with the traditional solver based on finite difference methods.

Digital Twin: Values, Challenges and Enablers From a Modeling Perspective

Abstract: Digital twin can be defined as a virtual representation of a physical asset enabled through data and simulators for real-time prediction, optimization, monitoring, controlling, and improved decision making. Recent advances in computational pipelines, multiphysics solvers, artificial intelligence, big data cybernetics, data processing and management tools bring the promise of digital twins and their impact on society closer to reality. Digital twinning is now an important and emerging trend in many applications. Also referred to as a computational megamodel, device shadow, mirrored system, avatar or a synchronized virtual prototype, there can be no doubt that a digital twin plays a transformative role not only in how we design and operate cyber-physical intelligent systems, but also in how we advance the modularity of multi-disciplinary systems to tackle fundamental barriers not addressed by the current, evolutionary modeling practices. In this work, we review the recent status of methodologies and techniques related to the construction of digital twins mostly from a modeling perspective. Our aim is to provide a detailed coverage of the current challenges and enabling technologies along with recommendations and reflections for various stakeholders.

A review of deep learning approaches for inverse scattering problems (invited review)

Abstract: In recent years, deep learning (DL) is becoming an increasingly important tool for solving inverse scattering problems (ISPs). This paper reviews methods, promises, and pitfalls of deep learning as applied to ISPs. More specifically, we review several state-of-the-art methods of solving ISPs with DL, and we also offer some insights on how to combine neural networks with the knowledge of the underlying physics as well as traditional non-learning techniques. Despite the successes, DL also has its own challenges and limitations in solving ISPs. These fundamental questions are discussed, and possible suitable future research directions and countermeasures will be suggested.

Two-Step Enhanced Deep Learning Approach for Electromagnetic Inverse Scattering Problems

Abstract: In this letter, a new deep learning (DL) approach is proposed to solve the electromagnetic inverse scattering (EMIS) problems. The conventional methods for solving inverse problems face various challenges including strong ill-conditions, high contrast, expensive computation cost, and unavoidable intrinsic nonlinearity. To overcome these issues, we propose a new two-step machine learning based approach. In the first step, a complex-valued deep convolutional neural network is employed to retrieve initial contrasts (permittivities) of dielectric scatterers from measured scattering data. In the second step, the previously obtained contrasts are input into a complex-valued deep residual convolutional neural network to refine the reconstruction of images. Consequently, the EMIS problem can be solved with much higher accuracy even for high-contrast objects. Numerical examples have demonstrated the capability of the newly proposed method with the improved accuracy. The proposed DL approach for EMIS problem serves a new path for realizing real-time quantitative microwave imaging for high-contrast objects.

Deep Learning for Magnetic Field Estimation

Abstract: This paper investigates the feasibility of novel data-driven deep learning (DL) models to predict the solution of Maxwell’s equations for low-frequency electromagnetic (EM) devices. With ground truth (empirical evidence) data being generated from a finite-element analysis solver, a deep convolutional neural network is trained in a supervised manner to learn a mapping for magnetic field distribution for topologies of different complexities of geometry, material, and excitation, including a simple coil, a transformer, and a permanent magnet motor. Preliminary experiments show DL model predictions in close agreement with the ground truth. A probabilistic model is introduced to improve the accuracy and to quantify the uncertainty in the prediction, based on Monte Carlo dropout. This paper establishes a basis for a fast and generalizable data-driven model used in the analysis, design, and optimization of EM devices.