Abstract : In recent years, there is tremendous growth in machine learning and statistical approaches to solve inverse problems involving PDEs. This mini symposium will explore ideas both theoretical and computational to advance understanding of the convergence, consistency, and numerical algorithms to solve PDE based inverse problems. We will focus on inverse problems with applications to imaging including Electrical Impedance Tomography, Diffuse Optical Tomography. The mini symposium is expected to bring experts from theory, computation, and practice to bridge the gap between these areas.
Organizer(s) : Department of Mathematics and Statistics, University of North Carolina at Charlotte, USA
[04498] Train Like a (Var)Pro: Efficient Training of DNNs
Format : Talk at Waseda University
Author(s) :
Elizabeth Newman (Emory University)
Lars Ruthotto (Emory University)
Bart van Bloemen Waanders (Sandia National Laboratories)
Joseph Hart (Sandia National Laboratories)
Abstract : Deep neural networks (DNNs) have excelled as high-dimensional function approximators and are trained by solving a challenging stochastic optimization problem. In this talk, we will make DNN training easier by exploiting separability of common architectures; i.e., linear in the final weights. We will leverage this linearity by eliminating the weights through variable projection. We will demonstrate the efficacy of this approach through numerical examples and will conclude with a discussion of extensions and new applications.
[05369] Machine Learning for Inverse Problems in Electrical Impedance Tomography
Format : Talk at Waseda University
Author(s) :
Hyeuknam Kwon (Yonsei University, Mirae campus)
Abstract : This paper discusses the application of machine learning techniques to solve inverse problems in electric impedance tomography (EIT). EIT is a non-invasive medical imaging technique used to reconstruct the distribution of conductivity within the human body using electrical measurements of surfaces. However, the inverse problem in EIT image reconstruction and its application suffers from various difficulties.The author provides these problems and machine learning techniques to solve them.
[04986] Data-Driven Design of Thin-Film Optical Systems using Deep Active Learning
Format : Talk at Waseda University
Author(s) :
Youngjoon Hong (Sungkyunkwan University)
Abstract : A deep learning aided optimization algorithm for the design of flat thin-film multilayer optical systems is developed. We introduce a deep generative neural network, based on a variational autoencoder, to perform the optimization of photonic devices. This algorithm allows one to find a near-optimal solution to the inverse design problem of creating an anti-reflective grating, a fundamental problem in material science. As a proof of concept, we demonstrate the method’s capabilities for designing an anti-reflective flat thin-film stack consisting of multiple material types. We designed and constructed a dielectric stack on silicon that exhibits an average reflection, which is lower than other recently published experiments in the engineering and physics literature. In addition to its superior performance, the computational cost of our algorithm based on the deep generative model is much lower than traditional nonlinear optimization algorithms. These results demonstrate that advanced concepts in deep learning can drive the capabilities of inverse design algorithms for photonics. In addition, we develop an accurate regression model using deep active learning to predict the total reflectivity for a given optical system. The surrogate model of the governing partial differential equations can then be broadly used in the design of optical systems and to rapidly evaluate their behavior.
[04138] Implicit Solutions of Electrical Impedance Tomography Using Deep Neural Network
Format : Talk at Waseda University
Author(s) :
Taufiquar Khan (UNC Charlotte)
Thilo Strauss (Bosch)
Abstract : In this talk, we will discuss deep learning approach for the electrical impedance tomography (EIT). In the last several decades, researchers have made significant improvement for image reconstruction for the EIT inverse problem. However, there is still need for much improvement. In this talk, we will discuss a shape reconstruction approach using machine learning. We propose a neural network architecture where the neural network model estimates the probability for a point of whether the conductivity belongs to the background region or to the non-homogeneous region. We present our numerical results to show the performance of the architecture and compare the proposed method with other known algorithms.
