Object Identification in Radar Imaging via the Reciprocity Gap Method

In this paper, we present an experimental method for locating and identifying objects in radar imaging, specifically problems that could arise in physical situations. The data for the forward problem are generated using a discretization of the Lippmann‐Schwinger equation, and the inverse problem of object location is solved using the reciprocity gap approach to the linear sampling method. The main new development in this paper is an exploration of determining the permittivity of the object from the back‐scattered data, utilizing another discretization of the Lippmann‐Schwinger equation. Abstract © AGU

Through-the-wall Radar Detection Using Machine Learning

This paper explores the through-the-wall inverse scattering problem via machine learning. The reconstruction method seeks to discover the shape, location, and type of hidden objects behind walls, as well as identifying certain material properties of the targets. We simulate RF sources and receivers placed outside the room to generate observation data with objects randomly placed inside the room. We experiment with two types of neural networks and use an 80-20 train-test split for reconstruction and classification

Large Solutions of Semilinear Elliptic Equations with Nonlinear Gradient Terms

We show that large positive solutions exist for the equation ( P ± ) : Δ u ± | ∇ u | q = p ( x ) u γ in Ω ⫅ R N ( N ≥ 3 ) for appropriate choices of γ \u3e 1 , q \u3e 0 in which the domain Ω is either bounded or equal to R N . The nonnegative function p is continuous and may vanish on large parts of Ω . If Ω = R N , then p must satisfy a decay condition as | x | → ∞ . For ( P + ) , the decay condition is simply ∫ 0 ∞ t ϕ ( t ) d t \u3c ∞ , where ϕ ( t ) = max | x | = t p ( x ) . For ( P − ) , we require that t 2 + β ϕ ( t ) be bounded above for some positive β . Furthermore, we show that the given conditions on γ and p are nearly optimal for equation ( P + ) in that no large solutions exist if either γ ≤ 1 or the function p has compact support in Ω

Acceleration of Boltzmann Collision Integral Calculation Using Machine Learning

The Boltzmann equation is essential to the accurate modeling of rarefied gases. Unfortunately, traditional numerical solvers for this equation are too computationally expensive for many practical applications. With modern interest in hypersonic flight and plasma flows, to which the Boltzmann equation is relevant, there would be immediate value in an efficient simulation method. The collision integral component of the equation is the main contributor of the large complexity. A plethora of new mathematical and numerical approaches have been proposed in an effort to reduce the computational cost of solving the Boltzmann collision integral, yet it still remains prohibitively expensive for large problems. This paper aims to accelerate the computation of this integral via machine learning methods. In particular, we build a deep convolutional neural network to encode/decode the solution vector, and enforce conservation laws during post-processing of the collision integral before each time-step. Our preliminary results for the spatially homogeneous Boltzmann equation show a drastic reduction of computational cost. Specifically, our algorithm requires O(n3) operations, while asymptotically converging direct discretization algorithms require O(n6), where n is the number of discrete velocity points in one velocity dimension. Our method demonstrated a speed up of 270 times compared to these methods while still maintaining reasonable accuracy

An Ultra-Sparse Approximation of Kinetic Solutions to Spatially Homogeneous Flows of Non-continuum Gas

We consider a compact approximation of the kinetic velocity distribution function by a sum of isotropic Gaussian densities in the problem of spatially homogeneous relaxation. Derivatives of the macroscopic parameters of the approximating Gaussians are obtained as solutions to a linear least squares problem derived from the Boltzmann equation with full collision integral. Our model performs well for flows obtained by mixing upstream and downstream conditions of normal shock wave with Mach number 3. The model was applied to explore the process of approaching equilibrium in a spatially homogeneous flow of gas. Convergence of solutions with respect to the model parameters is studied. © 2019 The Author

Anomaly Detection in the Molecular Structure of Gallium Arsenide Using Convolutional Neural Networks

This paper concerns the development of a machine learning tool to detect anomalies in the molecular structure of Gallium Arsenide. We employ a combination of a CNN and a PCA reconstruction to create the model, using real images taken with an electron microscope in training and testing. The methodology developed allows for the creation of a defect detection model, without any labeled images of defects being required for training. The model performed well on all tests under the established assumptions, allowing for reliable anomaly detection. To the best of our knowledge, such methods are not currently available in the open literature; thus, this work fills a gap in current capabilities

Defect Detection in Atomic Resolution Transmission Electron Microscopy Images Using Machine Learning

Point defects play a fundamental role in the discovery of new materials due to their strong influence on material properties and behavior. At present, imaging techniques based on transmission electron microscopy (TEM) are widely employed for characterizing point defects in materials. However, current methods for defect detection predominantly involve visual inspection of TEM images, which is laborious and poses difficulties in materials where defect related contrast is weak or ambiguous. Recent efforts to develop machine learning methods for the detection of point defects in TEM images have focused on supervised methods that require labeled training data that is generated via simulation. Motivated by a desire for machine learning methods that can be trained on experimental data, we propose two self-supervised machine learning algorithms that are trained solely on images that are defect-free. Our proposed methods use principal components analysis (PCA) and convolutional neural networks (CNN) to analyze a TEM image and predict the location of a defect. Using simulated TEM images, we show that PCA can be used to accurately locate point defects in the case where there is no imaging noise. In the case where there is imaging noise, we show that incorporating a CNN dramatically improves model performance. Our models rely on a novel approach that uses the residual between a TEM image and its PCA reconstruction

Distributional Collision Modeling for Monte Carlo Simulations

Abstract. In this paper we present the initial results in our development of Distributional DSMC (DDSMC) methods. By modifying Nanbu's method to allow distributed velocities, we have shown that DSMC methods are not limited to convergence in probability measure alone, but can achieve strong convergence for L 1 solutions of the Boltzmann equation and pointwise convergence for bounded solutions. We also present an initial attempt at a general distributional method and apply these methods to the Bobylev, Krook, and Wu space homogeneous solution of the Boltzmann equation

Existence and Nonexistence of Entire Positive Solutions of Semilinear Elliptic Systems

AbstractWe show that entire positive solutions exist for the semilinear elliptic system Δu=p(x)vα, Δv=q(x)uβ on RN, N≥3, for positive α and β, provided that the nonnegative functions p and q are continuous and satisfy appropriate decay conditions at infinity. We also show that entire solutions fail to exist if the functions p and q are of slow decay

Large solutions of semilinear elliptic equations with nonlinear gradient terms

We show that large positive solutions exist for the equation (P±):Δu±|∇u|q=p(x)uγ in Ω⫅RN(N≥3) for appropriate choices of γ>1,q>0 in which the domain Ω is either bounded or equal to RN. The nonnegative function p is continuous and may vanish on large parts of Ω. If Ω=RN, then p must satisfy a decay condition as |x|→∞. For (P+), the decay condition is simply ∫0∞tϕ(t)dt<∞, where ϕ(t)=max|x|=tp(x). For (P−), we require that t2+βϕ(t) be bounded above for some positive β. Furthermore, we show that the given conditions on γ and p are nearly optimal for equation (P+) in that no large solutions exist if either γ≤1 or the function p has compact support in Ω