Perfectly matched layers are extensively used to compute approximate solutions for Maxwell's equations in using a bounded computational domain, usually a rectangular solid. A smaller rectangular domain of interest is surrounded by layers designed to absorb outgoing waves in perfectly reflectionless manner. On the boundary of the computational domain, an absorbing boundary condition is imposed that

In the 50's Read and Shockley proposed a formula for the energy of small angle grain boundaries in polycrystals based on linearized elasticity and an ansatz on the distribution of incompatibilities of the lattice at the interface between two grains. The logarithmic scaling of this formula has been rigorously justified without any ansatz on the geometry of dislocations only recently in an article by

SIAM Review, Volume 67, Issue 1, Page 208-209, March 2025. The book Mathematical Pictures at a Data Science Exhibition aims to introduce the reader to the many mathematical ideas that congregate under the ever-expanding umbrella of data science. Given the meteoric rise of this field and the immense speed at which it often moves, this book acts as a welcome road map for graduate students and researchers

SIAM Review, Volume 67, Issue 1, Page 207-208, March 2025. Elegant Simulations covers various aspects of modeling and simulating mechanical systems described at the elementary level by many-interacting particles. The book presents the topics from an original and fresh point of view. The complex many-body dynamics is reproduced at the elementary level in terms of simple models that are easy to understand

SIAM Review, Volume 67, Issue 1, Page 206-207, March 2025. This is a bold book! Professor Zhu wants to provide the basic statistical knowledge needed by data scientists in a super-short volume. It reminds me a bit of Larry Wasserman’s All of Statistics (Springer, 2014), but is aimed at Masters students (often from fields other than statistics) or advanced undergraduates (also often from other fields)

SIAM Review, Volume 67, Issue 1, Page 205-206, March 2025. The first look at Probability Adventures brought back memories of a conference in Ubatuba, Brazil, in 2001, where as a young Master’s student I worried that true science had to be deadly serious. Fortunately, several inspiring teachers came to the rescue. Andrei Toom’s words resonated deeply with me when he began his lecture by saying, “Every

SIAM Review, Volume 67, Issue 1, Page 204-205, March 2025. Numerical Methods in Physics with Python by Alex Gezerlis is an excellent example of a textbook built on long and established teaching experience. The goals are clearly defined in the preface: Gezerlis aims to gently introduce undergraduate physics students to the branch of numerical methods and their concrete implementation in Python. To this

SIAM Review, Volume 67, Issue 1, Page 197-204, March 2025. The book under review was originally published under the auspices of the National Research Council in 1933 (the year John was born), and it was republished as a Dover edition in 1956 (three years before Rob was born). At 108 pages—including title page, preface, table of contents, and index—it’s very short. Even so, it contains a significant

SIAM Review, Volume 67, Issue 1, Page 195-196, March 2025.

SIAM Review, Volume 67, Issue 1, Page 176-193, March 2025. Abstract.This paper is intended to serve as a low-hurdle introduction to nonlocality for graduate students and researchers with an engineering mechanics or physics background who did not have a formal introduction to the underlying mathematical basis. We depart from simple examples motivated by structural mechanics to form a physical intuition

SIAM Review, Volume 67, Issue 1, Page 141-175, March 2025. Abstract.Sparse matrix computations are ubiquitous in scientific computing. Given the recent interest in scientific machine learning, it is natural to ask how sparse matrix computations can leverage neural networks (NNs). Unfortunately, multilayer perceptron (MLP) NNs are typically not natural for either graph or sparse matrix computations

SIAM Review, Volume 67, Issue 1, Page 139-140, March 2025.

SIAM Review, Volume 67, Issue 1, Page 107-137, March 2025. Abstract.A dynamical system is a transformation of a phase space, and the transformation law is the primary means of defining as well as identifying the dynamical system and is the object of focus of many learning techniques. However, there are many secondary aspects of dynamical systems—invariant sets, the Koopman operator, and Markov approximations—that

SIAM Review, Volume 67, Issue 1, Page 105-105, March 2025.

SIAM Review, Volume 67, Issue 1, Page 73-104, March 2025. Abstract.Methods inspired by artificial intelligence (AI) are starting to fundamentally change computational science and engineering through breakthrough performance on challenging problems. However, the reliability and trustworthiness of such techniques is a major concern. In inverse problems in imaging, the focus of this paper, there is increasing

SIAM Review, Volume 67, Issue 1, Page 71-71, March 2025.

SIAM Review, Volume 67, Issue 1, Page 3-70, March 2025. Abstract.Uncertainty is prevalent in engineering design and data-driven problems and, more broadly, in decision making. Due to inherent risk-averseness and ambiguity about assumptions, it is common to address uncertainty by formulating and solving conservative optimization models expressed using measures of risk and related concepts. We survey

SIAM Review, Volume 67, Issue 1, Page 1-1, March 2025.

This article provides the first mathematical analysis of the Density Matrix Embedding Theory (DMET) method. We prove that, under certain assumptions, (i) the exact ground‐state density matrix is a fixed‐point of the DMET map for non‐interacting systems, (ii) there exists a unique physical solution in the weakly‐interacting regime, and (iii) DMET is exact up to first order in the coupling parameter

We construct special Lagrangian pair of pants in general dimensions, inside the cotangent bundle of with the Euclidean structure, building upon earlier topological ideas of Matessi. The construction uses a combination of PDE and geometric measure theory.

We consider the global approximate controllability of the two‐dimensional incompressible Navier–Stokes system driven by a physically localized and degenerate force. In other words, the fluid is regulated via four scalar controls that depend only on time and appear as coefficients in an effectively constructed driving force supported in a given subdomain. Our idea consists of squeezing low mode controls

In this work, we study the co‐dimensional one interface limit and geometric motions of parabolic Ginzburg–Landau systems with potentials of high‐dimensional wells. The main result generalizes the one by Lin et al. (Comm. Pure Appl. Math. 65 (2012), no. 6, 833–888) to a dynamical case. In particular combining modulated energy methods and weak convergence methods, we derive the limiting harmonic heat

In this work, we study the critical long‐range percolation (LRP) on , where an edge connects and independently with probability 1 for and with probability for some fixed . Viewing this as a random electric network where each edge has a unit conductance, we show that with high probability the effective resistances from the origin 0 to and from the interval to (conditioned on no edge joining and ) both