chebgreen: Learning and Interpolating Continuous Empirical Green's Functions from Data

In this work, we present a mesh-independent, data-driven library, chebgreen, to mathematically model one-dimensional systems, possessing an associated control parameter, and whose governing partial differential equation is unknown. The proposed method learns an Empirical Green's Function for the associated, but hidden, boundary value problem, in the form of a Rational Neural Network from which we subsequently construct a bivariate representation in a Chebyshev basis. We uncover the Green's function, at an unseen control parameter value, by interpolating the left and right singular functions within a suitable library, expressed as points on a manifold of Quasimatrices, while the associated singular values are interpolated with Lagrange polynomials.

GRAVITAS: Graphical Reticulated Attack Vectors for Internet-of-Things Aggregate Security

Internet-of-Things (IoT) and cyber-physical systems (CPSs) may consist of thousands of devices connected in a complex network topology. The diversity and complexity of these components present an enormous attack surface, allowing an adversary to exploit security vulnerabilities of different devices to execute a potent attack. Though significant efforts have been made to improve the security of individual devices in these systems, little attention has been paid to security at the aggregate level. In this article, we describe a comprehensive risk management system, called GRAVITAS, for IoT/CPS that can identify undiscovered attack vectors and optimize the placement of defenses within the system for optimal performance and cost. While existing risk management systems consider only known attacks, our model employs a machine learning approach to extrapolate undiscovered exploits, enabling us to identify attacks overlooked by manual penetration testing (pen-testing). The model is flexible enough to analyze practically any IoT/CPS and provide the system administrator with a concrete list of suggested defenses that can reduce system vulnerability at optimal cost. GRAVITAS can be employed by governments, companies, and system administrators to design secure IoT/CPS at scale, providing a quantitative measure of security and efficiency in a world where IoT/CPS devices will soon be ubiquitous.