Network Calculus and Mu2e event building Network
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72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
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Modeling Data Flows with Network Calculus in Cyber-Physical Systems: Enabling Feature Analysis for Anomaly Detection Applications
The electric grid is becoming increasingly cyber-physical with the addition of smart technologies, new communication interfaces, and automated grid-support functions. Because of this, it is no longer sufficient to only study the physical system dynamics, but the cyber system must also be monitored as well to examine cyber-physical interactions and effects on the overall system. To address this gap for both operational and security needs, cyber-physical situational awareness is needed to monitor the system to detect any faults or malicious activity. Techniques and models to understand the physical system (the power system operation) exist, but methods to study the cyber system are needed, which can assist in understanding how the network traffic and changes to network conditions affect applications such as data analysis, intrusion detection systems (IDS), and anomaly detection. In this paper, we examine and develop models of data flows in communication networks of cyber-physical systems (CPSs) and explore how network calculus can be utilized to develop those models for CPSs, with a focus on anomaly and intrusion detection. This provides a foundation for methods to examine how changes to behavior in the CPS can be modeled and for investigating cyber effects in CPSs in anomaly detection applications.
97 MATHEMATICS AND COMPUTING↗
Smart Meter Pinging and Reading Through AMI Two-Way Communication Networks to Monitor Grid Edge Devices and DERs
Today’s power distribution system is changing to a power-electronics-enabled distribution system, especially with the increasing penetration of distributed energy resources (DERs). To monitor and manage those electronic devices and DERs at the grid edge, the advanced metering infrastructure (AMI) with two-way communications presents great potential. At present, extensive research explores the upstream communication from smart meters to electric utilities (e.g., meter reading) but few examine the downstream communication from the utilities to smart meters (e.g., meter pinging). This article discusses the AMI two-way communication and its recent industrial practice in the U.S., especially for applying the smart meter pinging functionality to monitor grid-edge devices and DERs. This paper then develops the two-way communication model and the network calculus method to quantify the impact of the two-way communication on the AMI network. In the end, the proposed method is validated with ns-3 simulation using the modified 13-node test feeder and real-world feeder systems.
24 POWER TRANSMISSION AND DISTRIBUTION↗
A method of determination of state variables for known plants.
State variable determination for linear time invariant plants with known parameters, noting noise suppressing characteristics of technique
NOISE SUPPRESSOR↗
Optimal design of distributed parameter systems.
Optimal design of RC lines distributed parameter systems using gradient technique and variational calculus
OPTIMIZATION↗
Theory and calculus of cubical complexes
Combination switching networks with multiple outputs may be represented by Boolean functions. Report has been prepared which describes derivation and use of extraction algorithm that may be adapted to simplification of such simultaneous Boolean functions.
Perlman, M.↗
Optical production systems using neural networks and symbolic substitution
Two optical implementations of production systems are advanced. The production systems operate on a knowledge base where facts and rules are encoded as formulas in propositional calculus. The first implementation is a binary neural network. An analog neural network is used to include reasoning with uncertainties. The second implementation uses a new optical symbolic substitution correlator. This implementation is useful when a set of similar situations has to be handled in parallel on one processor.
Botha, Elizabeth↗
Scalable algorithms for physics-informed neural and graph networks
Physics-informed machine learning (PIML) has emerged as a promising new approach for simulating complex physical and biological systems that are governed by complex multiscale processes for which some data are also available. In some instances, the objective is to discover part of the hidden physics from the available data, and PIML has been shown to be particularly effective for such problems for which conventional methods may fail. Unlike commercial machine learning where training of deep neural networks requires big data, in PIML big data are not available. Instead, we can train such networks from additional information obtained by employing the physical laws and evaluating them at random points in the space–time domain. Such PIML integrates multimodality and multifidelity data with mathematical models, and implements them using neural networks or graph networks. Here, we review some of the prevailing trends in embedding physics into machine learning, using physics-informed neural networks (PINNs) based primarily on feed-forward neural networks and automatic differentiation. For more complex systems or systems of systems and unstructured data, graph neural networks (GNNs) present some distinct advantages, and here we review how physics-informed learning can be accomplished with GNNs based on graph exterior calculus to construct differential operators; we refer to these architectures as physics-informed graph networks (PIGNs). We present representative examples for both forward and inverse problems and discuss what advances are needed to scale up PINNs, PIGNs and more broadly GNNs for large-scale engineering problems.
42 ENGINEERING↗
Accelerating gradient descent and Adam via fractional gradients
Here we propose a class of novel fractional-order optimization algorithms. We define a fractional-order gradient via the Caputo fractional derivatives that generalizes integer-order gradient. We refer it to as the Caputo fractional-based gradient, and develop an efficient implementation to compute it. A general class of fractional-order optimization methods is then obtained by replacing integer-order gradients with the Caputo fractional-based gradients. To give concrete algorithms, we consider gradient descent (GD) and Adam, and extend them to the Caputo fractional GD (CfGD) and the Caputo fractional Adam (CfAdam). We demonstrate the superiority of CfGD and CfAdam on several large scale optimization problems that arise from scientific machine learning applications, such as ill-conditioned least squares problem on real-world data and the training of neural networks involving non-convex objective functions. Numerical examples show that both CfGD and CfAdam result in acceleration over GD and Adam, respectively. We also derive error bounds of CfGD for quadratic functions, which further indicate that CfGD could mitigate the dependence on the condition number in the rate of convergence and results in significant acceleration over GD.
97 MATHEMATICS AND COMPUTING↗
System control of an autonomous planetary mobile spacecraft
The goal is to suggest the scheduling and control functions necessary for accomplishing mission objectives of a fairly autonomous interplanetary mobile spacecraft, while maximizing reliability. Goals are to provide an extensible, reliable system conservative in its use of on-board resources, while getting full value from subsystem autonomy, and avoiding the lure of ground micromanagement. A functional layout consisting of four basic elements is proposed: GROUND and SYSTEM EXECUTIVE system functions and RESOURCE CONTROL and ACTIVITY MANAGER subsystem functions. The system executive includes six subfunctions: SYSTEM MANAGER, SYSTEM FAULT PROTECTION, PLANNER, SCHEDULE ADAPTER, EVENT MONITOR and RESOURCE MONITOR. The full configuration is needed for autonomous operation on Moon or Mars, whereas a reduced version without the planning, schedule adaption and event monitoring functions could be appropriate for lower-autonomy use on the Moon. An implementation concept is suggested which is conservative in use of system resources and consists of modules combined with a network communications fabric. A language concept termed a scheduling calculus for rapidly performing essential on-board schedule adaption functions is introduced.
Dias, William C.↗
Heat exchanger expert system logic
The reduction is described of the operation and fault diagnostics of a Deep Space Network heat exchanger to a rule base by the application of propositional calculus to a set of logic statements. The value of this approach lies in the ease of converting the logic and subsequently implementing it on a computer as an expert system. The rule base was written in Process Intelligent Control software.
Cormier, R.↗
Nonlocal Kernel Network (NKN): a Stable and Resolution-Independent Deep Neural Network.
Neural operators have recently become popular tools for designing solution maps between function spaces in the form of neural networks. Differently from classical scientific machine learning approaches that learn parameters of a known partial differential equation (PDE) for a single instance of the input parameters at a fixed resolution, neural operators approximate the solution map of a family of PDEs [6, 7]. Despite their success, the uses of neural operators are so far restricted to relatively shallow neural networks and confined to learning hidden governing laws. In this work, we propose a novel nonlocal neural operator, which we refer to as nonlocal kernel network (NKN), that is resolution independent, characterized by deep neural networks, and capable of handling a variety of tasks such as learning governing equations and classifying images. Our NKN stems from the interpretation of the neural network as a discrete nonlocal diffusion reaction equation that, in the limit of infinite layers, is equivalent to a parabolic nonlocal equation, whose stability is analyzed via nonlocal vector calculus. The resemblance with integral forms of neural operators allows NKNs to capture long-range dependencies in the feature space, while the continuous treatment of node-to-node interactions makes NKNs resolution independent. The resemblance with neural ODEs, reinterpreted in a nonlocal sense, and the stable network dynamics between layers allow for generalization of NKN’s optimal parameters from shallow to deep networks. This fact enables the use of shallow-to-deep initialization techniques [8]. Our tests show that NKNs outperform baseline methods in both learning governing equations and image classification tasks and generalize well to different resolutions and depths.
97 MATHEMATICS AND COMPUTING↗
Data-driven Whitney forms for structure-preserving control volume analysis
Control volume analysis models physics via the exchange of generalized fluxes between subdomains. Here, we introduce a scientific machine learning framework adopting a partition of unity architecture to identify physically-relevant control volumes, with generalized fluxes between subdomains encoded via Whitney forms. The approach provides a differentiable parameterization of geometry which may be trained in an end-to-end fashion to extract reduced models from full field data while exactly preserving physics. The architecture admits a data-driven finite element exterior calculus allowing discovery of mixed finite element spaces with closed form quadrature rules. An equivalence between Whitney forms and graph networks reveals that the geometric problem of control volume learning is equivalent to an unsupervised graph discovery problem. The framework is developed for manifolds in arbitrary dimension, with examples provided for H(div) problems in $\mathbb{R}$ establishing convergence and structure preservation properties. Finally, we consider a lithium-ion battery problem where we discover a reduced finite element space encoding transport pathways from high-fidelity microstructure resolved simulations. The approach reduces the 5.89M finite element simulation to 136 elements while reproducing pressure to under 0.1% error and preserving conservation.
97 MATHEMATICS AND COMPUTING↗
Improvement on fuzzy controller design techniques
This paper addresses three main issues, which are somewhat interrelated. The first issue deals with the classification or types of fuzzy controllers. Careful examination of the fuzzy controllers designed by various engineers reveals distinctive classes of fuzzy controllers. Classification is believed to be helpful from different perspectives. The second issue deals with the design according to specifications, experiments related to the tuning of fuzzy controllers, according to the specification, will be discussed. General design procedure, hopefully, can be outlined in order to ease the burden of a design engineer. The third issue deals with the simplicity and limitation of the rule-based IF-THEN logical statements. The methodology of fuzzy-constraint network is proposed here as an alternative to the design practice at present. It is our belief that predicate calculus and the first order logic possess much more expressive power.
Wang, Paul P.↗
Cycle equivalence classes, orthogonal Weingarten calculus, and the mean field theory of memristive systems
Abstract It has been recently noted that for a class of dynamical systems with explicit conservation laws represented via projector operators, the dynamics can be understood in terms of lower dimensional equations. This is the case, for instance, of memristive circuits. Memristive systems are important classes of devices with wide-ranging applications in electronic circuits, artificial neural networks, and memory storage. We show that such mean-field theories can emerge from averages over the group of orthogonal matrices, interpreted as cycle-preserving transformations applied to the projector operator describing Kirchhoff’s laws. Our results provide insights into the fundamental principles underlying the behavior of resistive and memristive circuits and highlight the importance of conservation laws for their mean-field theories. In addition, we argue that our results shed light on the nature of the critical avalanches observed in quasi-two-dimensional nanowires as boundary phenomena.
97 MATHEMATICS AND COMPUTING↗
Tree tensor network hierarchical equations of motion based on time-dependent variational principle for efficient open quantum dynamics in structured thermal environments
In this work, we introduce an efficient method, TTN-HEOM, for exactly calculating the open quantum dynamics for driven quantum systems interacting with highly structured bosonic baths by combining the tree tensor network (TTN) decomposition scheme with the bexcitonic generalization of the numerically exact hierarchical equations of motion (HEOM). The method yields a series of quantum master equations for all core tensors in the TTN that efficiently and accurately capture the open quantum dynamics for non-Markovian environments to all orders in the system–bath interaction. These master equations are constructed based on the time-dependent Dirac–Frenkel variational principle, which isolates the optimal dynamics for the core tensors given the TTN ansatz. The dynamics converges to the HEOM when increasing the rank of the core tensors, a limit in which the TTN ansatz becomes exact. We introduce TENSO, tensor equations for non-Markovian structured open systems, as a general-purpose Python code to propagate the TTN-HEOM dynamics. We implement three general propagators for the coupled master equations: two fixed-rank methods that require a constant memory footprint during the dynamics and one adaptive-rank method with a variable memory footprint controlled by the target level of computational error. We exemplify the utility of these methods by simulating a two-level system coupled to a structured bath containing one Drude–Lorentz component and eight Brownian oscillators, which is beyond what can presently be computed using the standard HEOM. Our results show that the TTN-HEOM is capable of simulating both dephasing and relaxation dynamics of driven quantum systems interacting with structured baths, even those of chemical complexity, with an affordable computational cost.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Architectures and random properties of symplectic quantum circuits
Parametrized and random unitary (or orthogonal) n-qubit circuits play a central role in quantum information. As such, one could naturally assume that circuits implementing symplectic transformations would attract similar attention. However, this is not the case, as $\mathbb{SP}(d/2)$—the group of d × d unitary symplectic matrices—has thus far been overlooked. In this work, we aim at starting to fill this gap. We begin by presenting a universal set of generators $\mathcal{G}$ for the symplectic algebra $\mathfrak{sp}(d/2)$, consisting of one- and two-qubit Pauli operators acting on neighboring sites in a one-dimensional lattice. Here, we uncover two critical differences between such set, and equivalent ones for unitary and orthogonal circuits. Namely, we find that the operators in $\mathcal{G}$ cannot generate arbitrary local symplectic unitaries and that they are not translationally invariant. We then review the Schur–Weyl duality between the symplectic group and the Brauer algebra, and use tools from Weingarten calculus to prove that Pauli measurements at the output of Haar random symplectic circuits can converge to Gaussian processes. As a by-product, such analysis provides us with concentration bounds for Pauli measurements in circuits that form t-designs over $\mathbb{SP}(d/2)$. To finish, we present tensor-network tools to analyze shallow random symplectic circuits, and we use these to numerically show that computational-basis measurements anti-concentrate at logarithmic depth.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Discovery of Probabilistic Dirichlet-to-Neumann Maps on Graphs
Dirichlet-to-Neumann maps enable the coupling of multiphysics simulations across computational subdomains by ensuring continuity of state variables and fluxes at artificial interfaces. We present a novel method for learning Dirichlet-to-Neumann maps on graphs using Gaussian processes, specifically for problems where the data obey a conservation law arising from an underlying partial differential equation. Our approach combines discrete exterior calculus and nonlinear optimal recovery to infer relationships between vertex and edge values. This framework yields data-driven predictions with uncertainty quantification across the entire graph, even when observations are limited to a subset of vertices and edges. By minimizing the reproducing kernel Hilbert space norm while penalizing kernel complexity through maximum likelihood estimation, our method ensures that the resulting surrogate strictly enforces conservation laws without overfitting. We demonstrate our method on two representative applications: subsurface flow in fracture networks and arterial blood flow. Finally, the results demonstrate that the method maintains high accuracy and well-calibrated uncertainty estimates even under severe data scarcity, highlighting its potential for scientific applications where limited data and reliable uncertainty quantification are critical.
Dirichlet-to-Neumann map↗