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At least 955 records · Page 53

Model-Form Epistemic Uncertainty Quantification for Modeling with Differential Equations: Application to Epidemiology

Modeling real-world phenomena to any degree of accuracy is a challenge that the scientific research community has navigated since its foundation. Lack of information and limited computational and observational resources necessitate modeling assumptions which, when invalid, lead to model-form error (MFE). The work reported herein explored a novel method to represent model-form uncertainty (MFU) that combines Bayesian statistics with the emerging field of universal differential equations (UDEs). The fundamental principle behind UDEs is simple: use known equational forms that govern a dynamical system when you have them; then incorporate data-driven approaches – in this case neural networks (NNs) – embedded within the governing equations to learn the interacting terms that were underrepresented. Utilizing epidemiology as our motivating exemplar, this report will highlight the challenges of modeling novel infectious diseases while introducing ways to incorporate NN approximations to MFE. Prior to embarking on a Bayesian calibration, we first explored methods to augment the standard (non-Bayesian) UDE training procedure to account for uncertainty and increase robustness of training. In addition, it is often the case that uncertainty in observations is significant; this may be due to randomness or lack of precision in the measurement process. This uncertainty typically manifests as “noisy” observations which deviate from a true underlying signal. To account for such variability, the NN approximation to MFE is endowed with a probabilistic representation and is updated using available observational data in a Bayesian framework. By representing the MFU explicitly and deploying an embedded, data-driven model, this approach enables an agile, expressive, and interpretable method for representing MFU. In this report we will provide evidence that Bayesian UDEs show promise as a novel framework for any science-based, data-driven MFU representation; while emphasizing that significant advances must be made in the calibration of Bayesian NNs to ensure a robust calibration procedure.

97 MATHEMATICS AND COMPUTING↗

Mechanistic Insights into C–H Borylation of Arenes with Organoiridium Catalysts Embedded in a Microporous Metal–Organic Framework

Organometallic iridium catalysts can be used in conjunction with bispinacolatodiboron (B 2 Pin 2 ) to effect the borylation of a variety of substrates such as arenes, alkanes, heteroarenes, and oxygenates. Recently, efforts have also focused on integrating these catalysts into porous supports, such as metal–organic frameworks (MOFs). While the mechanism of homogeneous borylation systems has been thoroughly investigated experimentally and computationally, analogous studies in MOF-supported iridium catalysts have not been conducted. In this paper, we report the mechanistic investigation of a phenanthroline-iridium catalyst immobilized in the organic linker of Universitetet i Oslo (UiO)-67 (Zr 6 O 4 (OH) 4 (BPDC) 4 (PhenDC) 2 , BPDC = biphenyl-4,4'-dicarboxylate, PhenDC = 1,10-phenanthroline-4,4'-dicarboxylate). By using benzene as a model substrate, variable time normalization analysis (VTNA) of the kinetic data suggested a rate law consistent with zero-order in B 2 Pin 2 , and first-order in arene. A primary kinetic isotope effect (KIE) in the time course of benzene-d 6 borylation also provided complementary information about the role of the arene in the rate-determining step of the reaction. Characterization by techniques such as X-ray absorption spectroscopy (XAS) confirmed the presence of Ir(III), while pair distribution function (PDF) analysis suggested structures containing an Ir–Cl bond, further substantiated by X-ray photoelectron spectroscopy (XPS). Analysis of postcatalysis materials by inductively coupled plasma–optical emission spectroscopy (ICP-OES) revealed low boron accumulation, which may indicate an absence of boron in the resting state of the catalyst. Finally, in comparing borylation of benzene and toluene, a slight selectivity for benzene is observed, which is similar to the analogous homogeneous reaction, indicating the influence of substrate sterics on reactivity.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Scattering from a random layer embedded with dielectric needles

Intensity scattering from a random layer imbedded with small dielectric needles is studied for applications to coniferous vegetation. The phase matrix of a thin needle whose length may be appreciable compared to the incident wavelength is presented. The effects of needle orientation on scattering is taken into account by averaging the phase function over angles of orientation. The backscattering coefficient from the layer is computed by solving the radiative transfer equation. The effects of operating frequency, orientation and size of a needle on like- and cross-backscattering are demonstrated. It was found that in backscattering angular trends are mainly controlled by the orientation of the needles.

Eom, H. J.↗

Parallel quantum annealing

Quantum annealers of D-Wave Systems, Inc., offer an efficient way to compute high quality solutions of NP-hard problems. This is done by mapping a problem onto the physical qubits of the quantum chip, from which a solution is obtained after quantum annealing. However, since the connectivity of the physical qubits on the chip is limited, a minor embedding of the problem structure onto the chip is required. In this process, and especially for smaller problems, many qubits will stay unused. We propose a novel method, called parallel quantum annealing, to make better use of available qubits, wherein either the same or several independent problems are solved in the same annealing cycle of a quantum annealer, assuming enough physical qubits are available to embed more than one problem. Although the individual solution quality may be slightly decreased when solving several problems in parallel (as opposed to solving each problem separately), we demonstrate that our method may give dramatic speed-ups in terms of the Time-To-Solution (TTS) metric for solving instances of the Maximum Clique problem when compared to solving each problem sequentially on the quantum annealer. Additionally, we show that solving a single Maximum Clique problem using parallel quantum annealing reduces the TTS significantly.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Constructing a square-like copper cluster to boost C–C coupling for CO 2 electroreduction to ethylene

The CO 2 electroreduction reaction (CO 2 ER) to ethylene (C 2 H 4 ) offers the dual promise of lowering CO 2 emission while storing energy from renewable electricity, for which the development of highly efficient electrocatalysts is of great significance. Herein, by means of density functional theory (DFT) computations, we designed an electrocatalyst for CO 2 -to-C 2 H 4 conversion by anchoring a Cu 5 cluster supported on a MoS 2 monolayer with an S monovacancy (Cu 5 @MoS 2 ). Our results revealed that one Cu atom of the Cu 5 cluster was embedded into the framework of the defective MoS 2 monolayer, while the other four Cu atoms form a square-like island over the substrate surface. Interestingly, the C–C coupling between two *CO species can easily occur on the unique square-like active site with a low kinetic barrier of 0.56 eV to form the key *C 2 O 2 intermediate, which can then be hydrogenated to the C 2 H 4 product with a very low limiting potential (–0.32 eV). Significantly, alkaline conditions (pH = 13) are beneficial to further promote C 2 H 4 synthesis. Finally, our work may offer a new avenue to precisely modulate the structures of Cu clusters for converting CO 2 into high-value target products.

30 DIRECT ENERGY CONVERSION↗

Modular Security Apparatus for Managing Distributed Cryptography for Command-and-Control Messages on Operational Technology Networks (Module-OT)

Module-OT is a bump- in- the- wire solution acting as a secure conduit for data between devices or systems across a network. Using the latest in open-source cryptographic libraries, all defined communications undergo authentication, authorization, and encryption. The core system can be easily installed through industry standard processes, and the use of popular open-source packages allows for it to be customizable customized by the developer community or deployed in unique embedded environments.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Conservative supra-characteristics method for splitting the hyperbolic systems of gasdynamics for real and perfect gases

A conservative flux difference splitting is presented for the hyperbolic systems of gasdynamics. The stable robust method is suitable for wide application in a variety of schemes, explicit or implicit, iterative or direct, for marching in either time or space. The splitting is modeled on the local quasi one dimensional characteristics system for multi-dimensional flow similar to Chakravarthy's nonconservative split coefficient matrix method; but, as the result of maintaining global conservation, the method is able to capture sharp shocks correctly. The embedded characteristics formulation is cast in a primitive variable the volumetric internal energy (rather than the pressure) that is effective for treating real as well as perfect gases. Finally the relationship of the splitting to characteristics boundary conditions is discussed and the associated conservative matrix formulation for a computed blown wall boundary condition is developed as an example. The theoretical development employs and extends the notion of Roe of constructing stable upwind difference formulae by sending split simple one sided flux difference pieces to appropriate mesh sites. The developments are also believed to have the potential for aiding in the analysis of both existing and new conservative difference schemes.

Lombard, C. K.↗

Numerical study of large-eddy breakup and its effect on the drag characteristics of boundary layers

The break-up of a field of eddies by a flat-plate obstacle embedded in a boundary layer is studied using numerical solutions to the two-dimensional Navier-Stokes equations. The flow is taken to be incompressible and unsteady. The flow field is initiated from rest. A train of eddies of predetermined size and strength are swept into the computational domain upstream of the plate. The undisturbed velocity profile is given by the Blasius solution. The disturbance vorticity generated at the plate and wall, plus that introduced with the eddies, mix with the background vorticity and is transported throughout the entire flow. All quantities are scaled by the plate length, the unidsturbed free-stream velocity, and the fluid kinematic viscosity. The Reynolds number is 1000, the Blasius boundary layer thickness is 2.0, and the plate is positioned a distance of 1.0 above the wall. The computational domain is four units high and sixteen units long.

Kinney, R. B.↗

Smart structures research program at Virginia Tech

A review of the smart structures and avionics research and teaching program that started in 1979 at Virginia Tech is described. Current smart structures research include major efforts in the development of embedded and attached optical fiber and acoustic fiber sensors for cure monitoring, in-service lifetime structural testing, nondestructive evaluation, and impact and damage detection and analysis; of gradual material degradation; sensor signal multiplexing, processing and data handling to achieve near real-time distributed structural analysis; and the integration of embedded sensors, actuators and control electronics to achieve controlled structural response. Special campus facilities used for this work include an optical fiber fabrication facility, an autoclave for composite structure fabrication and curing, and laboratories for optical fiber sensor development, materials response and nondestructive evaluation, structural control testing and computer engineering.

Claus, R. O.↗

Exploring Discretization Error in Simulation-Based Aerodynamic Databases

This work examines the level of discretization error in simulation-based aerodynamic databases and introduces strategies for error control. Simulations are performed using a parallel, multi-level Euler solver on embedded-boundary Cartesian meshes. Discretization errors in user-selected outputs are estimated using the method of adjoint-weighted residuals and we use adaptive mesh refinement to reduce these errors to specified tolerances. Using this framework, we examine the behavior of discretization error throughout a token database computed for a NACA 0012 airfoil consisting of 120 cases. We compare the cost and accuracy of two approaches for aerodynamic database generation. In the first approach, mesh adaptation is used to compute all cases in the database to a prescribed level of accuracy. The second approach conducts all simulations using the same computational mesh without adaptation. We quantitatively assess the error landscape and computational costs in both databases. This investigation highlights sensitivities of the database under a variety of conditions. The presence of transonic shocks or the stiffness in the governing equations near the incompressible limit are shown to dramatically increase discretization error requiring additional mesh resolution to control. Results show that such pathologies lead to error levels that vary by over factor of 40 when using a fixed mesh throughout the database. Alternatively, controlling this sensitivity through mesh adaptation leads to mesh sizes which span two orders of magnitude. We propose strategies to minimize simulation cost in sensitive regions and discuss the role of error-estimation in database quality.

Aftosmis, Michael J.↗

Deep transfer operator learning for partial differential equations under conditional shift

Transfer learning enables the transfer of knowledge gained while learning to perform one task (source) to a related but different task (target), hence addressing the expense of data acquisition and labelling, potential computational power limitations and dataset distribution mismatches. Here, we propose a new transfer learning framework for task-specific learning (functional regression in partial differential equations) under conditional shift based on the deep operator network (DeepONet). Task-specific operator learning is accomplished by fine-tuning task-specific layers of the target DeepONet using a hybrid loss function that allows for the matching of individual target samples while also preserving the global properties of the conditional distribution of the target data. Inspired by conditional embedding operator theory, we minimize the statistical distance between labelled target data and the surrogate prediction on unlabelled target data by embedding conditional distributions onto a reproducing kernel Hilbert space. We demonstrate the advantages of our approach for various transfer learning scenarios involving nonlinear partial differential equations under diverse conditions due to shifts in the geometric domain and model dynamics. Our transfer learning framework enables fast and efficient learning of heterogeneous tasks despite considerable differences between the source and target domains.

42 ENGINEERING↗

Graph-EAM: An Interpretable and Efficient Graph Neural Network Potential Framework

The development of deep learning interatomic potentials has enabled efficient and accurate computations in quantum chemistry and materials science, circumventing computationally expensive ab initio calculations. However, the huge number of learnable parameters in deep learning models and their complex architectures hinder physical interpretability and affect the robustness of the derived potential. In this work, we propose graph-EAM, a lightweight graph neural network (GNN) inspired by the empirical embedded atom method to model the interatomic potential of single-element structures. Four material systems: platinum, niobium, silicon, and amorphous-carbon, for which quantum simulation data sets are publicly available, are examined to demonstrate that graph-EAM can achieve high energy and force prediction accuracy-comparable or better than existing state-of-the-art machine learning models-with much fewer parameters. It is also shown that the explicit inclusion of the angular information via three-body atomic density increases the prediction accuracy. In conclusion, the accuracy and efficiency of potentials obtained from graph-EAM can help accelerate the molecular dynamics simulation.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

High-temperature Majorana fermions in magnet-superconductor hybrid systems

Magnet-superconductor hybrid (MSH) structures represent one of the most promising platforms to realize, control, and manipulate Majorana modes using scanning tunneling methods. By depositing either chains or islands of magnetic atoms on the surface of a conventional, elemental superconductor such as Pb or Re, topological superconducting phases can emerge. They feature either localized Majorana bound states at the chain ends or dispersing chiral Majorana modes at the island's boundary. However, some of these experiments have not reached the spectral resolution to clearly distinguish between topological Majorana and trivial Shiba states due to very small superconducting gap sizes and experiments performed at sub-Kelvin temperatures. Here we consider superconducting substrates with unconventional spin-singlet pairing, including high-temperature d -wave and extended s -wave superconductors. We derive topological phase diagrams and compute edge states for cylinder and island geometries and discuss their properties. Several time-reversal invariant topological superconducting phases of the Zhang-Kane-Mele type are found and discussed. Addiotnally, we review one-dimensional MSH structures and show that parameters to realize topologically nontrivial magnetic chains embedded into a larger, two-dimensional substrate differ from the purely one-dimensional case. Quite generally we find that unconventional superconducting substrates work as well as the conventional s -wave substrates to realize topological phases. In particular, iron-based pnictide and chalcogenide superconductors are the most promising class of substrates for future high-temperature MSH systems.

36 MATERIALS SCIENCE↗

Development and Validation of Resistance-Capacitance Model for Phase Change Material Embedded in Porous Media

A simple and effective way to enhance PCM thermal conductivity is by embedding porous materials with high thermal conductivities. In this work, CFD was used to evaluate the melting of PCM embedded in metal foam supplied with constant heat flux. Good agreement between experimental and numerical results has been found with a mean PCM local temperature deviation of 1.62K and 2.97K in two locations. The CFD simulation time was 56 hours for 6.5 hours of flow time. A computationally efficient resistance capacitance-based model (RCM) was developed to improve simulation speed. The proposed RCM exhibited mean local temperature deviations of 1.86K and 2.96K when compared against the experimental data for two thermocouple positions, however, it was approximately 2.5x10 5 times faster than CFD. The charging time deviation was less than 1% compared to CFD, and no significant change in thermal energy stored was observed since the temperature differences were small enough to result in insignificant sensible heat deviation. A simulation cost-effectiveness index (CEI) considering accuracy and computational affordability was introduced; the CEI of the RCM solver is 10 3 times better compared to CFD for the prediction of local PCM temperature.

25 ENERGY STORAGE↗

QSpace - An open-source tensor library for Abelian and non-Abelian symmetries

This is the documentation for the tensor library QSpace (v4.0), a toolbox to exploit ‘quan tum symmetry spaces’ in tensor network states in the quantum many-body context. QSpace permits arbitrary combinations of symmetries including the abelian symmetries $\mathbb{Z}_n$ and U(1), as well as all non-abelian symmetries based on the semisimple classical Lie algebras: A n , B n , C n , and D n , or respectively, the special unitary group SU(n), the odd orthogonal group SO(2n+1), the symplectic group Sp(2n), and the even orthogonal group SO(2n). The code (C++ embedded via the MEX interface into Matlab) is available open source as of QSpace v4.0 on bitbucket under the Apache 2.0 license. QSpace is designed as a bottom-up approach for non-abelian symmetries. It starts from the defining representation and the respective Lie algebra. By explicitly comput ing and tabulating generalized Clebsch-Gordan coefficient tensors, QSpace is versatile in the type of operations that it can perform across all symmetries. At the level of an ap plication, much of the symmetry-related details are hidden within the QSpace C++ core libraries. Hence when developing tensor network algorithms with QSpace, these can be coded (nearly) as if there are no symmetries at all, despite being able to fully exploit general non-abelian symmetries.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Report of the Technology and Test Panel

The state of technology relative to the Tethered Satellite System (TSS) was reviewed. The technology areas which could benefit from the TSS were defined. To support TSS design studies it is necessary to develop tether dynamic model computer codes for definition of mission and tether requirements. Present major codes are very elaborate, expensive to run, and not very user friendly. An additional technology concern was related to the manufacturing of tethers. The development of complex tethers (nonconducting-taper/double taper long 100 km, conducting-embedded conduction, fiber optics, and superconducting) and their applications to space stations requires the development of manufacturing capabilities for both Earth-based as well as space-based systems.

Siemers, P.↗

Method and system for training dynamic nonlinear adaptive filters which have embedded memory

Described herein is a method and system for training nonlinear adaptive filters (or neural networks) which have embedded memory. Such memory can arise in a multi-layer finite impulse response (FIR) architecture, or an infinite impulse response (IIR) architecture. We focus on filter architectures with separate linear dynamic components and static nonlinear components. Such filters can be structured so as to restrict their degrees of computational freedom based on a priori knowledge about the dynamic operation to be emulated. The method is detailed for an FIR architecture which consists of linear FIR filters together with nonlinear generalized single layer subnets. For the IIR case, we extend the methodology to a general nonlinear architecture which uses feedback. For these dynamic architectures, we describe how one can apply optimization techniques which make updates closer to the Newton direction than those of a steepest descent method, such as backpropagation. We detail a novel adaptive modified Gauss-Newton optimization technique, which uses an adaptive learning rate to determine both the magnitude and direction of update steps. For a wide range of adaptive filtering applications, the new training algorithm converges faster and to a smaller value of cost than both steepest-descent methods such as backpropagation-through-time, and standard quasi-Newton methods. We apply the algorithm to modeling the inverse of a nonlinear dynamic tracking system 5, as well as a nonlinear amplifier 6.

Rabinowitz, Matthew↗

Faster approximate subgraph counts with privacy

One of the most common problems studied in the context of differential privacy for graph data is counting the number of non-induced embeddings of a subgraph in a given graph. These counts have very high global sensitivity. Therefore, adding noise based on powerful alternative techniques, such as smooth sensitivity and higher-order local sensitivity have been shown to give significantly better accuracy. However, all these alternatives to global sensitivity become computationally very expensive, and to date efficient polynomial time algorithms are known only for few selected subgraphs, such as triangles, k-triangles, and k-stars. In this paper, we show that good approximations to these sensitivity metrics can be still used to get private algorithms. Using this approach, we much faster algorithms for privately counting the number of triangles in real-world social networks, which can be easily parallelized. We also give a private polynomial time algorithm for counting any constant size subgraph using less noise than the global sensitivity; we show this can be improved significantly for counting paths in special classes of graphs

Nguyen, Dung↗