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DOE OSTI2020

General Analysis of Data Collected from DOE Lidar Buoy Deployments Off Virginia and New Jersey

Pacific Northwest National Laboratory (PNNL) operates two AXYS WindSentinel lidar buoys for the U.S. Department of Energy’s Wind Energy Technologies. The purpose of these buoys is to collect hub-height winds and supporting meteorological and oceanographic information to facilitate the development of offshore wind energy in the U.S. In general, each buoy is deployed for a year or more at a given location in order to capture at least a full annual cycle of weather conditions. The initial deployment for one buoy was off the coast of Virginia beginning in 2015, and the other buoy was first deployed off the coast of New Jersey beginning in 2016. Over the last two years, PNNL has had an opportunity to analyze the data collected during these first two deployments. This report describes a substantial analysis of data collected by the two lidar buoys operated off the coasts of Virginia and New Jersey. The centerpiece instrument for each buoy as deployed off Virginia and New Jersey is a lidar system, which is designed to measure the horizontal wind vector from approximately 40 m to 200 m above the sea surface with vertical resolution of 40 m. Since the initial deployments, the original lidars have been replaced with more powerful Leosphere 866 v2 systems. The analyses in this report will apply to the original Vindicator systems. In addition to the wind profiles from the lidars, the buoys collect near-surface measurements of wind speed and direction, air temperature, relative humidity, barometric pressure, and solar irradiance. Oceanographic variables measured include the two-dimensional wave spectrum, water temperature and conductivity, and ocean current vectors to a depth of 90 m. An assessment of overall data recovery and a basic analysis of the data collected was provided in a previous report This report substantially extends that analysis. The various sections describe the development and application of an inertial measurement unit (IMU) data recovery scheme for the New Jersey deployment; a climatological analysis of winds at hub height and at the surface together with thermodynamic variables measured at the surface for the full deployment periods; an analysis of oceanographic observations describe sea state; the development of a refinement for NOAA’s WaveWatch III model to allow its application to near-shore areas; a basic climatology of ocean currents observed from the buoys; an analysis of observed winds in the framework of Monin-Obukhov Similarity Theory; and the development and evaluation of techniques to extract turbulence intensity and turbulence kinetic energy from the lidars. The analyses contained in this report provide a great deal of new information about offshore conditions on the U.S. East Coast. In addition, the experience gained will inform both configurations and analysis of data from future deployments of these lidar buoy systems.

17 WIND ENERGY↗

DOE OSTI2022

Preliminary Reversible Solid Oxide System Specification

This report presents the preliminary documentation of a 10 MWe DC reversible solid oxide cell (rSOC) system designed to use both electrical and thermal energy from a nuclear power plant (NPP). The system is designed to consume 10 MWe DC in electrolysis mode while producing hydrogen from demineralized feedwater. In fuel cell mode, the same stacks produce 2.37 MWe DC of electricity by reacting hydrogen and oxygen, while generating water as a byproduct which is recycled to be used later in the electrolysis mode. The system detailed in this specification is a high-temperature steam electrolysis (HTSE) system when operated in the electrolysis mode. HTSE systems have the benefit of producing hydrogen at a higher efficiency than conventional low-temperature electrolysis (LTE) systems. In this report it is assumed that some of the heat required for HTSE operation comes from an NPP. Heat extraction from an NPP for use in electrolysis mode of the rSOC system allows preheating and vaporization of feedwater before recuperators and trim heaters raise the feed temperature to the approximately 800 °C before entering the solid oxide stacks. The purpose of an rSOC system in a utility company setting is to employ energy arbitrage with a dispatchable demand load which can consume excess electricity generation during times of low grid demand / high generation and can produce electricity for the grid during times of high grid demand / low generation. There is a wide range of energy storage technologies that could be used for utility-scale energy arbitrage (utility-scale battery storage is considered the baseline technology), the object of this work is not to compare and contrast rSOC technology with any of these other technologies, but only to present this preliminary design for consideration and for use in future conceptual or front end engineering design (FEED) work. This document is not meant to be a final specification or definitive description of the rSOC system, but it is meant to showcase preliminary process modeling results, provide boundary conditions and interface requirements such as input feed and utility stream flowrates, temperatures, and pressures as well as thermal and electrical energy requirements, and output conditions in both electrolysis mode and fuel cell mode. These results are intended to inform the future development of a conceptual demonstration-scale study to assess the technical and economic feasibility of a future demonstration of an rSOC integrated project at an NPP.

08 HYDROGEN↗

DOE OSTI2021

Utah FORGE: Well 16A(78)-32 Drilling Data

This dataset includes survey data, drilling data, daily reports, summaries of daily operations, and rig photos from the drilling of Utah FORGE well 16A(78)-32, which is a highly deviated deep well. It was completed 60 days ahead of schedule. Rig move in began 10/22/2020 and drilling commenced on 10/30/2020, and total depth was reached on 12/18/2020. Drilling was followed by a diagnostic fracture injection test (DFIT), logging, and circulating casing. The rig was released on 1/12/2021. The upper part of the well was drilled vertically through approximately 4,700 feet of sediments before penetrating into high strength, crystalline granite. The well was deviated at a 65 degree angle from vertical after reaching a depth of 6,000 ft. This angle was maintained for the remainder of the well's trajectory. The well ultimately reached a true vertical depth of 8,559 feet, and a total measured depth of 10,987 feet. Preliminary measurements indicate temperatures at the "toe" of the well will exceed 442 degrees F (228 degrees C). Approximately 74 ft of core of the granitic and metamorphic rocks that will form the FORGE reservoir was also recovered.

15 GEOTHERMAL ENERGY↗

DOE OSTI2020

Cybersecurity for Distance Relay Protection

This project is a DOE follow-up effort on the CREDC workshop held on September 13, 2018 in Cambridge, MA to discuss cybersecurity of distance relays, which considered the benefits, vulnerabilities and risk mitigations for the use of communication systems in power system protection. The objectives of this project are to define the taxonomy of relay protection and associated communications; define use cases describing approaches to reduce the cyber-attack surface on those protective relays; and evaluate the loss of operational functional capability from changes to communication coverage. Mitigating controls will also be evaluated to understand if there are other approaches to reduce attack surfaces while maintaining communications or partial communications. Distance relays are used to protect transmission lines of approximately 10 to 300 miles in length, by detecting short circuits (i.e., faults) on the lines and then tripping circuit breakers in the substation. Such protection systems are a subset of the power system and they incorporate sensing, logic and communication functions. Protection system exposure to cyberattack could be drastically limited by disconnecting relays from all vulnerable communication systems, but this may adversely impact overall power system performance in the absence of cyberattack. This project began with a use case analysis of protection systems with communications, as summarized in this report. It continued with modeling, testing and evaluation in a miniature power system (MPS), located in the Western Area Power Administration (WAPA) Electric Power Training Center (EPTC). The project also incorporated feedback from two industry meetings held in February and September 2019. The suggested next steps account for and complement the work already underway with DOE/CESER funding: 1. Study the performance of LCD and PC vs. PUTT, which is less reliant on communication system performance and GPS timing references. The PUTT scheme could prove to be more resilient to cyberattack or communications-related disruption. It could also be more tolerant of message re-routing with SDN/SDR communication systems. On the other hand, it will be more vulnerable to false tripping during dynamic events or to loss of the voltage signal. The optimum choice of scheme may depend on the specific power system and risk assessment. This study could provide a new template for evaluation based on business functions. 2. Research and develop new methods to detect and monitor distributed physical attacks, possibly using drones, video sensors, thermal sensors, machine learning and other advanced techniques. This will help mitigate the impact of cyberattack on the protection system, and will also help mitigate the impact of wild fires. 3. Implement a scalable PKI for use in electric utility protection systems. This will encourage widespread adoption of secure authentication methods that are already available, but not widely used at present. This will help secure engineering access to the relays. 4. Investigate the use of SDN in combination with SDR to achieve better cybersecurity and electromagnetic security of the network, incorporating path variability. This would help secure both engineering access and peer-to-peer GOOSE messaging. 5. Perform additional testing, with operator evaluation of “red button” scenarios, PUTT vs. LCD, relay mis-operations, and other cyberattacks in the EPTC. This is an important advantage of testing in the EPTC rather than by computer simulation or even hardware-in-the-loop simulation; the EPTC is already dedicated to managing the situational awareness, operator response times and other human impacts. One of the project objectives was to settle on a common nomenclature for this problem space. We have concluded that the OSI layer model, supplemented by ANSI device numbers and other IEEE standards, is already well-accepted by the industry. The IEEE PSRC knowledge base provides a great deal of public information

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2023

Analysis of backwash settings to maximize net water production in an engineering-scale ultrafiltration system for water reuse

Ultrafiltration (UF) has been widely utilized as water pretreatment for different applications especially in water reuse. The UF system operation is characterized by a filtration phase, where particles accumulate on the membrane surface resulting in an increase in the transmembrane pressure (TMP) and a cleaning phase, where foulants are removed through cleaning cycles including physical backwash and chemical-enhanced backwash (CEB). In this study, data from an engineering-scale UF system treating reclaimed wastewater were used to assess the impact of backwashing on the filtration process. TMP backwash trigger, backwash duration, and CEB frequency were purposely varied for a cycle-by-cycle investigation on the net water production, water recovery, initial operating TMP, and filtration cycle duration. As the TMP backwash trigger was varied between 62 and 145kPa, the maximum net water production (63 m 3 /d) was achieved at 103kPa and water recovery remained relatively constant at approximately 92%. Backwash durations of 45, 65, and 85s were performed where both net water production and water recovery yielded similar results (~63 m 3 /d and ~ 91%) compared with 103kPa TMP backwash trigger. The CEB frequency was also lowered from one every three backwashes (1/3) to 1/6 and 1/12 and resulted in decreased net water production and water recovery while the initial TMP increased. Interestingly, the total number of CEBs remained approximately constant regardless of their frequency. In conclusion, results suggest that CEB is an important fouling control process to maximize water production.

42 ENGINEERING↗

DOE OSTI2026

Small-𝑥 asymptotics of the leading-twist flavor-singlet quark TMDs

In this paper, we investigate the small-𝑥 behavior of the flavor-singlet, leading-twist quark transverse-momentum-dependent parton distribution functions (TMDs) using the light-cone operator treatment. This formalism allows us to express TMD operators at small 𝑥 in terms of polarized dipole amplitudes, enabling a systematic approach to their small-𝑥 evolution. We derive the evolution equations for these TMDs and solve them within the large-𝑁 𝑐 approximation under the linearized, double-logarithmic approximation, where 𝑁 𝑐 represents the number of quark colors. Expanding on previous work on unpolarized and helicity TMDs, we present the small-𝑥 asymptotics for a comprehensive set of TMDs, including the Sivers function, helicity worm-gear, transversity, pretzelosity, Boer-Mulders, and transversity worm-gear distributions. Our results provide a complete picture of the small-𝑥 asymptotic behavior for all leading-twist flavor-singlet quark TMDs. We also discuss the implications of our findings for phenomenological applications and outline potential avenues for further research, particularly in understanding nonlinear effects and extending beyond the double-logarithmic approximation and large-𝑁 𝑐 approximations.

Adamiak, Daniel [Thomas Jefferson National Acceler↗

DOE OSTI2023

AutoReP: Automatic ReLU Replacement for Fast Private Network Inference

The proliferation of the Machine-Learning-As-A-Service (MLaaS) market has brought to light a number of clients’ data privacy and security concerns. One promising solution is private inference (PI) techniques using cryptographic primitives. These techniques often come with high computation and communication overhead associated with the non-linear operator such as ReLU. Several approaches have been developed in reducing the number of ReLU operations, however, they either require a heuristic threshold selection or introduce significant accuracy drop. This work presents AutoReP, a gradient-based framework for non-linear operators reduction that aims to mitigate these concerns from a systematic perspective. AutoReP automates the process of discrete selection of ReLU and polynomial functions on neurons to accelerate PI applications. We also introduce distribution-aware polynomial approximation (DaPa) to accurately approximate ReLUs under given distribution, preserving model expressivity. Our experimental results demonstrate significant accuracy improvements of 6.12% (94.31%, 12.9K ReLU budget, CIFAR-10), 8.39% (74.92%, 12.9K ReLU budget, CIFAR-100), and 9.45% (63.69%, 55K ReLU budget, Tiny-ImageNet) over current state-of-the-art methods, e.g., SNL. Morever, AutoReP is applied to EfficientNet-B2 on ImageNet dataset, and achieved 75.55% accuracy with 176.1 × ReLU budget reduction.

Peng, Hongwu↗

DOE OSTI2020

A Multi-Function AAA Algorithm Applied to Frequency Dependent Line Modeling

Modeling of power distribution system components that are valid for a wide range of frequencies are crucial for highly accurate modeling of electromagnetic transient (EMT) events. This has recently become of interest due to the improvements needed for the resilient operation of distribution systems. Vector fitting (VF) is a very popular and commonly used algorithm for wide band representations of power system components in EMT simulations. In this research, we present a new multi-input rational approximation algorithm (MIAAA) and illustrate its advantages with respect to VF using examples of approximations of admittance matrices discussed in the literature. We show that MIAAA not only outperforms VF in terms of achieving better accuracy using lesser number of poles, but also has no numerical issues achieving convergence. In contrast to VF, MIAAA is not sensitive to the location of input sample points and it does not require good estimates for the location of the desired approximation poles. The novelty of this research work is the use of recent mathematical results to solve existing challenges in distribution system modeling and to develop rational approximations for power system models that intend to be optimal in terms of accuracy and performance.

41 EE - Solar Energy Technologies Office (EE-4S)↗

DOE OSTI2024

SPBMI Microgrid

The SPBMI Microgrid Project aims to achieve four primary objectives that support. the tribe’s strategic goals, plans, and mission: 1) Ensure the availability of resilient energy for five essential tribal facilities as identified in the San Pasqual Hazard Mitigation Plan and described in the San Pasqual Energy & Resiliency Plan; 2) Provide solar generation sufficient to achieve net-zero energy consumption at the five essential facilities; 3) Reduce the tribe’s lifetime levelized costs of energy (LCOE); and 4) Support tribal energy objectives including reducing greenhouse gas emissions. Secondary objectives include supporting local workforce development and employment, in part by utilizing commercially available and warranted technologies that can be operated and maintained by tribal staff. Expected outcomes from the project include substantially eliminating long-duration disruptions to essential tribal services due to utility outages (which totaled 34 hours in 2017); reducing lifetime energy costs by approximately $1.75 million; and producing approximately 6.5 GWh of renewable electricity over the system’s lifetime.

14 SOLAR ENERGY↗

DOE OSTI2021

A MIMO AAA Agorithm for Frequency Dependent Line Modeling

AAA algorithm↗

DOE OSTI2022

Introduction of the Adding and Doubling Method for Solving Bateman Equations for Nuclear Fuel Depletion

This paper introduces and evaluates the Adding and Doubling Method (ADM) for solving the Bateman equations for depletion systems with varying numbers of nuclides and compares it to the Chebyshev Rational Approximation Method (CRAM), both implemented in the reactor physics analysis application Griffin. ADM, when applied to the Crank-Nicolson Finite Difference method, can produce results comparable in accuracy and precision to CRAM with comparable run times for systems with 35 or 297 nuclides. For systems with more than 300 nuclides, the matrix-matrix operations required by ADM are significantly more costly than the matrix-vector operations required by CRAM, making CRAM the more efficient method for systems with large numbers of nuclides. ADM is an accurate method that maintains other advantages over CRAM in that it does not depend on pre-generated coefficients or require complex number operations. ADM also manages to outperform CRAM by a factor of more than 250 in terms of run time for depletion systems that require multiple Bateman solves while the depletion matrix and time step size remain constant over all depletion intervals.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2023

Conjugate Heat Transfer Analysis in Pressurized Helium Gas Cooling Channels

Los Alamos National Laboratory (LANL) is working with NorthStar Medical Radioisotopes (NMR) on their efforts to produce Mo-99 from the irradiation of Mo-100 targets. The NMR target consists of an Inconel window that allows the electron beam to penetrate and irradiate a stack of Mo-100 disks. The irradiation process generates large amounts of heat and is cooled using pressurized helium gas flowing at 400 g/s. LANL provides both numerical analysis support and experimental support. Computational fluid dynamics (CFD) and conjugate heat transfer (CHT) analysis are performed on the NMR target to analyze the helium flow and volumetric heating through the NMR system. In this iteration of numerical analysis, we update the Mo-100 disk thickness to 0.74 mm and the gap between the Inconel window and the first disk to 0.69 mm. Estimates of the heat flux from the electron beams from Monte Carlo N-Particle code (MCNP) analysis were combined with CFD to perform the CHT analysis. The pressure drop through the targets, force applied on the first disk, beam window and target disk temperatures are some of the quantities estimated using the simulations. The pressure drop through the target was estimated as 0.198 MPa, while the force due to venturi effects across the first disk was estimated to be 100 N. The results show maximum window temperatures over 600 °C and peak disk temperatures over 1600 °C. Past work has shown that beyond 650-700 °C, the Inconel window becomes susceptible to yield and rupture. The increased temperature in these results reduces the margin of error possible on beam spot size. The disk temperatures showed a sinusoidal distribution with the 6 th – 8 th disk from each window exhibiting highest disk temperatures. The peak temperature of the stainless steel housing was close to 316 °C and that of the laminations and spacers was approximately 582 °C.

43 PARTICLE ACCELERATORS↗

DOE OSTI2020

Initial Radiation of Nuclear Power Plant Components (CRADA NFE-17-06892 Final Report)

As advanced reactor concepts are developed, instrumentation and control (I&C) cables and sensors will play a significant role in assuring their operation is well understood, and safety-related process information can be collected reliably over the course of their design life. As a first step to develop acceptance criteria and define the limits of currently available nuclear I&C cable and sensor technology, a collaboration between Oak Ridge National Laboratory and Analysis and Measurement Services (AMS) Corporation was initiated under the Gateway for Accelerated Innovation in Nuclear (GAIN) Program. This collaborative effort focused on providing technical information related to the combined thermal and radiation aging of nuclear power plant (NPP) cables, companion NPP cable insulation samples, and two prototype temperature and two pressure sensors. This work was carried out using the instrumented gamma irradiation system that is part of the High Flux Isotope Reactor Gamma Irradiation Facility (HFIR GIF). This system provided the opportunity for the condition of the prototype sensors to be tracked during the irradiation in order to determine their functional limits with greater granularity when compared to a simple irradiation insertion at the HFIRGIF. Experimental assemblies for sensor irradiation were successfully completed, and sensor irradiation to accumulated dose of 3000 kGy at a rate of approximately 6 kGy/hr was carried out. Two prototype temperature assemblies were continuously monitored during exposure to 3000 kGy and found to have no observable degradation from the irradiation. Two pressure sensors were first irradiated to 1000 kGy. At which point, one of the sensors was found to operate normally; however, a second sensor failed the operability test. The operable pressure sensor output was then continuously monitored from 1000 kGy to 3000 kGy. The sensor output exhibited steady trendable drift versus the accumulated radiation dose. At the conclusion of the irradiation, the four test sensors were released for laboratory calibration checks. The calibration check of the temperature sensors found no significant change after irradiation compared to baseline measurements before irradiation; however, both pressure sensors failed the post-test calibration checks and both sensors were not functioning properly. These results will help inform sensor manufacturers and I&C design engineers of potential limitations of these types of sensors for use in high radiation environments associated with the compact configuration of new Small Modular Reactors (SMRs) such as NuScale’s reactor power module. Irradiations on NPP cables and companion samples were not completed due to programmatic delays, however a path forward that was based on lessons learned from this project was defined to accommodate future, comparable instrumented gamma irradiations at the HFIR GIF.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2022

A Retrospective Analysis of Distributed Solar Interconnection Timelines and Related State Mandates

Most distributed residential photovoltaic (PV) systems must secure an interconnection agreement prior to operation that ensures the local electrical system will operate safely within the broader electrical grid. PV installers generally submit an interconnection application to the local utility that provides all the necessary details the utility needs to evaluate the proposed system. To encourage timely execution of this process, many states’ utility commissions have established mandates that limit the maximum number of days allowed for utility review and approval of interconnection for certain small, often residential applications. In this paper, we derive the median and range of cycle times for the pre-installation approval phase of the interconnection process (i.e., from application submission to approval by the utility) across 24 U.S. states, using a data set of approximately 170,000 projects. We evaluate the percentage of projects that are approved within respective state-mandated timelines from 2017– 2019. We further evaluate how timelines have evolved since 2012 for a subset of five states: Arizona, California, Colorado, New Jersey, and New York. The analyses are divided into two size ranges: systems that are ≤10 kilowatts (kW), and systems that are 11–50 kW.

14 SOLAR ENERGY↗

DOE OSTI2023

Advancements in High-Q development for novel medium-velocity 644 MHz 5-cell elliptical superconducting RF cavities for continuous-wave operation in heavy-ion linacs

The Facility for Rare Isotope Beams is a world-leading center for experimental nuclear physics research, and relies on a first-in-kind superconducting RF driver linac to supply 400 kW beams of a uniquely large range of particles, from protons through the heaviest uranium ions. The FRIB400 project proposes to double the end energy of the current superconducting FRIB linac for the heaviest uranium ions from 200 MeV per nucleon (MeV/u) to 400 MeV/u, which equates to approximately 1 GeV for protons. The increased rare isotope production from higher-energy drive beams would deliver new and exciting capabilities to FRIB users, which include extending the facility's reach along the neutron drip-line, greatly increasing the facility's rare isotope yield, and significantly improving the precision of parameter measurements for the nuclear matter equation of state, which is a particularly timely complement to the recent advent of multi-messenger astronomy, and the study of neutron star mergers. The unique set of design parameters defined by the 400 MeV/u (uranium) energy goal, the physical size, continuous-wave operation, and cryogenic capacity of the extant facilities at FRIB, requires development of a first-in-kind beta = v/c = 0.65, 644 MHz 5-cell elliptical superconducting RF (SRF) cavity, with field-leading efficiency, measured by the cavity's intrinsic quality factor, Q_0. The field of SRF has recently experienced a very active period of development, which demonstrated the potential to raise the Q_0 of 1.3 GHz cavities by factors of two to three or more. In addition to uncovering fascinating new properties of the fundamental physics of superconducting RF phenomena, these improvements suggest substantial improvements could be made over the minimum Q_0 of the proposed FRIB400 upgrade SRF cavities, if these new techniques can be adapted to the beta = 0.65, 644 MHz regime. This work presents the first validation of the the novel beta = 0.65, 644 MHz 5-cell elliptical superconducting RF cavity design, and the first results of both conventional and advanced RF surface preparation techniques. In particular, this work focuses on two recently-developed high-Q_0 recipes: N-doping, and furnace baking, setting the current world-record Q_0 for this type of resonant cavity at 3.8 x 10^10 at the FRIB400 operating gradient of 17.5 MV/m. We also find evidence that these results may be further improved upon, and make the case for further RF surface preparation recipe optimization. We then pair these high-power RF investigations with techniques borrowed from material science to try to better understand the ways in which specific properties of the niobium material, such as grain structure and superconducting flux pinning force, can be related to its superconducting RF performance. These experiments better elucidate the effects of high-temperature annealing on niobium samples, which suggest methods of further optimizing cavity flux expulsion and thus SRF performance.Read

McGee, Kellen E.↗

DOE OSTI2022

Conductive Ink with Circular Life Cycle for Printed Electronics

Electronic waste carries energetic costs and an environmental burden rivaling that of plastic waste due to the rarity and toxicity of the heavy-metal components. Recyclable conductive composites are introduced for printed circuits formulated with polycaprolactone (PCL), conductive fillers, and enzyme/protectant nanoclusters. Circuits can be printed with flexibility (breaking strain ≈80%) and conductivity (≈2.1 × 10 4 S m -1 ). These composites are degraded at the end of life by immersion in warm water with programmable latency. Approximately 94% of the functional fillers can be recycled and reused with similar device performance. The printed circuits remain functional and degradable after shelf storage for at least 7 months at room temperature and one month of continuous operation under electrical voltage. Here, the present studies provide composite design toward recyclable and easily disposable printed electronics for applications such as wearable electronics, biosensors, and soft robotics.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Uncertainty propagation in feed-forward neural network models

We develop new uncertainty propagation methods for feed-forward neural network architectures with leaky ReLU activation functions subject to random perturbations in the input vectors. In particular, we derive analytical expressions for the probability density function (PDF) of the neural network output and its statistical moments as a function of the input uncertainty and the parameters of the network, i.e., weights and biases. A key finding is that an appropriate linearization of the leaky ReLU activation function yields accurate statistical results even for large perturbations in the input vectors. This can be attributed to the way information propagates through the network. We also propose new analytically tractable Gaussian copula surrogate models to approximate the full joint PDF of the neural network output. To validate our theoretical results, we conduct Monte Carlo simulations and a thorough error analysis on a multi-layer neural network representing a nonlinear integro-differential operator between two polynomial function spaces. Our findings demonstrate excellent agreement between the theoretical predictions and Monte Carlo simulations.

MLP networks↗

DOE OSTI2023

Nonlinear nanomechanical resonators approaching the quantum ground state

It is an open question whether mechanical resonators can be made nonlinear with vibrations approaching the quantum ground state. This requires the engineering of a mechanical nonlinearity far beyond what has been realized so far. Here we discover a mechanism to boost the Duffing nonlinearity by coupling the vibrations of a nanotube resonator to single-electron tunnelling and by operating the system in the ultrastrong-coupling regime. We find that thermal vibrations become highly nonlinear when lowering the temperature. The average vibration amplitude at the lowest temperature is 13 times the zero-point motion, with approximately 42% of the thermal energy stored in the anharmonic part of the potential. Our work may enable the realization of mechanical Schrödinger cat states, mechanical qubits and quantum simulators emulating the electron–phonon coupling.

36 MATERIALS SCIENCE↗