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At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Data-Driven Learning for the Mori--Zwanzig Formalism: A Generalization of the Koopman Learning Framework

A theoretical framework which unifies the conventional Mori--Zwanzig formalism and the approximate Koopman learning of deterministic dynamical systems from noiseless observation is presented. In this framework, the Mori--Zwanzig formalism, developed in statistical mechanics to tackle the hard problem of construction of reduced-order dynamics for high-dimensional dynamical systems, can be considered as a natural generalization of the Koopman description of the dynamical system. We next show that, similar to the approximate Koopman learning methods, data-driven methods can be developed for the Mori--Zwanzig formalism with Mori's linear projection operator. We have developed two algorithms to extract the key operators, the Markov and the memory kernel, using time series of a reduced set of observables in a dynamical system. We have adopted the Lorenz `96 system as a test problem and solved for the above operators. These operators exhibit complex behaviors, which are unlikely to be captured by traditional modeling approaches in Mori--Zwanzig analysis. The nontrivial generalized fluctuation-dissipation relationship, which relates the memory kernel with the two-time correlation statistics of the orthogonal dynamics, was numerically verified as a validation of the solved operators. Here we present numerical evidence that the generalized Langevin equation, a key construct in the Mori--Zwanzig formalism, is more advantageous in predicting the evolution of the reduced set of observables than the conventional approximate Koopman operators.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Koopman-based Differentiable Predictive Control for the Dynamics-Aware Economic Dispatch Problem

The dynamics-aware economic dispatch (DED) problem embeds low-level generator dynamics and operational constraints to enable near real-time scheduling of generation units in a power network. DED produces a more dynamic supervisory control policy than traditional economic dispatch (T-ED) that reduces overall generation costs. However, the incorporation of differential equations that govern the system dynamics makes DED an optimization problem that is computationally prohibitive to solve. In this work, we present a new data-driven approach based on differentiable programming to efficiently obtain offline parametric solutions to the underlying DED problem. In particular, we employ the recently proposed differentiable predictive control (DPC) for offline learning of explicit neural control policies based on identified Koopman operator (KO) model of the system dynamics. We demonstrate the high solution quality and five orders of magnitude computational-time savings of the DPC method over the original optimization-based DED approach on a 9-bus test power grid network.

King, Ethan↗
DOE OSTI2021

Bilinear dynamic mode decomposition for quantum control

Abstract Data-driven methods for establishing quantum optimal control (QOC) using time-dependent control pulses tailored to specific quantum dynamical systems and desired control objectives are critical for many emerging quantum technologies. We develop a data-driven regression procedure, bilinear dynamic mode decomposition (biDMD), that leverages time-series measurements to establish quantum system identification for QOC. The biDMD optimization framework is a physics-informed regression that makes use of the known underlying Hamiltonian structure. Further, the biDMD can be modified to model both fast and slow sampling of control signals, the latter by way of stroboscopic sampling strategies. The biDMD method provides a flexible, interpretable, and adaptive regression framework for real-time, online implementation in quantum systems. Further, the method has strong theoretical connections to Koopman theory, which approximates nonlinear dynamics with linear operators. In comparison with many machine learning paradigms minimal data is needed to construct a biDMD model, and the model is easily updated as new data is collected. We demonstrate the efficacy and performance of the approach on a number of representative quantum systems, showing that it also matches experimental results.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Data-driven learning of Mori–Zwanzig operators for isotropic turbulence

Developing reduced-order models for turbulent flows, which contain dynamics over a wide range of scales, is an extremely challenging problem. In statistical mechanics, the Mori–Zwanzig (MZ) formalism provides a mathematically exact procedure for constructing reduced-order representations of high-dimensional dynamical systems, where the effects due to the unresolved dynamics are captured in the memory kernel and orthogonal dynamics. Turbulence models based on MZ formalism have been scarce due to the limited knowledge of the MZ operators, which originates from the difficulty in deriving MZ kernels for complex nonlinear dynamical systems. In this work, we apply a recently developed data-driven learning algorithm, which is based on Koopman's description of dynamical systems and Mori's linear projection operator, on a set of fully resolved isotropic turbulence datasets to extract the Mori–Zwanzig operators. With data augmentation using known turbulence symmetries, the extracted Markov term, memory kernel, and orthogonal dynamics are statistically converged and the generalized fluctuation–dissipation relation can be verified. The properties of the memory kernel and orthogonal dynamics, and their dependence on the choices of observables are investigated to address the modeling assumptions that are commonly used in MZ-based models. A series of numerical experiments are then constructed using the extracted kernels to evaluate the memory effects on prediction. The results show that the prediction errors are strongly affected by the choice of observables and can be further reduced by including the past history of the observables in the memory kernel.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Model-Agnostic Algorithm for Real-Time Attack Identification in Power Grid using Koopman Modes

Malicious activities on measurements from sensors like Phasor Measurement Units (PMUs) can mislead the control center operator into taking wrong control actions resulting in disruption of operation, financial losses, and equipment damage. In particular, false data attacks initiated during power systems transients caused due to abrupt changes in load and generation can fool the conventional model-based detection methods relying on thresholds comparison to trigger an anomaly. In this paper, we propose a Koopman mode decomposition (KMD) based algorithm to detect and identify false data attacks in real-time. The Koopman modes (KMs) are capable of capturing the nonlinear modes of oscillation in the transient dynamics of the power networks and reveal the spatial embedding of both natural and anomalous modes of oscillations in the sensor measurements. The Koopman-based spatio-temporal nonlinear modal analysis is used to filter out the false data injected by an attacker. The performance of the algorithm is illustrated on the IEEE 68-bus test system using synthetic attack scenarios generated on GridSTAGE, a recently developed multivariate spatio-temporal data generation framework for simulation of adversarial scenarios in cyber-physical power systems.

Nandanoori, Sai Pushpak↗
DOE OSTI2020

Koopman–von Neumann approach to quantum simulation of nonlinear classical dynamics

Quantum computers can be used to simulate nonlinear non-Hamiltonian classical dynamics on phase space by using the generalized Koopman–von Neumann formulation of classical mechanics. The Koopman–von Neumann formulation implies that the conservation of the probability distribution function on phase space, as expressed by the Liouville equation, can be recast as an equivalent Schrödinger equation on Hilbert space with a Hermitian Hamiltonian operator and a unitary propagator. This Schrödinger equation is linear in the momenta because it derives from a constrained Hamiltonian system with twice the classical phase-space dimension. A quantum computer with finite resources can be used to simulate a finite-dimensional approximation of this unitary evolution operator. Quantum simulation of classical dynamics is exponentially more efficient than a deterministic Eulerian discretization of the Liouville equation if the Koopman–von Neumann Hamiltonian is sparse. Utilizing quantum walk techniques for state preparation and amplitude estimation for the calculation of observables leads to a quadratic improvement over classical probabilistic Monte Carlo algorithms.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Unitary representation of the Poincaré group for classical relativistic dynamics

We give a unitary irreducible representation of the proper Poincaré group that leads to an operational version of the classical relativistic dynamics of a massive spinless particle. Unlike quantum mechanics, in this operational theory there is no uncertainty principle between position and momentum. It will be shown that the theory contains the Koopman–von Neumann formalism as a particular case, and an explicit connection with relativistic Hamiltonian mechanics will be given.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Deep-Learning-Based Koopman Modeling for Online Control Synthesis of Nonlinear Power System Transient Dynamics

Power system stability and control have become more challenging due to the increasing uncertainty associated with renewable generation. Here, the performance of conventional control is highly driven by the physics-based offline-developed dynamic models that can deviate from the actual system characteristics under different operating conditions and/or configurations. Data-driven approaches based on online measurements can be a better solution to addressing these issues by capturing real-time operation conditions. This article describes a novel fully data-driven probabilistic framework to derive a linear representation of postcontingency grid dynamics and online prescribe control based on the derived model to enhance transient stability. The complex nonlinear power system dynamics is approximated by a linear model by using multiple neural network modules that infer distributions of the observations and introducing a Koopman layer to sample possible Koopman linear models from the inferred distributions. The trained model features linearity that can be easily incorporated into the existing linear control design paradigm and ease the controller design process. The effectiveness of Koopman-based control designs is validated through comparative case studies, which demonstrate increased prediction accuracy and control performance when applied to a power system with heterogeneous generator dynamics.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

Sludge Batch 10 Flowsheet Testing with Non-radioactive Simulants

Fourteen Chemical Processing Cell (CPC) simulations were performed with nonradioactive sludge simulants at the Aiken County Technology Laboratory in Aiken, SC. Four of these experiments were performed with Tank 51 sludge simulant. The remaining ten were performed with Tank 40 sludge simulant. The purpose of these experiments was to elucidate the chemistry and characteristics of Sludge Batch (SB) 10 as anticipated in the Defense Waste Processing Facility (DWPF). Experiments were performed at acid stoichiometries between 76% and 138% of the Koopman Minimum Acid requirement (85% - 144% of the Hsu acid requirement) and at REDuction/OXidation (REDOX) targets between 0.1 and 0.3. Testing examined the impact of coupled operations and sludge-only operations during Sludge Receipt and Adjustment Tank (SRAT) and Slurry Mix Evaporator (SME) processing at both design basis and nominal boilup rates. This report shares conclusions made as a result of this testing.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2022

Transition metal impurities in silicon: computational search for a semiconductor qubit

Abstract Semiconductors offer a promising platform for physical implementation of qubits, but their broad adoption is presently hindered by limited scalability and/or very low operating temperatures. Learning from the nitrogen-vacancy centers in diamond, our goal is to find equivalent optically active point defect centers in crystalline silicon, which could be advantageous for their scalability and integration with classical devices. Transition metal (TM) impurities in silicon are common paramagnetic deep defects, but a comprehensive theoretical study of the whole 3 d series that considers generalized Koopmans’ condition is missing. We apply the HSE06(+U) method to examine their potential as optically active spin qubits and identify seven TM impurities that have optically allowed triplet–triplet transitions within the silicon band gap. These results provide the first step toward silicon-based qubits with higher operating temperatures for quantum sensing. Additionally, these point defects could lead to spin-photon interfaces in silicon-based qubits and devices for mid-infrared free-space communications.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Nominal and adversarial synthetic PMU data for standard IEEE test systems

GridSTAGE (Spatio-Temporal Adversarial scenario GEneration) is a framework for the simulation of adversarial scenarios and the generation of multivariate spatio-temporal data in cyber-physical systems. GridSTAGE is developed based on Matlab and leverages Power System Toolbox (PST) where the evolution of the power network is governed by nonlinear differential equations. Using GridSTAGE, one can create several event scenarios that correspond to several operating states of the power network by enabling or disabling any of the following: faults, AGC control, PSS control, exciter control, load changes, generation changes, and different types of cyber-attacks. Standard IEEE bus system data is used to define the power system environment. GridSTAGE emulates the data from PMU and SCADA sensors. The rate of frequency and location of the sensors can be adjusted as well. Detailed instructions on generating data scenarios with different system topologies, attack characteristics, load characteristics, sensor configuration, control parameters are available in the Github repository - https://github.com/pnnl/GridSTAGE. There is no existing adversarial data-generation framework that can incorporate several attack characteristics and yield adversarial PMU data. The GridSTAGE framework currently supports simulation of False Data Injection attacks (such as a ramp, step, random, trapezoidal, multiplicative, replay, freezing) and Denial of Service attacks (such as time-delay, packet-loss) on PMU data. Furthermore, it supports generating spatio-temporal time-series data corresponding to several random load changes across the network or corresponding to several generation changes. A Koopman mode decomposition (KMD) based algorithm to detect and identify the false data attacks in real-time is proposed in https://ieeexplore.ieee.org/document/9303022. Machine learning-based predictive models are developed to capture the dynamics of the underlying power system with a high level of accuracy under various operating conditions for IEEE 68 bus system. The corresponding machine learning models are available at https://github.com/pnnl/grid_prediction.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2022

Dynamic mode decomposition with core sketch

With the increase in collected data volumes, either from experimental measurements or high fidelity simulations, there is an ever-growing need to develop computationally efficient tools to process, analyze, and interpret these datasets. Modal analysis techniques have gained great interest due to their ability to identify patterns in the data and extract valuable information about the system being considered. Dynamic mode decomposition (DMD) relies on elements of the Koopman approximation theory to compute a set of modes, each associated with a fixed oscillation frequency and a decay/growth rate. Extracting these details from large datasets can be computationally expensive due to the need to implement singular value decomposition of the input data matrix. Sketching algorithms have become popular in numerical linear algebra where statistical theoretic approaches are utilized to reduce the cost of major operations. A sketch of a matrix is another matrix, which is significantly smaller, but still sufficiently approximates the original system. We put forth an efficient DMD framework, SketchyDMD, based on a core sketching algorithm that captures information about the range and corange (their mutual relationship) of input data. The proposed sketching-based framework can accelerate various portions of the DMD routines, compared to classical methods that operate directly on the raw input data. We conduct numerical experiments using the spherical shallow water equations as a prototypical model in the context of geophysical flows. In conclusion, we show that the proposed SketchyDMD is superior to existing randomized DMD methods that are based on capturing only the range of the input data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2021

In Situ Performance of the Low Frequency Array for Advanced ACTPol

The Advanced Atacama Cosmology Telescope Polarimeter (AdvACT) is an upgrade for the Atacama Cosmology Telescope using Transition Edge Sensor (TES) detector arrays to measure cosmic microwave background (CMB) temperature and polarization anisotropies in multiple frequencies. The low frequency (LF) array was deployed early 2020. It consists of 292 TES bolometers observing in two bands centered at 27 GHz and 39 GHz. At these frequencies, it is sensitive to synchrotron radiation from our galaxy as well as to the CMB, and complements the AdvACT arrays operating at 90, 150 and 230 GHz. We present the initial LF array on-site characterization, including the time constant, optical efficiency and array sensitivity.

Superconducting detectors↗
NASA NTRS2016

The Atacama Cosmology Telescope: The Polarization-Sensitive ACTPol Instrument

The Atacama Cosmology Telescope (ACT) makes high angular resolution measurements of anisotropies in the Cosmic Microwave Background (CMB) at millimeter wavelengths. We describe ACTPol, an upgraded receiver for ACT, which uses feedhorn-coupled, polarization-sensitive detector arrays, a 3deg field of view, 100 mK cryogenics with continuous cooling, and meta material antireflection coatings. ACTPol comprises three arrays with separate cryogenic optics: two arrays at a central frequency of 148 GHz and one array operating simultaneously at both 97 GHz and 148 GHz. The combined instrument sensitivity, angular resolution, and sky coverage are optimized for measuring angular power spectra, clusters via the thermal Sunyaev-Zel'dovich (SZ) and kinetic SZ signals, and CMB lensing due to large-scale structure. The receiver was commissioned with its first 148 GHz array in 2013, observed with both 148 GHz arrays in 2014, and has recently completed its first full season of operations with the full suite of three arrays. This paper provides an overview of the design and initial performance of the receiver and related systems.

Telescope↗
DOE OSTI2024

The Simons Observatory: Design, Integration, and Testing of the Small Aperture Telescopes

The Simons Observatory (SO) is a cosmic microwave background survey experiment that includes small-aperture telescopes (SATs) observing from an altitude of 5200 m in the Atacama Desert in Chile. The SO SATs will cover six spectral bands between 27 and 280 GHz to search for primordial B-modes to a sensitivity of σ(r) = 0.002, with quantified systematic errors well below this value. Each SAT is a self-contained cryogenic telescope with a 35° field of view, 42 cm diameter optical aperture, 40 K half-wave plate, 1 K refractive optics, and <0.1 K focal plane that holds >12,000 transition edge sensor detectors. We describe the nominal design of the SATs and present details about the integration and testing for one operating at 93 and 145 GHz.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2026

An efficient explicit implementation of a near-optimal quantum algorithm for simulating linear dissipative differential equations

We propose an efficient block-encoding technique for the implementation of the Linear Combination of Hamiltonian Simulations (LCHS) for simulating dissipative initial-value problems. This algorithm approximates a target nonunitary operator as a weighted sum of Hamiltonian evolutions, thereby emulating a dissipative problem by mixing various time scales. We introduce an efficient encoding of the LCHS into a quantum circuit based on a simple coordinate transformation that turns the dependence on the summation index into a trigonometric function. Classically, this method is equivalent to the use of a highly accurate Fejér-Clenshaw-Curtis quadrature formula. Quantumly, this significantly simplifies block-encoding of a dissipative problem and allows one to perform an exponential number of Hamiltonian simulations by a single Quantum Signal Processing (QSP) circuit. The resulting LCHS circuit has high success probability and the selector scales logarithmically with the number of terms in the LCHS sum and linearly with time. Careful analysis of error convergence proves that this method is more efficient than other LCHS circuits that have recently appeared in the literature. We verify the quantum circuit and its scaling by simulating it on a digital emulator of fault-tolerant quantum computers and, as a test problem, solve the advection-diffusion equation. The proposed algorithm can be used for simulating a wide class of nonunitary initial-value problems including the Liouville equation with added dissipation and linear embeddings of nonlinear systems, such as the Koopman-von Neumann and Carleman embeddings.

Novikau, I [Lawrence Livermore National Laboratory↗
DOE OSTI2024

The Simons Observatory: Cryogenic half wave plate rotation mechanism for the small aperture telescopes

We present the requirements, design, and evaluation of the cryogenic continuously rotating half-wave plate (CHWP) for the Simons Observatory (SO). SO is a cosmic microwave background polarization experiment at Parque Astronómico de Atacama in northern Chile that covers a wide range of angular scales using both small (Ø0.42 m) and large (Ø6 m) aperture telescopes. In particular, the small aperture telescopes (SATs) focus on large angular scales for primordial B-mode polarization. To this end, the SATs employ a CHWP to modulate the polarization of the incident light at 8 Hz, suppressing atmospheric 1/f noise and mitigating systematic uncertainties that would otherwise arise due to the differential response of detectors sensitive to orthogonal polarizations. The CHWP consists of a 505 mm diameter achromatic sapphire HWP and a cryogenic rotation mechanism, both of which are cooled down to ~50 K to reduce detector thermal loading. Under normal operation, the HWP is suspended by a superconducting magnetic bearing and rotates with a constant 2 Hz frequency, controlled by an electromagnetic synchronous motor. We find that the number of superconductors and the number of magnets that make up the superconducting magnetic bearing are important design parameters, especially for the rotation mechanism’s vibration performance. The rotation angle is detected through an angular encoder with a noise level of 0.07 μrad √ $\overline{s}$. During a cooldown process, the rotor is held in place by a grip-and-release mechanism that serves as both an alignment device and a thermal path. In this paper, we provide an overview of the SO SAT CHWP: its requirements, hardware design, and laboratory performance.

47 OTHER INSTRUMENTATION↗