Applying Dynamical Systems Theory to Improve Analysis of Time Series Transcriptional Data from Bioproduction Processes
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09 BIOMASS FUELS↗
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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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Dynamic System Scaling Applied to Zr-4 Cladding under RIA Conditions
The research and development lifecycle for new fuel designs currently has an ideal 20-25 year timeline. Efforts are currrently underway to accelerate fuel design and development using high performance fuel modeling codes and reduced scale experiments with new instrumentation techniques. However current tools available require a full scale prototype to be designed and tested for fuel qualification. The thermal-hydraulics community has leveraged scaling methodologies to use reduced scale integral effect test facilities (Westinghouse AP600/1000, NuScale Power Module) in lieu of building full scale prototypes for reactor design certification. Dynamic System Scaling (DSS) is a recent development to scaling methodologies that enable the tracking and quantification of dynamic scaling distortions experienced throughout a transient. Recent TREAT experiments performed reactivity initiated accident (RIA) pulses on UO2 fuel rodlets in Zr-4 cladding and were accompanied by BISON predictions for the cladding temperature. DSS is applied to pyrometer data of outer cladding temperatures and two BISON predictions after peak cladding temperature has been reached. One BISON case uses a constant gap conductance value between the fuel and cladding and the other using a conventional gap conductance model. Results from the DSS analysis show that there is good agreement between both BISON predictions and the experimental data and that there is not a significant distortion seen between using either gap conductance model.
11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
Theoretical Development of Controller Transfer applied to Dynamical Systems
Data-driven control strategies suffer from the necessity of training and its associated computational time and cost. This motivates the continuous increase of popularity of transfer learning based methods. In this paper, we have investigated transfer learning in the context of controller for dynamical systems. First, we have derived conditions under which controller can be transferred between two linear dynamical systems. Furthermore, we have introduced a novel algorithm to design the transferable and non-transferable control components for linear systems. Secondly, we have derived conditions under which a stabilizing controller can be transferred between two different nonlinear dynamical systems. Furthermore, we have used the notion of zero dynamics to transform the nonlinear dynamics into global normal form, to derive the transferability conditions on the controller. Finally, we have numerically evaluated the performance of our transfer learning based methods for two sets of example linear and nonlinear dynamical systems.
Chakraborty, Indrasis↗
An ideal MHD δW stability analysis that bypasses the Newcomb equation
In the following work, we demonstrate the efficacy of a Riccati δW ideal MHD stability analysis that bypasses the numerically intractable integration of the Newcomb equation. By transforming the linear Newcomb equation into a quadratic Riccati equation, an accurate and equivalent δW analysis is performed that is shown to enjoy some numerical advantages. Additionally, we demonstrate that the Riccati approach is better conditioned than its Newcomb counterpart at the magnetic axis, and we apply dynamical systems insights to examine its behavior at singular points. We further discuss the constraints involved in solving for the extremal admissible perturbations of a δW analysis.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Dynamics Informed Optimization for Resilient Energy Systems
Optimal mitigation planning for highly disruptive contingencies to a transmission-level power system requires optimization with dynamic power system constraints, due to the key role of dynamics in system stability to major perturbations. We formulate a generalized disjunctive program to determine optimal grid component hardening choices for protecting against major failures, with differential algebraic constraints representing system dynamics (specifically, differential equations representing generator and load behavior and algebraic equations representing instantaneous power balance over the transmission system). We optionally allow stochastic optimal pre-positioning across all considered failure scenarios, and optimal emergency control within each scenario. This novel formulation allows, for the first time, analyzing the resilience interdependencies of mitigation planning, preventive control, and emergency control. Using all three strategies in concert is particularly effective at maintaining robust power system operation under severe contingencies, as we demonstrate on the Western System Coordinating Council (WSCC) 9-bus test system using synthetic multi-device outage scenarios. Towards integrating our modeling framework with real threats and more realistic power systems, we explore applying hybrid dynamics to power systems. Our work is applied to basic RL circuits with the ultimate goal of using the methodology to model protective tripping schemes in the grid. Finally, we survey mitigation techniques for HEMP threats and describe a GIS application developed to create threat scenarios in a grid with geographic detail.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Surrogate Aerodynamics Modeling Applied to Surrogate Structural Dynamical Systems.
Abstract not provided.
Smith, Jonathan↗
Real-time spin systems from lattice field theory
We construct a lattice field theory method for computing the real-time dynamics of spin systems in a thermal bath. This is done by building on previous work of Takano with Schwinger-Keldysh and functional differentiation techniques. We derive a Schwinger-Keldysh path integral for generic spin Hamiltonians, then demonstrate the method on a simple system. Our path integral has a sign problem, which generally requires exponential run time in the system size, but requires only linear storage. The latter may place this method at an advantage over exact diagonalization, which is exponential in both. Our path integral is amenable to contour deformations, a technique for reducing sign problems.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Construction of approximate invariants for nonintegrable Hamiltonian systems
We present a method to construct high-order polynomial approximate invariants (AI) for nonintegrable Hamiltonian dynamical systems and apply it to a modern ring-based particle accelerator. Taking advantage of a special property of one-turn transformation maps expressed as square matrices, AIs can be constructed order by order iteratively. Evaluating AI with simulation data, we observe that AI’s fluctuation is actually a measure of chaos. Through minimizing the fluctuations, the stable region of long-term motions, i.e., the dynamic aperture of the accelerator, could be enlarged.
36 MATERIALS SCIENCE↗
Construction of approximate invariants for non-integrable Hamiltonian systems
We present a method to construct high-order polynomial approximate invariants (AI) for non integrable Hamiltonian dynamical systems, and apply it to a modern ring-based particle accelerator. Taking advantage of a special property of one-turn transformation maps in the form of a square matrix, AIs can be constructed order-by-order iteratively. Evaluating AI with simulation data, we observe that AI’s fluctuation is actually a measure of chaos. Through minimizing the fluctuations, the stable region of long-term motions, i.e., the dynamic aperture of the accelerator, could be enlarged.
43 PARTICLE ACCELERATORS↗
Stage-local partitioned two-step runge-kutta methods for large systems of ordinary differential equations
We introduce stage-local partitioned two-step Runge-Kutta methods are an extension of standard two-step Runge-Kutta methods, which are an alternative to the standard additive two-step Runge-Kutta methods currently existing in the literature. Furthermore, these new schemes are designed with an eye towards truly N-partitioned systems and leverage local stage approximations to make several computationally interesting approximations viable. Specifically, the focus on local stage approximations makes possible the construction of truly asynchronous schemes, in the parallel sense, possible. In addition, we show that an implicit-explicit approach to these schemes can lead to methods that require the inversion of only local nonlinear systems.
Applied Dynamical Systems↗
Quantum Algorithm for Linear Non-unitary Dynamics with Near-Optimal Dependence on All Parameters
We introduce a family of identities that express general linear non-unitary evolution operators as a linear combination of unitary evolution operators, each solving a Hamiltonian simulation problem. This formulation can exponentially enhance the accuracy of the recently introduced linear combination of Hamiltonian simulation (LCHS) method [An, Liu, and Lin, Physical Review Letters, 2023]. For the first time, this approach enables quantum algorithms to solve linear differential equations with both optimal state preparation cost and near-optimal scaling in matrix queries on all parameters.
Applied Dynamical Systems↗
Operator inference for non-intrusive model reduction with quadratic manifolds
This paper proposes a novel approach for learning a data-driven quadratic manifold from high-dimensional data, then employing this quadratic manifold to derive efficient physics-based reduced-order models. The key ingredient of the approach is a polynomial mapping between high-dimensional states and a low-dimensional embedding. This mapping consists of two parts: a representation in a linear subspace (computed in this work using the proper orthogonal decomposition) and a quadratic component. The approach can be viewed as a form of data-driven closure modeling, since the quadratic component introduces directions into the approximation that lie in the orthogonal complement of the linear subspace, but without introducing any additional degrees of freedom to the low-dimensional representation. Combining the quadratic manifold approximation with the operator inference method for projection-based model reduction leads to a scalable non-intrusive approach for learning reduced-order models of dynamical systems. Further, applying the new approach to transport-dominated systems of partial differential equations illustrates the gains in efficiency that can be achieved over approximation in a linear subspace.
42 ENGINEERING↗
Deterministic Dual Dynamic Programming Applied to Optimal Power System Restoration
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Engineering - Electronic and electrical engineerin↗
Applying Quantum Computing to Simulate Power System Dynamics
Power system dynamics are generally modeled by high dimensional nonlinear differential-algebraic equations due to a large number of generators, loads, and transmission lines. Thus, its computational complexity grows exponentially with the system size. This paper demonstrates the potential use of quantum computing algorithms to model the power system dynamics. Leveraging a symbolic programming framework, we equivalently convert the power system dynamics’ differential algebraic equations (DAEs) into ordinary differential equations (ODEs), where the data of the state vector can be encoded into quantum computers via amplitude encoding. The system's nonlinearity is captured by Taylor polynomial expansion, the quantum state tensor, and Hamiltonian simulation, whereas state variables can be updated by a quantum linear equation solver. Our results show that quantum computing can simulate the dynamics of the power system with high accuracy, whereas its complexity is polynomial in the logarithm of the system dimension. Our work also illustrates the use of scientific machine learning tools for implementing scientific computing concepts, e.g., Taylor expansion, DAEs/ODEs transform, and quantum computing solver, in the field of power engineering.
Tran, Huynh↗
Heisenberg spin chain as a worldsheet coordinate for lightcone quantized string
Although the energy spectrum of the Heisenberg spin chain on a circle defined by H = 1 4 Σ k = 1 M σ k x σ k + 1 x + σ k y σ k + 1 y + Δ σ k z σ k + 1 z is well known for any fixed M, the boundary conditions vary according to whether Mϵ 4N + r, where r = -1,0,1,2, and also according to the parity of the number of overturned spins in the state, In string theory all these cases must be allowed because interactions involve a string with M spins breaking into strings with M 1 < M and M - M 1 spins (or vice versa). We organize the energy spectrum and degeneracies of H in the case Δ = 0 where the system is equivalent to a system of free fermions. In spite of the multiplicity of special cases, in the limit M → ∞ the spectrum is that of a free compactified worldsheet field. Such a field can be interpreted as a compact transverse string coordinate x(σ) ≡ x(σ) + R 0 . We construct the bosonization formulas explicitly in all separate cases, and for each sector give the Virasoro conformal generators in both fermionic and bosonic formulations. Furthermore from calculations in the literature for selected classes of excited states, there is strong evidence that the only change for Δ ≠ 0 is a change in the compactification radius R 0 → R Δ . As Δ→ -1 this radius goes to infinity, giving a concrete example of noncompact space emerging from a discrete dynamical system. Finally we apply our work to construct the three string vertex implied by a string whose bosonic coordinates emerge from this mechanism.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Preconditioning for Hyper-reduction in Reduced Order Models
Many projection-based reduced order models (pROM) that utilize the governing equation and data to accelerate physical simulations can be applied to nonlinear dynamical systems. To avoid full order model (FOM) scale update for each time step, hyperreduction techniques are developed to sample high dimensional nonlinear terms. Our study aims to investigate if preconditioning the least-squares problem used for the nonlinear approximation can improve the robustness of the condition number of the problem while achieving high accuracy. In our study, we use the row-normalization matrix motivated by the Christoffel function as the preconditioner and solve the corresponding weighted least-squares problem. Numerical results for Lagrangian hydrodynamics examples are analyzed to explore how the preconditioner works compared to existing hyper-reduction techniques.
97 MATHEMATICS AND COMPUTING↗
Monitoring the daily evolution and extent of snow drought
Abstract. Snow droughts are commonly defined as below-average snowpack at a point in time, typically 1 April in the western United States (wUS). This definition is valuable for interpreting the state of the snowpack but obscures the temporal evolution of snow drought. Borrowing from dynamical systems theory, we applied phase diagrams to visually examine the daily evolution of snow water equivalent (SWE) and accumulated precipitation conditions in maritime, intermountain, and continental snow climates in the wUS using station observations as well as spatially distributed estimates of SWE and precipitation. Using a percentile-based drought definition, phase diagrams of SWE and precipitation highlighted decision-relevant aspects of snow drought such as onset, evolution, and termination. The phase diagram approach can be used in tandem with spatially distributed estimates of daily SWE and precipitation to reveal variability in snow drought type and extent. When combined with streamflow or other environmental data, phase diagrams and spatial estimates of snow drought conditions can help inform drought monitoring and early warning systems and help link snow drought type and evolution to impacts on ecosystems, water resources, and recreation. A web tool is introduced allowing users to create real-time or historic snow drought phase diagrams.
54 ENVIRONMENTAL SCIENCES↗
Building a Prospective LCA Framework to Analyze Emerging Technologies in a Dynamic System Context
NREL's Lifecycle Analysis Integration into Opensource Numerical models (LiAISON) framework computes temporally explicit life cycle impacts and resource uses for specific technologies (foreground) in a dynamic system context (background). LiAISON computes results for a series of environmental mid-points enabling an analysis of prospective tradeoffs of emerging technologies toward 2100. This prospective feature is of critical importance when analyzing present-day emerging technologies whose large-scale impacts during deployment phases will occur in different, future system contexts. LiAISON systematically accounts for dynamic system changes by applying an integrated background of the future energy-economy-land-climate system, generated by exogenous integrated assessment models (IAMs). Using IAM scenarios, LiAISON generates a time-series of life cycle inventory (LCI) databases, which are then used to calculate the impacts per functional unit per time step. This expands current practice of using static, future system assumptions, e.g., a specific grid-mix each year. Further, IAM scenarios are provided in a standardized format of shared-socioeconomic pathways (SSP) and representative concentration pathways (RCP) combinations. These are coherent, regularly, published, and peer-reviewed scenario combinations that establish a reproducible and standardized societal and climate mitigation futures context. They are comparable across IAMs and expand the system boundary of the traditional LCA by including dimensions such as societal and behavioral changes. We apply the framework to assess two emerging Power-to-Hydrogen processes, high temperature electrolysis using solid oxide fuel cell (HT-SOE) and polymer electrolyte membrane electrolysis (PEME). We compare the technologies to a baseline Hydrogen production process via steam methane reforming. Despite the decarbonized electricity systems' beneficial effects on the PtH2 processes' carbon intensities, we find environmental tradeoffs, which require technology improvements via learning-by-doing to be alleviated. Future work via ongoing collaborations will focus on linking the framework to other energy-economy-land-climate models and open-source life cycle inventory databases.
ENERGY PLANNING, POLICY, AND ECONOMY↗