Search NASA⌕ Search

SEARCH · Search NASA

Results for “optimization, stochastic methods, complex systems”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

Stochastic self-tuning hybrid algorithm for reaction-diffusion systems

Many biochemical phenomena involve reactants with vastly different concentrations, some of which are amenable to continuum-level descriptions, while the others are not. We present a hybrid self-tuning algorithm to model such systems. The method combines microscopic (Brownian) dynamics for diffusion with mesoscopic (Gillespie-type) methods for reactions and remains efficient in a wide range of regimes and scenarios with large variations of concentrations. Furthermore, its accuracy, robustness, and versatility are balanced by redefining propensities and optimizing the mesh size and time step. We use a bimolecular reaction to demonstrate the potential of our method in a broad spectrum of scenarios: from almost completely reaction-dominated systems to cases where reactions rarely occur or take place very slowly. The simulation results show that the number of particles present in the system does not degrade the performance of our method. This makes it an accurate and computationally efficient tool to model complex multireaction systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2017

Reconfigurable Cellular Composite Structures for Lighter than Air Vehicles with Scalable Size and Endurance

Engineered non-stochastic cellular materials show promising characteristics on the laboratory scale,with nearly ideal specific stiffness and strength scaling at ultralight mass density. These propertiessuggest performance benefits in any application with combined stiffness and mass constraints, suchas air vehicles. We investigate here the application of re-configurable cellular composite materialsand structures to lighter than air vehicles. We describe the properties and applicability of these materials,provide an example analysis of governing loading conditions associated with airships, showan example optimization method for navigating the design space, and describe how recent advancesin cellular material manufacturing and reconfiguration enable system performance benefits includingnew concepts of operation. Lastly, we propose lighter than air vehicles that are assembled andmaintained in-flight, eliminating structural compromises associated with transitional flight modesand ground handling.Engineered non-stochastic cellular material properties suggest performance benefits in lighter than air vehicles due tostiffness and mass constraints that are intrinsic to the airship design problem. Recent advances in cellular materialmanufacturing and reconfiguration enable system performance benefits including new concepts of operation, such aslighter than air vehicles that are assembled and maintained in-flight, eliminating structural compromises associatedwith transitional flight modes and ground handling. Existing engineered cellular materials display properties allowinglarge large scale airships design as monocoque cellular solids. Inevitable improvements in cellular material propertiesand manufacturing will improve feasibility even further. Given the suggestion that the two most significant technologygaps exist across all current airship projects are manufacturing and assembly processes and ground handling [7],a strategy that encompasses construction and maintenance in flight could provide critical rephrasing of the systemdesign problem through these new concepts of operation. Refactoring of traditional manufacturing, operation, andservice process constraints could extend to other domains in aerospace systems and manufacturing in general.In future work, the complexity of the design task would benefit from a form of optimization in order to find themost suitable geometry for a chosen application. For example, the Sequential Least SQuares Programming (SLSQP)function from within the SciPy Minimize library is a multiobjective constrained optimization method that has beenapplied to fixed wing aircraft design. [17] In this situation it would allow for several objective functions such as drag,bending stiffness, buoyancy and cost of transport to be incorporated into a composite objective function.

Copplestone, Grace↗
DOE OSTI2024

A Distributionally Robust Optimization Framework for Stochastic Assessment of Power System Flexibility in Economic Dispatch

Given the complexity of power systems, particularly the high-dimensional variability of net loads, accurately depicting the entire operational range of net loads poses a challenge. To address this, recent methodologies have sought to gauge the maximum range of net load uncertainty across all buses. In this paper, we consider the stochastic nature of the net load and introduce a distributionally robust optimization framework that assesses system flexibility stochastically, accommodating a minimal extent of system violations. We verify the proposed method by solving the flexibility of the economic dispatch problem on four distinct IEEE standard test systems. Compared to traditional deterministic flexibility evaluations, our approach consistently yields less conservative flexibility outcomes.

distributionally robust optimization↗
DOE OSTI2017

RISK MONITORING CAPABILITES FROM DYNAMIC PRA DATA

Risk Monitors (RMs) are software tools that are employed in nuclear power plants to monitor the safety properties of the plant itself during operation. These safety properties are generated using classical PRA methods which are typically based on static Boolean structures such as Fault-Trees (FTs) and Event-Trees (ETs). The outcomes of these methods are Core Damage Frequency (CDF) and risk importance values of plant components (e.g., valves and pumps). Examples of Risk Importance Measures (RIMs) commonly used are: Risk Achievement Worth (RAW), Risk Reduction Worth (RRW), Birnbaum (B) and Fussell-Vesely (FV) [1,2]. In a RM these values are updated in real time once plant components status is updated (e.g., under maintenance, off-line, testing). In addition, RMs can be used to optimize maintenance schedules so those safety features of the plant are below plant standard values. This paper presents an approach to create temporal profiles of RIMs (i.e., RM capabilities) given a temporal change of the plant configuration. Instead of employing data generated by ETs and FTs, the proposed approach will employ data generated by Dynamic PRA methods. In contrast to classical PRA methods, Dynamic PRA methods couple stochastic methods with safety analysis codes to determine risk associate to complex systems such as nuclear plants. Compared to classical PRA methods, they can evaluate with higher resolution the safety impact of timing and sequencing of events on the accident progression. We will describe how classical RIMs can be generated by Dynamic PRA data and then we will show how the temporal profiles of the RIMs can be generated given a temporal profile of the system configuration.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

DiaMonD: An Integrated Multifaceted Approach to Mathematics at the Interfaces of Data, Models, and Decisions

For many problems in computational science and engineering, the so-called forward problem—solution of the underlying mathematical model to yield output quantities of interest, given input parameters—is difficult enough for frontier complex models, which are often characterized by coupled multiphysics and possibly stochastic behavior over a wide range of length and time scales. However, we face the need to move beyond the forward problem, to address what is often the ultimate goal of CS&E: decision making. This requires us to tackle a spectrum of mathematical problems that subsume, and are thus even more difficult than, the forward problem. First, given experimental data, we wish to estimate unknown parameters characterizing a model of a natural or engineered system by solving an inverse problem. Second, we seek the optimal configuration of the system (or experiments) by solving an optimal design problem. Third, the optimal operation of the system must be determined by solving an optimal control problem. And fourth, we must quantify uncertainties as they propagate through all of the preceding problems, from data to model inference to prediction and finally to optimal design and control. Optimal mathematical methods and algorithms for such end-to-end, data-to-decisions modeling and simulation of complex problems—requiring integrated solution of forward, inverse, optimization, and UQ problems for large, multiphysics, multiscale models—entails challenges of the highest order, while also presenting great opportunities for applied mathematics research. Unfortunately, research on forward, inverse, optimization, and UQ problems has all-too-often progressed in isolation. This has led to mathematical methods that perform well when considering the forward simulation in isolation, but are prohibitive or suboptimal or unstable when combined with other methods within the framework of inversion, optimization, or UQ. The reverse is also true: general-purpose methods developed within the inversion, optimization, and UQ fields often become prohibitive when applied to complex CS&E problems since they do not exploit their structure.

58 GEOSCIENCES↗
DOE OSTI2020

Methods for R&D Portfolio Analysis and Evaluation (Workshop Report)

The Workshop on Methods for R&D Portfolio Analysis and Evaluation convened on 17–18 July 2019 at the National Renewable Energy Laboratory in Golden, Colorado, and examined strengths and weaknesses of the various methodologies applicable to R&D portfolio modeling, analysis, and decision support, given pragmatic constraints such as data availability, uncertainties in estimating the impact of R&D spending, and practical operational overheads. Participants employed their deep expertise in approaches such as stochastic optimization, real options, Monte-Carlo analysis, Bayesian networks, decision theory, complex systems analysis, deep uncertainty, and technology-evolution modeling to critique the initial example models developed by the project’s core team and to conduct thought experiments grounded in real-life technology models, progress data, expert elicitation, and portfolio information. This engagement of participants’ methodological expertise with the practical requirements of real-life portfolio decision support yielded ideas for improved approaches, alternative methodological hypotheses, and hybridization of methodologies that are well-grounded theoretically, computationally sound, and realistically executable given data availability and other practical constraints.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2020

Methods for R&D Portfolio Analysis and Evaluation (Workshop Report)

The Workshop on Methods for R&D Portfolio Analysis and Evaluation convened on 17-18 July 2019 at the National Renewable Energy Laboratory in Golden, Colorado, and examined strengths and weaknesses of the various methodologies applicable to R&D portfolio modeling, analysis, and decision support, given pragmatic constraints such as data availability, uncertainties in estimating the impact of R&D spending, and practical operational overheads. Participants employed their deep expertise in approaches such as stochastic optimization, real options, Monte-Carlo analysis, Bayesian networks, decision theory, complex systems analysis, deep uncertainty, and technology-evolution modeling to critique the initial example models developed by the project’s core team and to conduct thought experiments grounded in real-life technology models, progress data, expert elicitation, and portfolio information. This engagement of participants’ methodological expertise with the practical requirements of real-life portfolio decision support yielded ideas for improved approaches, alternative methodological hypotheses, and hybridization of methodologies that are well-grounded theoretically, computationally sound, and realistically executable given data availability and other practical constraints.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2015

Improved Sampling Algorithms in the Risk-Informed Safety Margin Characterization Toolkit

The RISMC approach is developing advanced set of methodologies and algorithms in order to perform Probabilistic Risk Analyses (PRAs). In contrast to classical PRA methods, which are based on Event-Tree and Fault-Tree methods, the RISMC approach largely employs system simulator codes applied to stochastic analysis tools. The basic idea is to randomly perturb (by employing sampling algorithms) timing and sequencing of events and internal parameters of the system codes (i.e., uncertain parameters) in order to estimate stochastic parameters such as core damage probability. This approach applied to complex systems such as nuclear power plants requires to perform a series of computationally expensive simulation runs given a large set of uncertain parameters. These types of analysis are affected by two issues. Firstly, the space of the possible solutions (a.k.a., the issue space or the response surface) can be sampled only very sparsely, and this precludes the ability to fully analyze the impact of uncertainties on the system dynamics. Secondly, large amounts of data are generated and tools to generate knowledge from such data sets are not yet available. This report focuses on the first issue and in particular employs novel methods that optimize the information generated by the sampling process by sampling unexplored and risk-significant regions of the issue space: adaptive (smart) sampling algorithms. They infer system response from surrogate models constructed from existing samples and predict the most relevant location of the next sample. It is therefore possible to understand features of the issue space with a small number of carefully selected samples. In this report, we will present how it is possible to perform adaptive sampling using the RISMC toolkit and highlight the advantages compared to more classical sampling approaches such Monte-Carlo. We will employ RAVEN to perform such statistical analyses using both analytical cases but also another RISMC code: RELAP-7.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2024

Enhancing Distribution System Resilience: A First-Order Meta-RL Algorithm for Critical Load Restoration

The increasing frequency of extreme events and the integration of distributed energy resources (DERs) into modern grids have elevated the need for resilient and efficient critical load restoration strategies in distribution systems. However, the stochastic nature of renewable DERs, limited energy resource availability and the intricate nonlinearities inherent in complex grid control problem make the problem challenging. Although reinforcement learning (RL) and warm-start RL methods have shown promising results, their performance often falls short in rapidly adapting to new, unseen situations and typically requires exhaustive problem-specific tuning. To address these gaps, we propose a First-Order Meta-based RL (FOM-RL) algorithm within an online framework for adaptive and robust critical load restoration. By harnessing local DERs as the enabling technology, FOM-RL allows the RL agent to swiftly adapt to new unseen scenarios by leveraging previously acquired knowledge of different tasks. Experimental results provide evidence that proposed algorithm learns more efficiently and showcases generalization capabilities across diverse set of operational scenarios. Moreover, a rigorous theoretical analysis yields a tight sublinear regret bound, sensitive to temporal variability, with a task-averaged optimality gap bounded by O(VM+D*/(Tsquare root(M))). These results suggest that optimality improves with task similarity and an increased number of tasks M, reaffirming the efficacy and scalability of the proposed approach in addressing the complexities of critical load restoration in distribution systems.

complexity theory↗
DOE OSTI2018

Gradient-based optimization for regression in the functional tensor-train format

Predictive analysis of complex computational models, such as uncertainty quantification (UQ), must often rely on using an existing database of simulation runs. In this paper we consider the task of performing low-multilinear-rank regression on such a database. Specifically we develop and analyze an efficient gradient computation that enables gradient-based optimization procedures, including stochastic gradient descent and quasi-Newton methods, for learning the parameters of a functional tensor-train (FT). We compare our algorithms with 22 other nonparametric and parametric regression methods on 10 real-world data sets and show that for many physical systems, exploiting low-rank structure facilitates efficient construction of surrogate models. Here, we use a number of synthetic functions to build insight into behavior of our algorithms, including the rank adaptation and group-sparsity regularization procedures that we developed to reduce overfitting. Finally we conclude the paper by building a surrogate of a physical model of a propulsion plant on a naval vessel.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

A Large Deviations Analysis of Certain Qualitative Properties of Parallel Tempering and Infinite Swapping Algorithms

Parallel tempering, or replica exchange, is a popular method for simulating complex systems. The idea is to run parallel simulations at different temperatures, and at a given swap rate exchange configurations between the parallel simulations. From the perspective of large deviations it is optimal to let the swap rate tend to infinity and it is possible to construct a corresponding simulation scheme, known as infinite swapping. In this paper we propose a novel use of large deviations for empirical measures for a more detailed analysis of the infinite swapping limit in the setting of continuous time jump Markov processes. Using the large deviations rate function and associated stochastic control problems we consider a diagnostic based on temperature assignments, which can be easily computed during a simulation. Here we show that the convergence of this diagnostic to its a priori known limit is a necessary condition for the convergence of infinite swapping. Finally, the rate function is also used to investigate the impact of asymmetries in the underlying potential landscape, and where in the state space poor sampling is most likely to occur.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Next-Cycle Optimal Dilute Combustion Control via Online Learning of Cycle-to-Cycle Variability Using Kernel Density Estimators

Dilute combustion using exhaust gas recirculation (EGR) presents a cost-effective method for increasing the efficiency of spark-ignition (SI) engines. However, the maximum amount of EGR that can be used at a given condition is limited by a rapid increment of cycle-to-cycle variability (CCV). This study describes a methodology to design a model-based stochastic optimal controller to adjust the cycle-to-cycle fuel injection quantity in order to reduce CCV and further extend the dilute limit. Given the complexity and chaotic nature of combustion events, the controller was enhanced with online learning in order to identify the statistical properties of combustion efficiency, which are needed to generate predictions for next-cycle events. This study showed that a kernel density estimator (KDE) can be used to learn the combustion properties in real time and can be incorporated into the feedback policy in order to calculate the optimal control command. Experimental results suggested that the dilute limit can be extended from 18.5% to 21% EGR fraction at an operating condition relevant for highway cruising. Additionally, the proposed controller can achieve a large CCV reduction with less fuel enrichment compared to previous methods, overall contributing to an increase in 0.2% indicated fuel conversion efficiency.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2019

A mixed $\ell_1$ regularization approach for sparse simultaneous approximation of parameterized PDEs

We introduce and assess a novel sparse polynomial technique for the simultaneous approximation of parameterized partial differential equations (PDEs) with deterministic and stochastic inputs. Our approach treats the numerical solution as a jointly sparse reconstruction problem through the reformulation of the standard basis pursuit denoising, where the set of jointly sparse vectors is infinite. To achieve global reconstruction of sparse solutions to parameterized elliptic PDEs over both physical and parametric domains, we combine the standard measurement scheme developed for compressed sensing in the context of bounded orthonormal systems with a novel mixed-norm based $\ell_1$ regularization method that exploits both energy and sparsity. Moreover, we are able to prove that, with minimal sample complexity, error estimates comparable to the best $s$-term and quasi-optimal approximations are achievable, while requiring only {\em a priori} bounds on polynomial truncation error with respect to the energy norm.Finally, we perform extensive numerical experiments on several high-dimensional parameterized elliptic PDE models to demonstrate the superior recovery properties of the proposed approach.

97 MATHEMATICS AND COMPUTING↗
NASA NTRSDate not supplied

Hardware-Efficient Quantum Optimization Layered Algorithms and Experiments

Quantum optimization algorithms, such as QAOA, that implement parametrized stochastic optimization solvers attempt to identify low-energy solutions of Ising systems by exploiting available quantum effects in noisy-intermediate scale machines. Engineering a well-performing parametrized quantum optimization circuit is indeed an exercise in balancing the trade-off between expressivity and implementation complexity. We show that, for MaxCut QAOA circuits defined on native hardware topology (Rigetti’s Aspen Quantum Processors), error-mitigation techniques recover simulated features of the noiseless theory. Moreover, we explore a design space for QAOA-like ansatze that perform well in theory as well as in hardware for fully-connected problems. We also discuss how efficient coherence and entanglement detection methods that could be coupled with quantum optimization experiments require only linear overhead in benchmarking time.

quantum computing↗
DOE OSTI2024

Super Resolving Unrolled Neural Networks for Remote Sensing

In remote sensing systems, the capabilities of the system are constrained by the complex interactions between size, weight, and power (SWAP) of potential designs. In electro-optical (EO) systems, examples of these critical parameters include the system’s sensitivity and resolution. Those parameters can be increased by ever larger optical apertures and focal planes but at the cost of more SWAP. Multi-image super resolution (MISR) techniques allow resolution to be enhanced via computation rather than more sophisticated optical hardware. These algorithms combine multiple images together into a single, higher resolution image, trading temporal resolution and computation for spatial resolution. Fielded MISR techniques, such as Drizzle, can require several hundred images to create a single super resolved image, implying reduced temporal resolution, increased data acquisition load, and limiting mission applications. Iterative techniques, such as model-based image reconstruction and compressive sensing, have been shown to create super resolved images using fewer images than Drizzle. They do this by posing an optimization problem that balances accuracy between a highly accurate physical model and an image model. In the case of super resolution, the physical model is defined by the relation between low resolution input images and the desired high resolution output image. The image model encodes some assumptions about the super resolved image. These assumptions are meant to suppress reconstruction artifacts that arise due to deterministic physical model error, stochastic measurement noise, and potential undersampling. In practice, the performance of iterative methods are limited by imaging models compatible with optimization. Deep learning-based methods can effectively learn image models of arbitrary complexity, but lack the theoretical explainability and robustness of iterative techniques. Consensus equilibrium (CE) generalizes the iterative techniques beyond optimization, enabling blackbox algorithms such as traditional and neural image denoisers to be used as the image model. CE-based approaches retain much of the explainability and robustness of iterative techniques while allowing the expressiveness of machine learning image models to be used. Additionally, by unrolling iterations of CE with an embedded image denoiser, the image denoiser can be further trained and specialized to the specific application with potentially higher quality reconstructions. Under this project, we demonstrated the feasibility of training an unrolled neural network based upon CE. While we didn’t train one, we showed that the CE process is differentiable and its gradient can be tractably computed. We also explored the usage of a variants of CE akin to generative neural works. Most importantly, we applied the CE framework to a number of problems including non-blind deconvolution, upsampling, single-image super resolution, MISR, event-based sensing, and saturated deconvolution. Our MISR prototype creates high quality reconstructions with an order of magnitude fewer images than previous approaches and, critically, produces these reconstructions fast enough for practical usage.

47 OTHER INSTRUMENTATION↗
DOE OSTI2018

Final Technical Report: Mathematical Foundations for Uncertainty Quantification in Materials Design

We developed path-wise information theory-based and goal-oriented sensitivity analysis and parameter identification methods for complex high-dimensional dynamics and in particular of non-equilibrium extended molecular systems. The combination of these novel methodologies provided the first methods in the literature which are capable to handle UQ questions for stochastic complex systems with some or all of the following features: (a) multi-scale stochastic models such as (bio)chemical reaction networks, with a very large number of parameters, (b) spatially distributed systems such as Kinetic Monte Carlo or Langevin Dynamics, (c) non-equilibrium processes typically associated with coupled physico-chemical mechanisms, driven boundary conditions, hybrid micro-macro systems, etc. A particular computational challenge arises in simulations of multi-scale reaction networks and molecular systems. Mathematical techniques were applied to in silico prediction of novel materials with emphasis on the effect of microstructure on model uncertainty quantification (UQ). We outline acceleration methods to make calculations of real chemistry feasible followed by two complementary tasks on structure optimization and microstructure-induced UQ.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Constant-complexity stochastic simulation algorithm with optimal binning

At the molecular level, biochemical processes are governed by random interactions between reactant molecules, and the dynamics of such systems are inherently stochastic. When the copy numbers of reactants are large, a deterministic description is adequate, but when they are small, such systems are often modeled as continuous-time Markov jump processes that can be described by the chemical master equation. Gillespie’s Stochastic Simulation Algorithm (SSA) generates exact trajectories of these systems, but the amount of computational work required for each step of the original SSA is proportional to the number of reaction channels, leading to computational complexity that scales linearly with the problem size. The original SSA is therefore inefficient for large problems, which has prompted the development of several alternative formulations with improved scaling properties. We describe an exact SSA that uses a table data structure with event time binning to achieve constant computational complexity with respect to the number of reaction channels for weakly coupled reaction networks. We present a novel adaptive binning strategy and discuss optimal algorithm parameters. We compare the computational efficiency of the algorithm to existing methods and demonstrate excellent scaling for large problems. This method is well suited for generating exact trajectories of large weakly coupled models, including those that can be described by the reaction-diffusion master equation that arises from spatially discretized reaction-diffusion processes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Day-Ahead Optimal Operation for Multi-Energy Residential Systems with Renewables

The intermittency and stochasticity nature of distributed renewable energy sources has introduced great challenges to the efficiency and security of energy distribution system operations. To address the negative impacts of intermittent renewable energy sources, this paper proposes here a day-ahead optimal operation strategy utilizing distributed energy resources based on the framework of the interconnected multi-energy system. First, a framework and mathematical models of multi-energy residential systems (MERS) are proposed. Based on the characteristics of residential energy distribution networks, the complex MERS models are reformulated to relieve the computational burden. Furthermore, the uncertainty factors such as renewable energy generation fluctuations and demand variations are handled by a reformulated chance con-strained programming technique. The feasibility and effectiveness of the proposed method are validated through a combined electric power and natural gas test system. Compared to similar models and methods in the existing literature, the proposed method performs better in terms of solution time, model scalability, and robustness in handling uncertainties.

24 POWER TRANSMISSION AND DISTRIBUTION↗