Search NASA⌕ Search

SEARCH · Search NASA

Results for “decomposition algorithms”

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 OSTI2020

Optimization-Driven Scenario Grouping

Scenario decomposition algorithms for stochastic programs compute bounds by dualizing all nonanticipativity constraints and solving individual scenario problems independently. Here, we develop an approach that improves on these bounds by reinforcing a carefully chosen subset of nonanticipativity constraints, effectively placing scenarios into groups. Specifically, we formulate an optimization problem for grouping scenarios that aims to improve the bound by optimizing a proxy metric based on information obtained from evaluating a subset of candidate feasible solutions. We show that the proposed grouping problem is NP-hard in general, identify a polynomially solvable case, and present two formulations for solving the problem: a matching formulation for a special case and a mixed-integer programming formulation for the general case. We use the proposed grouping scheme as a preprocessing step for a particular scenario decomposition algorithm and demonstrate its effectiveness in solving standard test instances of two-stage 0–1 stochastic programs. Using this approach, we are able to prove optimality for all previously unsolved instances of a standard test set. Additionally, we implement this scheme as a preprocessing step for PySP, a publicly available and widely used implementation of progressive hedging, and compare this grouping approach with standard grouping approaches on large-scale stochastic unit commitment instances. Finally, the idea is extended to propose a finitely convergent algorithm for two-stage stochastic programs with a finite feasible region.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Decomposition and Algorithmic Approaches for Solving Large-Scale Process Family Design Problems

Our most recent work expands the water desalination case study from 76 variants to 10,897 variants using the equation-oriented model built in Pyomo as part of the PARETO project. Using the discretization formulation presented in Stinchfield (2024a), rather than solving for all 10,897 variants simultaneously, we decompose the formulation into subproblems containing subsets of variants from the process family. We solve the overall problem with Progressive Hedging (PH) deployed in parallel on a distributed HPC cluster using the open-source Python package mpi-sppy (Knueven et al., 2023). This approach allowed us to solve this process family design problem to ~1.5% relative optimality gap in about 5 hours; in comparison, Gurobi reached ~50% relative optimality gap in about 6 hours (Stinchfield et al., 2024b). However, this approach still requires discretization of the common unit module design ranges; additionally, PH acts as a heuristic for MILP’s with gap-closing capabilities. Ideally, we would not have to use ML surrogates or discretization to solve this problem, instead solving the process family design problem with the equation-oriented model directly to achieve the most accurate results. However, recall that we did not consider solving the MINLP directly due to complexity and size. In this work, we aim to decompose and solve this large-scale MINLP using a Structured Nonlinear Global Optimization algorithm presented by Cao and Zavala (2019).

Stinchfield, Georgia↗
DOE OSTI2019

A biomimetic approach to fast selection of optimal controlled variables using multiagent algorithms and a decomposition approach

Selection of primary controlled variables (CVs) with due consideration of economic loss and ease of control is an important step for achieving optimal plant operation under design and off-design conditions. However, the computational expense of the combinatorial optimization step that is undertaken for CV selection renders the existing approaches unaffordable for fast selection of optimal CVs. Two approaches are proposed in this paper for improving the computational efficiency of the optimization step. Typically, the CV selection process is typically executed by considering the entire plant together. Opposed to that, the first approach proposed here seeks to decompose the process plant into multiple partitions based on the connectivity strength. Then the CV selection algorithm can be executed on each partition independently. The decomposition algorithm is biomimetic and has been developed, in analogy to neuroscience, mimicking how the information about the connectivity information is extracted using a dynamic casual model. This approach can significantly decrease the number of combinatorial optimization problems that needs to be solved and facilitates parallelization of the solution. In the second approach, a multiagent optimization framework is proposed that utilizes metaheuristic optimization strategies such as the efficient ant colony algorithm, simulated annealing and the genetic algorithm. These two approaches can be used by themselves or in combination. This framework enables cooperative search by a group of algorithmic agents facilitated through an information sharing protocol. These two approaches are applied to a toy problem and an acid gas removal unit as part of an integrated gasification combined cycle. This study shows how the computational time and economic and control performance of the optimal CV sets vary as the number of partitions are changed.

42 ENGINEERING↗
DOE OSTI2023

Projective Hedging Algorithms for Multistage Stochastic Programming, Supporting Distributed and Asynchronous Implementation

Here we propose a decomposition algorithm for multistage stochastic programming that resembles the progressive hedging method of Rockafellar and Wets but is provably capable of several forms of asynchronous operation. We derive the method from a class of projective operator splitting methods fairly recently proposed by Combettes and Eckstein, significantly expanding the known applications of those methods. Our derivation assures convergence for convex problems whose feasible set is compact, subject to some standard regularity conditions and a mild “fairness” condition on subproblem selection. The method’s convergence guarantees are deterministic and do not require randomization, in contrast to other proposed asynchronous variations of progressive hedging. Computational experiments described in an online appendix show the method to outperform progressive hedging on large-scale problems in a highly parallel computing environment.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Decomposition of Nonlinear Dynamical Systems Using Koopman Gramians

In this paper we propose a new Koopman operator approach for nonlinear model decomposition using Koopman gramians. We introduce Koopman operators and discuss the notion of a input-Koopman operator. We show how input-Koopman operators can be used to cast a nonlinear system into the classical state-space form, as well as conditions under which input and state observable functions are well separated. We extend an existing method of dynamic mode decomposition for learning Koopman operators from data known as deep dynamic mode decomposition, for systems with control or disturbances. We illustrate the accuracy of the method on learning an input-state separable Koopman operator for an example system, even when the underlying system exhibits mixed state-input terms. Finally, we introduce a nonlinear decomposition algorithm, based on Koopman gramians, that maximizes internal subsystem observability and disturbance rejection from unwanted noise in other subsystems. To relieve the NP-hardness of the decomposition problem, we derive a relaxation based on Koopman gramians and multi-way partitioning. We illustrate our algorithm on a swing dynamics model for a IEEE 39 bus and discuss our findings.

Learning, Control, Distributed Control, koopman op↗
DOE OSTI2020

Pass-efficient methods for compression of high-dimensional turbulent flow data

The future of high-performance computing, specifically on future Exascale computers, will presumably see memory capacity and bandwidth fail to keep pace with data generated, for instance, from massively parallel partial differential equation (PDE) systems. Current strategies proposed to address this bottleneck entail the omission of large fractions of data, as well as the incorporation of in situ compression algorithms to avoid overuse of memory. To ensure that post-processing operations are successful, this must be done in a way that a sufficiently accurate representation of the solution is stored. Moreover, in situations where the input/output system becomes a bottleneck in analysis, visualization, etc., or the execution of the PDE solver is expensive, the number of passes made over the data must be minimized. In the interest of addressing this problem, this work focuses on the utility of pass-efficient, parallelizable, low-rank, matrix decomposition methods in compressing high-dimensional simulation data from turbulent flows. Additionally, a particular emphasis is placed on using coarse representation of the data – compatible with the PDE discretization grid – to accelerate the construction of the low-rank factorization. This includes the presentation of a novel single-pass matrix decomposition algorithm for computing the so-called interpolative decomposition. The methods are described extensively and numerical experiments on two turbulent channel flow data are performed. In the first (unladen) channel flow case, compression factors exceeding 400 are achieved while maintaining accuracy with respect to first- and second-order flow statistics. In the particle-laden case, compression factors of 100 are achieved and the compressed data is used to recover particle velocities. These results show that these compression methods can enable efficient computation of various quantities of interest in both the carrier and disperse phases.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

A multiscale flux basis for mortar mixed discretizations of Stokes–Darcy flows

A multiscale flux basis algorithm is developed for the Stokes–Darcy flow problem. The method is based on a non-overlapping domain decomposition algorithm, where the global problem is reduced to a coarse scale mortar interface problem that is solved by an iterative solver. Subdomain solves are required at each interface iteration, so the cost for the method without a multiscale basis can be high when the number of subdomains or the condition number of the interface problem is large. Here the proposed algorithm involves precomputing a multiscale flux basis, which consists of the flux (or velocity trace) response from each mortar degree of freedom. It is computed by each subdomain independently before the interface iteration begins. The subdomain solves required at each iteration are substituted by a linear combination of the multiscale basis. This may lead to a significant reduction in computational cost since the number of subdomain solves is fixed, depending only on the number of mortar degrees of freedom associated with a subdomain. Several numerical examples are carried out to demonstrate the efficiency of the multiscale flux basis implementation for large-scale Stokes–Darcy problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Scalable and fast heterogeneous molecular simulation with predictive parallelization schemes

Multiscale and inhomogeneous molecular systems are challenging topics in the field of molecular simulation. In particular, modeling biological systems in the context of multiscale simulations and exploring material properties are driving a permanent development of new simulation methods and optimization algorithms. In computational terms, those methods require parallelization schemes that make a productive use of computational resources for each simulation and from its genesis. Here, we introduce the heterogeneous domain decomposition approach, which is a combination of an heterogeneity-sensitive spatial domain decomposition with an a priori rearrangement of subdomain walls. Within this approach and paper, the theoretical modeling and scaling laws for the force computation time are proposed and studied as a function of the number of particles and the spatial resolution ratio. We also show the new approach capabilities, by comparing it to both static domain decomposition algorithms and dynamic load-balancing schemes. Specifically, two representative molecular systems have been simulated and compared to the heterogeneous domain decomposition proposed in this work. Finally, these two systems comprise an adaptive resolution simulation of a biomolecule solvated in water and a phase-separated binary Lennard-Jones fluid.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Graph-Based Representations and Applications to Process Simulation

Rapid and robust convergence of a process flowsheet is critical to enable large-scale simulations that address core scientific questions related to process design, optimization, and sustainability. However, due to the highly coupled and nonlinear nature of chemical processes, efficiently solving a flowsheet remains a challenge. In this work, we show that graph representations of the underlying physical phenomena in unit operations may help identify potential avenues to systematically reformulate the network of equations and enable more robust topology-based convergence of flowsheets. To this end, we developed graph abstractions of the governing equations of vapor-liquid and liquid-liquid equilibrium separation equipment. These graph abstractions consist of a mesh of interconnected variable nodes and equation nodes that are systematically generated through PhenomeNode, a new open-source library in Python developed in this study. We show that partitioning the graph into separate mass, energy, and equilibrium subgraphs can help decouple nonlinearities and guide decomposition algorithms. By employing the graph abstraction on an industrial separation process for separating glacial acetic acid from water, we implemented a new block decomposition scheme in BioSTEAM and demonstrated that this can accelerate convergence over a traditional sequential modular approach.

Distillation↗
DOE OSTI2019

Stochastic multiscale flux basis for Stokes-Darcy flows

Three algorithms are developed for uncertainty quantification in modeling coupled Stokes and Darcy flows. The porous media may consist of multiple regions with different properties. The permeability is modeled as a non-stationary stochastic variable, with its log represented as a sum of local Karhunen-Loève (KL) expansions. The problem is approximated by stochastic collocation on either tensor-product or sparse grids, coupled with a multiscale mortar mixed finite element method for the spatial discretization. A non-overlapping domain decomposition algorithm reduces the global problem to a coarse scale mortar interface problem, which is solved by an iterative solver, for each stochastic realization. In the traditional domain decomposition implementation, each subdomain solves a local Dirichlet or Neumann problem in every interface iteration. To reduce this cost, two additional algorithms based on deterministic or stochastic multiscale flux basis are introduced. The basis consists of the local flux (or velocity trace) responses from each mortar degree of freedom. It is computed for each subdomain independently before the interface iteration begins. The use of the multiscale flux basis avoids the need for subdomain solves on each iteration. The deterministic basis is computed at each stochastic collocation and used only at this realization. The stochastic basis is formed by further looping over all local realizations of a subdomain's KL region before the stochastic collocation begins. It is used over multiple realizations. Numerical tests are presented to illustrate the performance of the three algorithms, with the stochastic multiscale flux basis showing significant savings in computational cost compared to the other two algorithms.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

On the Convergence of Overlapping Schwarz Decomposition for Nonlinear Optimal Control

Here, we study the convergence properties of an overlapping Schwarz decomposition algorithm for solving nonlinear optimal control problems (OCPs). The algorithm decomposes the time domain into a set of overlapping subdomains, and solves all subproblems defined over subdomains in parallel. The convergence is attained by updating primal-dual information at the boundaries of overlapping subdomains. We show that the algorithm exhibits local linear convergence, and that the convergence rate improves exponentially with the overlap size. We also establish global convergence results for a general quadratic programming, which enables the application of the Schwarz scheme inside second-order optimization algorithms (e.g., sequential quadratic programming). The theoretical foundation of our convergence analysis is a sensitivity result of nonlinear OCPs, which we call "exponential decay of sensitivity" (EDS). Intuitively, EDS states that the impact of perturbations at domain boundaries (i.e., initial and terminal time) on the solution decays exponentially as one moves into the domain. Here, we expand a previous analysis available in the literature by showing that EDS holds for both primal and dual solutions of nonlinear OCPs, under uniform second-order sufficient condition, controllability condition, and boundedness condition. We conduct experiments with a quadrotor motion planning problem and a partial differential equations (PDE) control problem to validate our theory, and show that the approach is significantly more efficient than alternating direction method of multipliers and as efficient as the centralized interior-point solver.

42 ENGINEERING↗
DOE OSTI2018

A Fast Solver for Implicit Integration of the Vlasov--Poisson System in the Eulerian Framework

In this paper, we present a domain decomposition algorithm to accelerate the solution of Eulerian-type discretizations of the linear, steady-state Vlasov equation. The steady-state solver then forms a key component in the implementation of fully implicit or nearly fully implicit temporal integrators for the nonlinear Vlasov--Poisson system. The solver relies on a particular decomposition of phase space that enables the use of sweeping techniques commonly used in radiation transport applications. The original linear system for the phase space unknowns is then replaced by a smaller linear system involving only unknowns on the boundary between subdomains, which can then be solved efficiently with Krylov methods such as GMRES. Steady-state solves are combined to form an implicit Runge--Kutta time integrator, and the Vlasov equation is coupled self-consistently to the Poisson equation via a linearized procedure or a nonlinear fixed-point method for the electric field. Finally, numerical results for standard test problems demonstrate the efficiency of the domain decomposition approach when compared to the direct application of an iterative solver to the original linear system.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

An efficient computational approach to model statistical correlations in photon counting x-ray detectors

Purpose: To introduce and evaluate an increment matrix approach (IMA) describing the signal statistics of energy-selective photon counting detectors including spatial–spectral correlations between energy bins of neighboring detector pixels. The importance of the occurring correlations for image-based material decomposition is studied. Methods: An IMA describing the counter increase patterns in a photon counting detector is proposed. This IMA has the potential to decrease the number of required random numbers compared to Monte Carlo simulations by pursuing an approach based on convolutions. To validate and demonstrate the IMA, an approximate semirealistic detector model is provided, simulating a photon counting detector in a simplified manner, e.g., by neglecting count rate-dependent effects. In this way, the spatial–spectral correlations on the detector level are obtained and fed into the IMA. The importance of these correlations in reconstructed energy bin images and the corresponding detector performance in image-based material decomposition is evaluated using a statistically optimal decomposition algorithm. Results: The results of IMA together with the semirealistic detector model were compared to other models and measurements using the spectral response and the energy bin sensitivity, finding a good agreement. Correlations between the different reconstructed energy bin images could be observed, and turned out to be of weak nature. These correlations were found to be not relevant in image-based material decomposition. An even simpler simulation procedure based on the energy bin sensitivity was tested instead and yielded similar results for the image-based material decomposition task, as long as the fact that one incident photon can increase multiple counters across neighboring detector pixels is taken into account. Conclusions: The IMA is computationally efficient as it required about 10{sup 2} random numbers per ray incident on a detector pixel instead of an estimated 10{sup 8} random numbers per ray as Monte Carlo approaches would need. The spatial–spectral correlations as described by IMA are not important for the studied image-based material decomposition task. Respecting the absolute photon counts and thus the multiple counter increases by a single x-ray photon, the same material decomposition performance could be obtained with a simpler detector description using the energy bin sensitivity.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2021

Data-Driven Adaptive Damping Controller for Wind Power Plants with Doubly-Fed Induction Generators

This paper presents an adaptive damping controller for wind power plants in which the turbines are equipped with doubly-fed induction generators. The controller is designed to respond to an input control signal that is triggered according to the system operating conditions. A processing unit continuously estimates the electromechanical modes of oscillation based on real-time streaming data acquired from a phasor measurement unit that is strategically positioned on the grid. The decision to trigger (or not trigger) the control signal is automatic, based on the relative damping of the dominant mode. The modes are estimated using the dynamic mode decomposition algorithm with time-delay embedding. Numerical simulations performed on the two-area system demonstrate that the proposed controller enhances the rotor angle stability for both small-signal and large disturbances, and is adaptive to changing grid conditions.

damping controller↗
DOE OSTI2020

Joint Planning of EV Fast Charging Stations and Power Distribution Systems With Balanced Traffic Flow Assignment

To tackle the challenges introduced by the fast-growing charging demand of electric vehicles (EVs), the power distribution systems (PDSs) and fast charging stations (FCSs) of EVs should be planned and operated in a more coordinated fashion. However, existing planning approaches generally aim to minimize investment costs in PDSs while ignoring the risk of worsening traffic conditions. To overcome this research gap, this article integrates the interests of traffic networks into PDS and FCS joint planning model to mitigate negative impacts on traffic conditions caused by installing FCSs. First, a novel microscopic method that is different from traditional assignment methods is proposed to simulate the influences of FCSs on traffic flows and EV charging loads. Then, a multiobjective joint planning model is developed to minimize both the planning costs and unbalanced traffic flows. A new bilayer Benders decomposition algorithm is designed to solve the proposed joint planning model. Numerical results on two practical systems in China validate the feasibility of our microscopic method by comparing the simulated results with real data. Compared with existing approaches, it is also demonstrated that the proposed joint planning approach helps to balance traffic flow assignments and relieve traffic congestion.

bilayer expanded Benders decomposition↗
DOE OSTI2021

Data-Driven Adaptive Damping Controller for Wind Power Plants with Doubly-Fed Induction Generators: Preprint

This paper presents an adaptive damping controller for wind power plants in which the turbines are equipped with doubly-fed induction generators. The controller is designed to respond to an input control signal that is triggered according to the system operating conditions. A processing unit continuously estimates the electromechanical modes of oscillation based on real-time streaming data acquired from a phasor measurement unit that is strategically positioned on the grid. The decision to trigger (or not trigger) the control signal is automatic, based on the relative damping of the dominant mode. The modes are estimated using the dynamic mode decomposition algorithm with time-delay embedding. Numerical simulations performed on the two-area system demonstrate that the proposed controller enhances the rotor angle stability for both small-signal and large disturbances, and is adaptive to changing grid conditions.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2018

An Algorithm for Enhancing the Image Contrast of Electron Tomography

Abstract Three-dimensional (3D) reconstruction of a single protein molecule is essential for understanding the relationship between the structural dynamics and functions of the protein. Electron tomography (ET) provides a tool for imaging an individual particle of protein from a series of tilted angles. Individual-particle electron tomography (IPET) provides an approach for reconstructing a 3D density map from a single targeted protein particle (without averaging from different particles of this type of protein), in which the target particle was imaged from a series of tilting angles. However, owing to radiation damage limitations, low-dose images (high noise, and low image contrast) are often challenging to be aligned for 3D reconstruction at intermediate resolution (1–3 nm). Here, we propose a computational method to enhance the image contrast, without increasing any experimental dose, for IPET 3D reconstruction. Using an edge-preserving smoothing-based multi-scale image decomposition algorithm, this method can detect the object against a high-noise background and enhance the object image contrast without increasing the noise level or significantly decreasing the image resolution. The method was validated by using both negative staining (NS) ET and cryo-ET images. The successful 3D reconstruction of a small molecule (<100 kDa) indicated that this method can be used as a supporting tool to current ET 3D reconstruction methods for studying protein dynamics via structure determination from each individual particle of the same type of protein.

47 OTHER INSTRUMENTATION↗