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Numerical analyses of transitions between restricted problem of three bodies and problem of two fixed centers and Kepler problem
Equivalence of optimal control problems and transformation of optimal control problems with compact control regions into Lagrange problems
In the United States, as much as 30% of the 19 EJ that commercial buildings consume is considered excess. Much of the excess energy is due to the inability to manage building operations efficiently. Because almost 20% of the total primary energy consumption is associated with commercial buildings, significant energy reductions in this sector are needed to mitigate climate change. Therefore, many cities and states are mandating periodic “tune-ups” of these buildings to eliminate excess energy consumption. Although the benefits of tune-ups and retro-commissioning are clear, focusing these mandates to look for specific opportunities has been a challenge because of the lack of studies that document the prevalence of opportunities. Therefore, we analyzed building automation system data from 151 buildings across the United States to document common operational problems and opportunities to improve building operations. This analysis showed that opportunities to improve building operations exist in almost every building. These opportunities were not strongly correlated with building vintage or size, but were reflective of how the buildings are operated. The prevalence of the top 20 opportunities ranged between 74% and 23%, with 40% of these associated with air-handling units. The rest of the opportunities are associated with schedules, chilled and hot-water distribution, and zone controls. Of the 151 buildings, 69 of them implemented corrective actions of some or all opportunities that were identified. Implementation varied across the Re-tuning categories, with 60% for schedule opportunities, 50% for zone opportunities, over 40% for the air-handling unit and hot-water opportunities, and 35% of the chilled-water opportunities. There was wide variation in whole building energy savings, ranging from 0 to 50% and 0 to 18 $/m2 with median percent annual whole building savings of 12% and median normalized annual cost savings of $1.75/m2. In addition to documenting these key findings, the paper provides a list of opportunities that can be automatically and continuously identified and corrected and offers a list of those opportunities that should be the focus of the mandates.
There are two common ways to evaluate algorithms: performance on benchmark problems derived from real applications and analysis of performance on parametrized families of problems. The two approaches complement each other, each having its advantages and disadvantages. The planning community has concentrated on the first approach, with few ways of generating parametrized families of hard problems known prior to this work. Our group's main interest is in comparing approaches to solving planning problems using a novel type of computational device - a quantum annealer - to existing state-of-the-art planning algorithms. Because only small-scale quantum annealers are available, we must compare on small problem sizes. Small problems are primarily useful for comparison only if they are instances of parametrized families of problems for which scaling analysis can be done. In this technical report, we discuss our approach to the generation of hard planning problems from classes of well-studied NP-complete problems that map naturally to planning problems or to aspects of planning problems that many practical planning problems share. These problem classes exhibit a phase transition between easy-to-solve and easy-to-show-unsolvable planning problems. The parametrized families of hard planning problems lie at the phase transition. The exponential scaling of hardness with problem size is apparent in these families even at very small problem sizes, thus enabling us to characterize even very small problems as hard. The families we developed will prove generally useful to the planning community in analyzing the performance of planning algorithms, providing a complementary approach to existing evaluation methods. We illustrate the hardness of these problems and their scaling with results on four state-of-the-art planners, observing significant differences between these planners on these problem families. Finally, we describe two general, and quite different, mappings of planning problems to QUBOs, the form of input required for a quantum annealing machine such as the D-Wave II.
NASA's AATT Program is investigating potential ground-based decision support tool (DST) development for en route controllers and managers. NASA's previous work in en route DST development has focused on Transition airspace, where aircraft are impacted by constraints associated with the transition of aircraft from en route to terminal airspace. This paper investigates the problems associated with aircraft in non-transitional en route airspace, termed Constrained Airspace. A literature search was performed to catalog previously identified constrained airspace problems. The results of this search were investigated with industry representatives to validate these problems were significant in constrained airspace. Three general problem areas were identified. The first problem area involves negative impacts caused by a loss of airspace (e.g., activation of Special Use Airspace (SUA), weather cell formation, and overloaded sectors). The second problem area is the lack of identifying and taking advantage of gained airspace (e.g., SUA deactivation, weather dissipation, and sector loading reductions). The third problem area is unforeseen negative impacts caused by the acceptance of user routing requests (e.g., a route change into an area of congestion that negated the users intended benefit). Based upon the problems identified, an operational concept was developed for a DST to help handle these problems efficiently. The goal is to strategically identify constrained airspace problems and to provide functionality to support ARTCC TMUs in resolving the identified impacts. The capability lends itself well to TMU and Airline Operations Center (AOC) collaboration.
During the first phase of the Consortium for Advanced Simulation of Light Water Reactors (CASL) program, the Virtual Environment for Reactor Applications (VERA) was developed with a focus on capabilities for high-fidelity, multiphysics simulation of pressurized water reactors (PWRs). During this development effort, a set of progression problems was created ranging from smaller pin cell calculations to larger 3D full-core calculations. These progression problems helped to guide the development of the software and served as benchmarks against which to test VERA. Since 2019, efforts have been made to extend the capabilities of VERA to model boiling water reactors (BWRs). Because BWR simulations come with many unique challenges, a set of BWR progression problems was developed to aid in this new effort. The BWR progression problems range from 2D lattice calculations to 3D mini-core problems, and reference neutronic solutions were computed using continuous-energy Monte Carlo codes. MPACT, one of the neutronics code in VERA, was benchmarked using the BWR progression problems. The code is capable of computing solutions to all problems. The eigenvalues computed by MPACT agree well with the Monte Carlo reference solutions. (authors)
The restricted Three-Body-Problem considers the motion of an infinitesimal mass under the gravitational attraction of two finite masses, which revolve about their common center of gravity in coplanar circles. It is well known that Euler's problem of two fixed centers, consisting of the motion of an infinitesimal mass under the gravitational attraction of two finite masses fixed in space, can be solved by elliptic functions. The idea presented here is to take the solution of Euler's problem as the solution of the restricted Three-Body-Problem by allowing the initial values to be functions of time now. Differential equations for the perturbed initial values are established. These equations can be given in closed form by using the fact that the transformation to the perturbed initial values of Euler's problem is canonical. Thus, an approximation can be obtained for the solution of the restricted Three-Body-Problem. The method can also be used to represent classes of neighboring trajectories for guidance purposes.
This work focuses on using variations of the Frank-Wolfe (FW) algorithm for solving unit commitment problems with high volumes of demand responsive loads on the power grid. We present a formulation of the unit commitment problem with demand responsive loads. We then show through reformulation and relaxations of the problem that variations of the Frank-Wolfe algorithm can be used to determine the time series decisions for the demand responsive loads. We show through computational experiments on the IEEE Reliability Test System that the timeseries of demand responsive load decisions obtained through our approach are near optimal and describe how large-scale parallel implementations of our approach can be highly computationally efficient.
We propose a Bayesian physics-informed neural network (B-PINN) to solve both forward and inverse nonlinear problems described by partial differential equations (PDEs) and noisy data. In this Bayesian framework, the Bayesian neural network (BNN) combined with a PINN for PDEs serves as the prior while the Hamiltonian Monte Carlo (HMC) or the variational inference (VI) could serve as an estimator of the posterior. B-PINNs make use of both physical laws and scattered noisy measurements to provide predictions and quantify the aleatoric uncertainty arising from the noisy data in the Bayesian framework. Compared with PINNs, in addition to uncertainty quantification, B-PINNs obtain more accurate predictions in scenarios with large noise due to their capability of avoiding overfitting. We conduct a systematic comparison between the two different approaches for the B-PINNs posterior estimation (i.e., HMC or VI), along with dropout used for quantifying uncertainty in deep neural networks. Our experiments show that HMC is more suitable than VI with mean field Gaussian approximation for the B-PINNs posterior estimation, while dropout employed in PINNs can hardly provide accurate predictions with reasonable uncertainty. Finally, we replace the BNN in the prior with a truncated Karhunen-Loève (KL) expansion combined with HMC or a deep normalizing flow (DNF) model as posterior estimators. The KL is as accurate as BNN and much faster but this framework cannot be easily extended to high-dimensional problems unlike the BNN based framework.
We introduce the Swath Segment Selection problem (SSSP). The SSSP consists of a constrained geometric covering problem and a capacitated resource problem. It comes from the real-life problem of scheduling on- and off-times for air or space-borne instruments that image a target by flying over and collecting a swath of information.
This paper analyzes a popular computational framework to solve infinite-dimensional Bayesian inverse problems, discretizing the prior and the forward model in a finite-dimensional weighted inner product space. We demonstrate the benefit of working on a weighted space by establishing operator-norm bounds for finite element and graph-based discretizations of Matérn-type priors and deconvolution forward models. For linear-Gaussian inverse problems, we develop a general theory to characterize the error in the approximation to the posterior. We also embed the computational framework into ensemble Kalman methods and MAP estimators for nonlinear inverse problems. Furthermore, our operator-norm bounds for prior discretizations guarantee the scalability and accuracy of these algorithms under mesh refinement.
A theory for obtaining approximate solutions to nonlinear problems whose exact solutions require the use of large computational procedures is described. The technique represents in some respects a generalization of the method of base and comparison solutions for flows depending on a parameter. For the generalized problem, the input variable is no longer a parameter but a function that is incremented over its entire domain. After performing calculations for a base configuration and a small number of variations of it, solutions for a large class of configurations can be obtained by forming linear combinations of the solution increments. For a restricted class of problems, approximate solutions can be obtained for general variations of a base configuration by using a function-space derivative estimate obtained from a base solution and a single variation.
We present MENDER, a knowledge based system that implements software design techniques that are specialized to automatically compile generate-and-patch problem solvers that satisfy global resource assignments problems. We provide empirical evidence of the superior performance of generate-and-patch over generate-and-test: even with constrained generation, for a global constraint in the domain of '2D-floorplanning'. For a second constraint in '2D-floorplanning' we show that even when it is possible to incorporate the constraint into a constrained generator, a generate-and-patch problem solver may satisfy the constraint more rapidly. We also briefly summarize how an extended version of our system applies to a constraint in the domain of 'multiprocessor scheduling'.
Restricted three-body problem is solved using solutions of eulers problem of two fixed centers
Two-center problem orbit as intermediate orbit for restricted three-body problem
Three body problem zero velocity curves - euler two center problem by graphical analysis - guidance systems
Coupled-cluster Green’s function (GFCC) calculation has drawn much attention in the recent years for targeting the molecular and material electronic structure problems from a many-body perspective in a systematically improvable way. However, GFCC calculations on scientific computing clusters usually suffer from expensive higher di- mensional tensor contractions in the complex space, expensive inter-process communi- cation, and severe load imbalance, which limits it’s routine use for tackling electronic structure problems. Here we present a numerical library prototype that is specifically designed for large-scale GFCC calculations. The design of the library is focused on a systematically optimal computing strategy to improve its scalability and efficiency. The performance of the library is demonstrated by the relevant profiling analysis of running GFCC calculations on remote giant computing clusters. The capability of the library is highlighted by computing a wide near valence band of a fullerene C60 molecule for the first time at the GFCCSD level that shows excellent agreement with the experimental spectrum.
This dataset accompanies the publication "GenASiS: General Astrophysical Simulation System. II. Self-gravitating Baryonic Matter." This dataset contains simulation outputs from GenASiS for the test problems described in that publication.