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Nonlinear optimization problems that are encountered in science and industry are examined. A method of projecting the gradient vector onto a set of linear contraints is developed, and a program that uses this method is presented. The algorithm that generates this projection matrix is based on the Gram-Schmidt method and overcomes some of the objections to the Rosen projection method.
The precise and rapid exploration of transition states (TSs) is a major challenge when studying atmospheric reactions due to their complexity. In this work, a Monte Carlo Transition State Search Method (MCTSSM), which integrates Monte Carlo sampling technique with transition state optimization methods using an efficient computer script, has been developed for transition state searches. The efficiency and the potential application in atmospheric reactions of this method have been demonstrated by three types of test suits related to the reactions of atmospheric volatile organic compounds (VOCs): (1) OH addition, (2) OH hydrogen-abstraction, and (3) the other reactive group (e.g. Cl, O3, NO3), especially for the reaction of β-pinene-sCI (stabilized Criegee Intermediates) with water. It was shown that the application of this method with effective restricted parameters has greatly simplified the time-consuming and tedious manual search procedure for transition state (TS) of the bimolecular reaction systems.
Neural manifolds summarize the intrinsic structure of the information encoded by a population of neurons. Advances in experimental techniques have made simultaneous recordings from multiple brain regions increasingly commonplace, raising the possibility of studying how these manifolds relate across populations. However, when the manifolds are nonlinear and possibly code for multiple unknown variables, it is challenging to extract robust and falsifiable information about their relationships. We introduce a framework, called the method of analogous cycles, for matching topological features of neural manifolds using only observed dissimilarity matrices within and between neural populations. We demonstrate via analysis of simulations and in vivo experimental data that this method can be used to correctly identify multiple shared circular coordinate systems across both stimuli and inferred neural manifolds. Conversely, the method rejects matching features that are not intrinsic to one of the systems. Further, as this method is deterministic and does not rely on dimensionality reduction or optimization methods, it is amenable to direct mathematical investigation and interpretation in terms of the underlying neural activity. We thus propose the method of analogous cycles as a suitable foundation for a theory of cross-population analysis via neural manifolds.
At the outset ARPA-e’s grid optimization competition sought to test a hypothesis that modern nonlinear optimization methods had reached a level of performance and reliability necessary to optimize energy grids using nonlinear power flow equations. The results demonstrated by this project and the other participants in the grid optimization competition have demonstrated beyond any shadow of doubt that this hypothesis is true. This result suggest that the mathematical optimization technology now exists to produce a revolution in power grid optimization software, which would improve the efficiency of energy grid operations to the broad benefit of society.
This document outlines the progress made under NASA Cooperative Research Agreement NCC2- 5226 for the period 10/01/97-09/30/98. The work statement originally proposed was meant to extend over the period of two complete years of which only one was funded. Consequently, only a portion of the goals were achieved. Similar work will continue in our group under different sponsorship and will be available in the form of conference and journal publications. The following sections summarize the technical accomplishments obtained during the last year. Details of these accomplishments can be found in the accompanying paper that was presented at the AIAA 37th Aerospace Sciences and Exhibit Meeting which was held in Reno, NV in January of this year. The original proposal outlined a research program meant to lay down the foundation for the development of high-fidelity, fully-coupled aerodynamic/structural optimization methods applicable to a variety of aerospace applications including the design optimization of High Speed Civil Transport (HSCT) configurations. The necessary research and development work was divided into two main efforts which addressed the necessities of the long term goal. Initially, our experience in the simulation of unsteady aeroelastic flows was directly applied to existing aerodynamic optimization techniques in order to provide insight into the effects of aeroelastic deformations on the performance of aircraft which have been designed based on purely aerodynamic cost functions. The intention was to follow up this work with a detailed investigation into the basic research work that has to be completed for the development of an optimization framework which efficiently allows the truly coupled design of aero-structural systems. This follow-up effort was not funded. The outcome of our efforts during the past year was the development of a coupled aero-structural analysis and design environment that was applied to the design of a complete aircraft configuration.
High-brightness X-rays, as produced at synchrotrons and X-ray free electron laser (XFEL) facilities, are used to characterize materials in a variety of scientific experiments. In most cases, effective use of the high-energy light requires precisely-aligned focusing optics; one example being a compound refractive lens (CRL). To align a CRL, the position and rotation must be optimized along four axes. In practice, this is a labor-intensive, time-consuming manual process that can monopolize scarce experimental time at the necessary X-ray facilities. Models of the expected Xray transmission function suggest that this task can be automated; however, the temporally-varying intensity at X-ray free electron laser facilities preclude the direct use of standard implementations of optimization solvers such as steepest descent algorithms. In this paper, we propose a novel technique to estimate the gradient of noisy functions with temporally-varying amplitudes. We construct this dynamicamplitude correction by systematically sampling a fixed central location within the standard finite difference stencil, accounting for the observed changes in time, and normalizing the difference quotients against those fluctuations. In addition to a rigorous error analysis of the sampling technique, we demonstrate its efficacy in stochastic descent optimization methods. Further, we demonstrate how this approach may be implemented to optimize X-ray focusing optics at synchrotrons or XFEL facilities
This study present a test case in which the Bayesian Optimization method is applied to a simulation-based reactor core design optimization problem. The test case aims to showcase the potential of an automated design optimization algorithm for reactor designs by streamlining the reactor core design workflow, given the high computational cost of simulations. The contributions of this work are threefold. First, the existing HTGR model is converted into a simulation-based design optimization test case by developing a pipeline that enables modification of key design parameters and evaluates design performance based on simulation outputs. Second, Bayesian Optimization is implemented and adapted to demonstrate the feasibility of automatic design optimization for nuclear reactor core. Proposed approach leverages Gaussian Process models to characterize the relationship between design variables and performance metrics, while incorporating novel acquisition functions that balance exploration of the design space with exploitation of promising configurations. This implementation lays the foundation for the future developments of reactor design optimization algorithms.
In this paper, we consider dispatchability as the set of all admissible nodal wind power injections that will not cause infeasibility in real-time dispatch (RTD). Our work reveals that the dispatchability of the affine policy based RTD (AF-RTD) is a polytope whose coefficients are linear functions of the generation schedule and the gain matrix of affine policy. Two mathematical formulations of the dispatchability maximized energy and reserve dispatch (DM-ERD) are proposed. The first one maximizes the distance from the forecast to the boundaries of the dispatchability polytope subject to the available production cost or reserve cost. Provided the forecast value and variance of wind power, the generalized Gauss inequality (GGI) is adopted to evaluate the probability of infeasible RTD without the exact probability distribution of wind power. Combining the first formulation and the GGI approach, the second one minimizes the total cost subject to a desired reliability level through dispatchability maximization. Efficient convex optimization based algorithms are developed to solve these two models. Different from the conventional robust optimization method, our model does not rely on the specific uncertainty set of wind generation and directly optimizes the uncertainty accommodation capability of the power system. The proposed method is also compared with the affine policy based robust energy and reserve dispatch (AR-ERD). Case studies on the PJM 5-bus system illustrate the proposed concept and method. Experiments on the IEEE 118-bus system demonstrate the applicability of our method on moderate sized systems and its scalability to large dimensional uncertainty.
The volatility of metabolites can influence their biological roles and inform optimal methods for their detection. Yet, volatility information is not readily available for the large number of described metabolites, limiting the exploration of volatility as a fundamental trait of metabolites. Here, we adapted methods to estimate vapor pressure from the functional group composition of individual molecules (SIMPOL.1) to predict the gas-phase partitioning of compounds in different environments. We implemented these methods in a new open pipeline called volcalc that uses chemoinformatic tools to automate these volatility estimates for all metabolites in an extensive and continuously updated pathway database: the Kyoto Encyclopedia of Genes and Genomes (KEGG) that connects metabolites, organisms, and reactions. We first benchmark the automated pipeline against a manually curated data set and show that the same category of volatility (e.g., nonvolatile, low, moderate, high) is predicted for 93% of compounds. We then demonstrate how volcalc might be used to generate and test hypotheses about the role of volatility in biological systems and organisms. Specifically, we estimate that 3.4 and 26.6% of compounds in KEGG have high volatility depending on the environment (soil vs. clean atmosphere, respectively) and that a core set of volatiles is shared among all domains of life (30%) with the largest proportion of kingdom-specific volatiles identified in bacteria. With volcalc , we lay a foundation for uncovering the role of the volatilome using an approach that is easily integrated with other bioinformatic pipelines and can be continually refined to consider additional dimensions to volatility. The volcalc package is an accessible tool to help design and test hypotheses on volatile metabolites and their unique roles in biological systems.
The paper presents two path planners suitable for planetary rovers. The first is based on fuzzy description of the terrain, and genetic algorithm to find a traversable path in a rugged terrain. The second planner uses a global optimization method with a cost function that is the path distance divided by the velocity limit obtained from the consideration of the rover static and dynamic stability. A description of both methods is provided, and the results of paths produced are given which show the effectiveness of the path planners in finding near optimal paths. The features of the methods and their suitability and application for rover path planning are compared
Time-optimal control theory applied to launch vehicle regulation and the newton-raphson optimization method
Object localization and its application in tele-autonomous systems are studied. Two object localization algorithms are presented together with the methods of extracting several important types of object features. The first algorithm is based on line-segment to line-segment matching. Line range sensors are used to extract line-segment features from an object. The extracted features are matched to corresponding model features to compute the location of the object. The inputs of the second algorithm are not limited only to the line features. Featured points (point to point matching) and featured unit direction vectors (vector to vector matching) can also be used as the inputs of the algorithm, and there is no upper limit on the number of the features inputed. The algorithm will allow the use of redundant features to find a better solution. The algorithm uses dual number quaternions to represent the position and orientation of an object and uses the least squares optimization method to find an optimal solution for the object's location. The advantage of using this representation is that the method solves for the location estimation by minimizing a single cost function associated with the sum of the orientation and position errors and thus has a better performance on the estimation, both in accuracy and speed, than that of other similar algorithms. The difficulties when the operator is controlling a remote robot to perform manipulation tasks are also discussed. The main problems facing the operator are time delays on the signal transmission and the uncertainties of the remote environment. How object localization techniques can be used together with other techniques such as predictor display and time desynchronization to help to overcome these difficulties are then discussed.
An electric power grid is exceedingly faced with extreme events, such as physical attacks and natural disasters. In comparison, the underground natural gas pipeline-based transportation network is considered less vulnerable to such environmental threats. We consider that the overhead power transmissions can be hardened by replacing segments of electric power system with underground natural gas pipelines as an energy transportation system to counter effect extreme events which can damage interdependent infrastructures severely. This project investigates an extension of the power system planning problem considering extreme events and identifies the feasibility of solving this problem with advanced modeling and optimization methods. The proposed planning framework is formulated as a two-stage optimization problem. It is found that the integrated planning introduces the additional cost of pipeline planning and the operation constraints into the power system planning. However, gas pipelines are generally less exposed to extreme events, which can provide a more resilient power transmission for supplying the electrical loads. It is with this potential for enhancing the power grid resilience that the proposed integrated expansion of electricity and natural gas system is considered an optimal layout for the transportation of energy.
Proteins interact to form protein complex to carry out biological functions such as catalytic chemical reaction. Therefore, it is important to develop computational methods to predict protein-protein interaction and the structures of protein complexes to study and enhance protein function. In this project, we successfully developed several deep learning methods to predict inter-protein contacts and the reinforcement learning and optimization methods to reconstruct protein complex structures from predicted inter-chain contacts. The methods were integrated with the MULTICOM protein complex structure prediction system and applied to predict the complex structures of biomass production-related proteins of green algae. During the two and a half years of research and development, all the specific milestones of the project were achieved successfully. 16 publications/manuscripts were produced. 10 software tools were developed. A patent application was submitted. Our MULTICOM predictors leveraging some tools developed in this project were ranked among the top predictors in the 15th Critical Assessment of Techniques for Protein Structure Prediction (CASP15) in 2022.
Advanced nuclear reactors are a key part of the future of nuclear energy both in the United States and globally. They offer unique benefits for various energy-demanding applications, including use in remote locations, compact size, modular manufacturing, remote monitoring, low and/or variable power rating operation, and reliance on novel technologies to enhance operational safety. To achieve economic feasibility, advanced reactors must significantly reduce their workforces in comparison with the current fleet. Achieving this reduction will occur through reducing staff workloads using technology to achieve autonomous or semi-autonomous operations, demonstrated by comprehensive testing and validation activities. These operations will require both software and hardware platforms during the design and testing phases. While simulations are useful during the design phase, their performance can significantly deviate during actual deployment on hardware. This report presents the outcomes of a collaborative technical initiative between the U.S. Department of Energy (DOE) Microreactor Program (MRP) and Advanced Sensors and Instrumentation (ASI) Program. The collaboration utilized the Microreactor Automated Control System (MACS) hardware platform to bridge the gap between theoretical reactor design and actual startup and control operations. Two key use cases were investigated: facilitating the startup testing period and demonstrating supervisory control. The first use case details the key Microreactor Applications Research Validation and Evaluation (MARVEL) reactor startup physics testing activities conducted using the MACS platform. These activities included drum worth measurements, shutdown margin assessment, temperature feedback analysis, and scram time evaluation, as well as unique testing that would apply to the MARVEL reactor to demonstrate the testing methodologies in a low-risk environment. The MACS platform, serving as a surrogate representation of the MARVEL reactor, proved instrumental in performing these tests. The exercise revealed aspects that led to optimized processes, refined hardware design, and enhanced base software capabilities. By maturing methods and technologies in this manner, the initiative promises to reduce wasted time in the actual on-site reactor deployment effort, thereby saving significant time and resources. The second use case focuses on the development and implementation of supervisory control methods aimed at managing core tilt, which can result from asymmetrical operations or manufacturing imperfections in fuel rods or reactivity control devices. A key objective was to assess and compare the use of artificial intelligence (AI) for supervisory control. The effort aimed to define the role of supervisory control to enhance performance without risking control instability. This effort explored three distinct approaches: rules-based (RB) methods, optimization techniques, and reinforcement learning (RL) algorithms. Each approach was evaluated for its ease of implementation, its usability, and its effectiveness in responding to asymmetries in neutron flux. Comparative analysis of these approaches provided valuable insights into their applicability and effectiveness, offering a robust framework for advanced reactor operations. Together, these two use cases highlight the potential of hardware test beds to help streamline the design, operation, and control of advanced nuclear reactors. This collaborative effort underscores the importance of continued innovation and experimentation in achieving the next generation of safe, reliable, and economically viable nuclear energy solutions.
Random perturbation procedure for control variable functions optimization using hybrid computer method for analog solutions and digital storage
An algorithm for maximum likelihood (ML) estimation is developed with an efficient method for approximating the sensitivities. The ML algorithm relies on a new optimization method referred to as a modified Newton-Raphson with estimated sensitivities (MNRES). MNRES determines sensitivities by using slope information from local surface approximations of each output variable in parameter space. With the fitted surface, sensitivity information can be updated at each iteration with less computational effort than that required by either a finite-difference method or integration of the analytically determined sensitivity equations. MNRES eliminates the need to derive sensitivity equations for each new model, and thus provides flexibility to use model equations in any convenient format. A random search technique for determining the confidence limits of ML parameter estimates is applied to nonlinear estimation problems for airplanes. The confidence intervals obtained by the search are compared with Cramer-Rao (CR) bounds at the same confidence level. The degree of nonlinearity in the estimation problem is an important factor in the relationship between CR bounds and the error bounds determined by the search technique. Beale's measure of nonlinearity is developed in this study for airplane identification problems; it is used to empirically correct confidence levels and to predict the degree of agreement between CR bounds and search estimates.
This paper discusses a neural network tool for more effective aircraft design evaluations during wind tunnel tests. Using a hybrid neural network optimization method, we have produced fast and reliable predictions of aerodynamical coefficients, found optimal flap settings, and flap schedules. For validation, the tool was tested on a 55% scale model of the USAF/NASA Subsonic High Alpha Research Concept aircraft (SHARC). Four different networks were trained to predict coefficients of lift, drag, moment of inertia, and lift drag ratio (C(sub L), C(sub D), C(sub M), and L/D) from angle of attack and flap settings. The latter network was then used to determine an overall optimal flap setting and for finding optimal flap schedules.