A power grid network is an interconnected network of coupled devices that generate, transmit and distribute power to consumers. These complex and usually large-scale systems have high dimensional models that are computationally expensive to simulate especially in real time applications, stability analysis, and control design. Model order reduction (MOR) tackles this issue by approximating these high dimensional models with reduced high-fidelity representations. When the internal description of the models is not available, the reduced representations are constructed by data. In this dissertation, we investigate four problems regarding the MOR and data-driven modeling of the power networks model, particularly the swing equations. We first develop a parametric MOR approach for linearized parametric swing equations that preserves the physically-meaningful second-order structure of the swing equations dynamics. Parameters in the model correspond to variations in operating conditions. We employ a global basis approach to develop the parametric reduced model. We obtain these local bases by $mathcal{H}_2$-based interpolatory model reduction and then concatenate them to form a global basis. We develop a framework to enrich this global basis based on a residue analysis to ensure bounded $mathcal{H}_2$ and $mathcal{H}_infty$ errors over the entire parameter domain. Then, we focus on nonlinear power grid networks and develop a structure-preserving system-theoretic model reduction framework. First, to perform an intermediate model reduction step, we convert the original nonlinear system to an equivalent quadratic nonlinear model via a lifting transformation. Then, we employ the $mathcal{H}_2$-based model reduction approach, Quadratic Iterative Rational Krylov Algorithm (Q-IRKA). Using a special subspace structure of the model reduction bases resulting from Q-IRKA and the structure of the underlying power network model, we form our final reduction basis that yields a reduced model of the same second-order structure as the original model. Next, we focus on a data-driven modeling framework for power network dynamics by applying the Lift and Learn approach. Once again, with the help of the lifting transformation, we lift the snapshot data resulting from the simulation of the original nonlinear swing equations such that the resulting lifted-data corresponds to a quadratic nonlinearity. We then, project the lifted data onto a lower dimensional basis via a singular value decomposition. By employing a least-squares measure, we fit the reduced quadratic matrices to this reduced lifted data. Moreover, we investigate various regularization approaches. Finally, inspired by the second-order sparse identification of nonlinear dynamics (SINDY) method, we propose a structure-preserving data-driven system identification method for the nonlinear swing equations. Using the special structure on the right-hand-side of power systems dynamics, we choose functions in the SINDY library of terms, and enforce sparsity in the SINDY output of coefficients. Throughout the dissertation, we use various power network models to illustrate the effectiveness of our approaches. / Doctor of Philosophy / Power grid networks are interconnected networks of devices responsible for delivering electricity to consumers, e.g., houses and industries for their daily needs. There exist mathematical models representing power networks dynamics that are generally nonlinear but can also be simplified by linear dynamics. Usually, these models are complex and large-scale and therefore take a long time to simulate. Hence, obtaining models of much smaller dimension that can capture the behavior of the original systems with an acceptable accuracy is a necessity. In this dissertation, we focus on approximation of power networks model through the swing equations. First, we study the linear parametric power network model whose operating conditions depend on parameters. We develop an algorithm to replace the original model with a model of smaller dimension and the ability to perform in different operating conditions. Second, given an explicit representation of the nonlinear power network model, we approximate the original model with a model of the same structure but smaller dimension. In the cases where the mathematical models are not available but only time-domain data resulting from simulation of the model is at hand, we apply an already developed framework to infer a model of a small dimension and a specific nonlinear structure: quadratic dynamics. In addition, we develop a framework to identify the nonlinear dynamics while maintaining their original physically-meaningful structure.

Developing machine learning enabled smart manufacturing is promising for composite structures assembly process. It requires accurate predictive analysis on deformation of the composite structures to improve production quality and efficiency of composite structures assembly. The novel composite structures assembly involves two challenges: (i) the highly nonlinear and anisotropic properties of composite materials; and (ii) inevitable uncertainty in the assembly process. To overcome those problems, we propose a neural network Gaussian process model considering input uncertainty for composite structures assembly. Deep architecture of our model allows us to approximate a complex system better, and consideration of input uncertainty enables robust modeling with complete incorporation of the process uncertainty. Our case study shows that the proposed method performs better than benchmark methods for highly nonlinear systems. / Master of Science / Composite materials are becoming more popular in many areas due to its nice properties, yet computational modeling of them is not an easy task due to their complex structures. More-over, the real-world problems are generally subject to uncertainty that cannot be observed,and it makes the problem more difficult to solve. Therefore, a successful predictive modeling of composite material for a product is subject to consideration of various uncertainties in the problem.The neural network Gaussian process (NNGP) is one of statistical techniques that has been developed recently and can be applied to machine learning. The most interesting property of NNGP is that it is derived from the equivalent relation between deep neural networks and Gaussian process that have drawn much attention in machine learning fields. However,related work have ignored uncertainty in the input data so far, which may be an inappropriate assumption in real problems.In this paper, we derive the NNGP considering input uncertainty (NNGPIU) based on the unique characteristics of composite materials. Although our motivation is come from the manipulation of composite material, NNGPIU can be applied to any problem where the input data is corrupted by unknown noise. Our work provides how NNGPIU can be derived theoretically; and shows that the proposed method performs better than benchmark methods for highly nonlinear systems.

Mechanical metamaterials are novel materials that display unique properties from their underlying microstructure topology rather than the constituent material they are made from. Their effective properties displayed at macroscale depend on the design of their microstructural topology. In this work, two classes of mechanical metamaterials are studied within the 2D-space. The first class is made of trusses, referred to as truss-based mechanical metamaterials. These materials are studied through their application to a beam component, where finite element analysis is performed to determine how truss-based microstructures affect the displacement behavior of the beam. This analysis is further subsidized with the development of a graphical user interface, where users can design a beam made of truss-based microstructures to see how their design affects the beam's behavior. The second class of mechanical metamaterial investigated is made of self-assembled structures, called spinodoids. Their smooth topology makes them less prone to high stress concentrations present in truss-based mechanical metamaterials. A large database of spinodoids is generated in this study. Through data-driven modeling the geometry of the spinodoids is coupled with their Young's modulus value to approach inverse design under uncertainty. To see mechanical metamaterials applied to industry they need to be better understood and thoroughly characterized. Furthermore, more tools that specifically help push the ease in the design of these metamaterials are needed. This work aims to improve the understanding of mechanical metamaterials and develop efficient computational design strategies catered solely for them. / Master of Science / Mechanical metamaterials are hierarchical materials involving periodically or aperiodically repeating unit cell arrangements in the microscale. The design of the unit cells allows these materials to display unique properties that are not usually found in traditionally manufactured materials. This will enable their use in a multitude of potential engineering applications. The presented study seeks to explore two classes of mechanical metamaterials within the 2D-space, including truss-based architectures and spinodoids. Truss-based mechanical metamaterials are made of trusses arranged in a lattice-like framework, where spinodoids are unit cells that contain smooth structures resulting from mimicking the two phases that coexist in a phase separation process called spinodal decomposition. In this research, computational design strategies are applied to efficiently model and further understand these sub-classes of mechanical metamaterials.

Esta tesis investiga el problema de gestión de tesorería desde un punto de vista multidimensional. La gestión de tesorería trata de equilibrar la cantidad que se mantiene en efectivo y la que se dedica a inversiones a corto plazo. Normalmente, los tesoreros toman decisiones basándose en el nivel óptimo de tesorería por motivos operativos y de precaución. En esta tesis exploramos las oportunidades para mejorar la toma decisiones derivadas de modelar la incertidumbre presente en los flujos de caja con la ayuda de procedimientos basados en datos en un entorno multiobjetivo. Por un lado, los tesoreros pueden conseguir ahorros a través de la previsión de tesorería. Para ello, realizamos un estudio empírico con el objetivo de aprovechar las más recientes técnicas de aprendizaje automático como paso clave para conectar el análisis de los datos disponibles con los procesos de optimización en la gestión de tesorería. Por otro lado, los tesoreros pueden estar interesados no solo en el coste sino también en al riesgo asociado a sus decisiones. Por esta razón, tratamos el problema de gestión de tesorería desde una perspectiva multiobjetivo, considerando tanto el coste como el riesgo. Además, debido a la cambiante situación financiera actual, exploramos la selección de modelos de gestión de tesorería en función de diferentes condiciones operativas y de su robustez. También demostramos la utilidad de las previsiones a través de un nuevo modelo de gestión de tesorería que mejora el estado del arte al garantizar soluciones óptimas. Como la mayoría de las empresas trabaja con sistemas de tesorería con múltiples cuentas bancarias, desarrollamos un marco para la formulación y solución del problema de gestión de tesorería con múltiples cuentas bancarias. Finalmente, en un intento de acercar teoría y práctica, también ofrecemos una librería de software en Python para usuarios interesados en la construcción de sistemas de ayuda a la toma de decisiones en gestión de tesorería. / This thesis investigates the cash management problem from a multidimensional perspective. Cash management focuses on finding the balance between cash holdings and short-term investments. Typically, cash managers make decisions based usually on a firm's optimal cash balance for operational and precautionary purposes. We here explore the opportunities for improved decision-making derived from modeling cash flow uncertainty with the help of data-driven procedures within a multiobjective context. On the one hand, cash managers may achieve cost savings by forecasting future cash flows. To this end, we perform an empirical analysis of daily cash flow time-series to take advantage of modern machine learning techniques as a key step to connect data analysis and optimization methods in cash management. On the other hand, cash managers may be interested not only in the cost but also in the risk associated to decision-making. Thus, we address the cash management problem from a multiobjective perspective focusing on both cost and risk. In addition, under the current situation of time-varying financial circumstances, the selection of cash management models according to operating conditions and its robustness are worth considering questions. We also show the utility of forecasts through a new cash management model which outperforms the state-of-the-art by guaranteeing optimal solutions. Since most firms usually deal with cash management systems with multiple accounts, we develop a framework to formulate and solve the multiple bank accounts cash management problem. Finally, in an attempt to fill the gap between theory and practice, we also provide a software library in Python for practitioners interested in building decision support systems for cash management. / Esta tesi investiga el problema de gestió de tresoreria des d'un punt de vista multidimensional. La gestió de tresoreria tracta d'equilibrar la quantitat que es manté en efectiu i la que es dedica a inversions a curt termini. Normalment, el tresorers prenen decisions basant-se en el nivell òptim de tresoreria per motius operatius i de precaució. En aquesta tesi explorem les oportunitats per millorar la presa de decisions derivades de modelitzar la incertesa present en els fluxos de caixa amb l'ajuda de procediments basats en dades. Per un costat, els tresorers poden aconseguir estalvis de costos mitjançant la previsió de tresoreria. Per tal d'aconseguir-ho, realitzem d'un estudi empíric amb l'objectiu d'aprofitar les més recents tècniques d'aprenentatge automàtic per connectar l'anàlisi de les dades disponbiles amb els procesos d'optimització en la gestió de tresoreria. Per altra banda, els tresorers poden estar interessats no sols en el cost sinó també en el risc associat a les seues decisions. Per tant, tractem el problema de gestió de tresoreria des d'un punt de vista multiobjectiu, fixant-se tant en el cost com en el risc. A més a més, degut a la canviant situació financera actual, explorem la selecció de models de gestió de tresoreria en funció de diferents condicions operatives i de la seua robustesa. També demostrem la utilitat de les previsions mitjançant un nou model de tresoreria que millora l'estat de l'art al garantir solucions òptimes. Com que la majoria d'empreses treballa amb sistemes de tresoreria amb múltiples comptes bancaris, desenvolupem un marc per a la formulació i solució del problema de gestió de tresoreria amb múltiples comptes bancaris. Finalment, en un intent d'apropar teoria i pràctica, també oferim un llibreria en Python per a usuaris interessats en la construcció de sistemes d'ajuda a la presa de decisions en la gestió de tresoreria. / Salas Molina, F. (2017). DATA-DRIVEN DECISION-MAKING AND ITS APPLICATION TO THE CORPORATE CASH MANAGEMENT PROBLEM [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/95408

With the emphasis on high standards and fiscal accountability, there is a heightened need to inform the research linking student achievement to the allocation of resources. This mixed methods inquiry sought to study how schools utilized Title 1 and Title 1 stimulus funding from 2009-2011 to determine if correlations existed between areas of resource utilization and student achievement by studying both the use of funding and the processes that fifteen elementary and middle Title 1 schools in southern California utilized. The focus was to document resource use of Title 1 and Title 1 stimulus allocations and determine if a correlation existed between expenditures and improved student achievement (quantitative) and to discover themes that existed in student achievement improvement, especially including factors that affect the decision making process at the school (qualitative). Findings suggested that expenditures for professional development and programs for at-risk students played a key role in student achievement growth. The leadership of the school principal was also an indicator of student achievement growth. The use of Title 1 monies, including the increase in Title 1 stimulus monies, were beneficial to schools and positively contributed to the increase in student achievement. Overall, money, when spent well, led to improved student achievement.

<p dir="ltr">Systems biology dynamic models, which are based on differential equations, offer a flexible and accurate framework to explain physiological properties emerging from complex biochem- ical or biological systems. These models enable explicit quantification and interpretation, allowing for simulation and perturbation analysis to study biological features and their inter- actions, as well as understanding system progression and convergence under various initial conditions. However, their application in human disease systems is limited due to unknown kinetics parameters under disease conditions and a reductionist paradigm that fails to cap- ture the complexity of diseases. Meanwhile, the advent of omics technologies provides high- resolution molecular measurements from single cells and spatially resolved samples, as well as comprehensive disease-specific molecular signatures from large patient cohorts. This wealth of data holds the promise for characterizing complex biological systems, necessitating ad- vanced systems biology models and computational tools that can harness multi-omics data to reliably depict biological processes. However, this endeavor faces the challenge of nonlinear relationships between omics data and the system’s dynamic properties, such as the global or local low-rank gene expression patterns across cell types and the nonlinear complexities within transcriptional regulatory networks revealed by single-cell RNA sequencing.</p><p dir="ltr">The overall goal of this report is to develop new computational frameworks, AI-empowered methods, and related mathematical theories to explicitly represent and approximate the dy- namics of complex biological systems by using biological omics data. Our aim is to unravel the intricacies of context-specific dynamic systems using multi-Omics data. Specifically, we solved two different but related computational tasks and enabled the first-of-its-kind methods to (1) identify local low-rank matrices from large omics data, and (2) a robust optimization strategy to approximate metabolic flux. Subsequently, we delve into the realm of data-driven and AI-powered systems biology, harnessing the power of statistical learning and artificial intelligence to approximate differential equations or their representations. This research en- deavor not only contributes to the advancement of subspace modeling but also offers insights into a wide array of complex phenomena across diverse domains, with profound implications for computational biology and beyond.</p>

付記する学位プログラム名: デザイン学大学院連携プログラム / 京都大学 / 新制・課程博士 / 博士(情報学) / 甲第25418号 / 情博第856号 / 新制||情||143(附属図書館) / 京都大学大学院情報学研究科知能情報学専攻 / (主査)特定教授 黒橋 禎夫, 教授 河原 達也, 教授 楠見 孝 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM

Refrigeration is a fast-growing industry and has become an integral part of various industries such as food storage, pharmaceutical, residential, chemical, and data centers. Rising global temperatures have increased the need for more energy-efficient and environmentally conscious refrigeration systems. A consistent functioning refrigeration system requires good fault detection and diagnosis (FDD) system to detect faults before failures occur. A good FDD system can help reduce maintenance costs and increase energy savings. The refrigerant present in the chillers consists of greenhouse gases. Certain faults, such as refrigerant leakage, result in the release of refrigerant into the atmosphere, which has an environmental impact. Hence, an effective FDD system for chillers is important for accurately detecting and diagnosing faults. This thesis aims to build a data-driven FDD system for vapor-compression chillers. The purpose of this thesis is to address the variable operating conditions and fault conditions that occur during the operation of a chiller system. The operating conditions vary depending on the control logic, climate, and other factors that can occur in a system with multiple components. Faults can occur to varying degrees within a system. Early fault detection and diagnosis lead to prompt maintenance dispatching. It is imperative that an FDD system accommodates these conditions and accurately detect faults. This thesis uses two types of data to build an FDD model. The experimental data provided by ASHRAE RP-1043, which contained both normal and fault conditions, were used. The ASHRAE dataset contains normal conditions and seven fault conditions at the four severity levels. Other types of data used were simulated data generated using the ASHRAE RP-1043 model and a small chiller model developed by the author. Simulated data supplemented the experimental dataset with different normal operating conditions and fault severity levels. A hybrid architecture consisting of a dimensionality reduction method and classifier was proposed. This architecture facilitates the comparison of machine learning and deep learning techniques, and may be employed to develop a hybrid model that incorporates both approaches. Time series data was used to train and test this architecture. A deviation matrix method, which is a preprocessing method applied to the training and testing datasets, was proposed. This method was used with steady-state data to develop a 2D Convolutional Neural Network (CNN), Artificial Neural Network (ANN), and Support Vector Machine (SVM). The deviation matrix method proved effective for machine learning and deep learning models to detect and diagnose faults for different normal and fault severity levels. A study using steady-state time-series data and complete test cycle data was conducted to build and test the hybrid architecture. It was concluded that using steady-state time-series data yielded a higher classification accuracy for faults. The deviation matrix method was applied to the simulation and experimental data, and 2D CNN, ANN, and SVM were used to study these datasets. It was concluded that some parts of the training data could be substituted with the simulation data to obtain acceptable classification accuracy. The 2D CNN, ANN, and SVM were able to diagnose faults in the test data containing different severity levels from the training set and small-chiller data. The SVM was also effective in detecting near-normal operations. / Dissertation / Doctor of Philosophy (PhD)

This research evaluates data-driven demand models using natural language processing techniques and analytical approaches. The first essay offers a comprehensive review of data-driven newsvendor literature and applies natural language processing techniques, including latent semantic analysis, latent Dirichlet allocation and cluster analysis to analyze the text data. This study highlights emerging trends and future research directions in the field of data-driven newsvendor research. The second essay contributes to the data-driven newsvendor inventory management literature by proposing nonparametric approaches that include Tobit and quantile regression incorporating leverage values under conditions of homogeneity and heterogeneity. Lastly, the third essay addresses the optimization of healthcare facility location and resource allocation in post-earthquake scenarios, presenting a linear programming model with telemedicine integration for effective disaster response. This study applies the model to the 2005 Kashmir earthquake in Pakistan. These essays collectively highlight the potential of data-driven methodologies in enhancing decision-making processes across diverse domains, while also pointing towards future research directions to address inherent complexities and uncertainties of the models.

There has been significant growth in online social science experiments in order to understand behavior at-scale, with finer-grained data collection. Considerable work is required to perform data analytics for custom experiments. In this dissertation, we design and build composable and extensible automated software pipelines for evaluating social phenomena through iterative experiments and modeling. To reason about experiments and models, we design a formal data model. This combined approach of experiments and models has been done in some studies without automation, or purely conceptually. We are motivated by a particular social behavior, namely collective identity (CI). Group or CI is an individual's cognitive, moral, and emotional connection with a broader community, category, practice, or institution. Extensive experimental research shows that CI influences human decision-making. Because of this, there is interest in modeling situations that promote the creation of CI in order to learn more from the process and to predict human behavior in real life situations. One of our goals in this dissertation is to understand whether a cooperative anagram game can produce CI within a group. With all of the experimental work on anagram games, it is surprising that very little work has been done in modeling these games. Also, abduction is an inference approach that uses data and observations to identify plausibly (and preferably, best) explanations for phenomena. Abduction has broad application in robotics, genetics, automated systems, and image understanding, but have largely been devoid of human behavior. We use these pipelines to understand intra-group cooperation and its effect on fostering CI. We devise and execute an iterative abductive analysis process that is driven by the social sciences. In a group anagrams web-based networked game setting, we formalize an abductive loop, implement it computationally, and exercise it; we build and evaluate three agent-based models (ABMs) through a set of composable and extensible pipelines; we also analyze experimental data and develop mechanistic and data-driven models of human reasoning to predict detailed game player action. The agreement between model predictions and experimental data indicate that our models can explain behavior and provide novel experimental insights into CI. / Doctor of Philosophy / To understand individual and collective behavior, there has been significant interest in using online systems to carry out social science experiments. Considerable work is required for analyzing the data and to uncover interesting insights. In this dissertation, we design and build automated software pipelines for evaluating social phenomena through iterative experiments and modeling. To reason about experiments and models, we design a formal data model. This combined approach of experiments and models has been done in some studies without automation, or purely conceptually. We are motivated by a particular social behavior, namely collective identity (CI). Group or CI is an individual’s cognitive, moral, and emotional connection with a broader community, category, practice, or institution. Extensive experimental research shows that CI influences human decision-making, so there is interest in modeling situations that promote the creation of CI to learn more from the process and to predict human behavior in real life situations. One of our goals in this dissertation is to understand whether a cooperative anagram game can produce CI within a group. With all of the experimental work on anagrams games, it is surprising that very little work has been done in modeling these games. In addition, to identify best explanations for phenomena we use abduction. Abduction is an inference approach that uses data and observations. Abduction has broad application in robotics, genetics, automated systems, and image understanding, but have largely been devoid of human behavior. In a group anagrams web-based networked game setting we do the following. We use these pipelines to understand intra-group cooperation and its effect on fostering CI. We devise and execute an iterative abductive analysis process that is driven by the social sciences. We build and evaluate three agent-based models (ABMs). We analyze experimental data and develop models of human reasoning to predict detailed game player action. We claim our models can explain behavior and provide novel experimental insights into CI, because there is agreement between the model predictions and the experimental data.