X-ray tomography is an imaging technique to inspect objects' internal structures with externally measured data by X-ray radiation non-destructively. However, there are concerns about X-ray radiation damage and tomographic acquisition speed in real-life applications. Strategies with insufficient measurements, such as measurements with insufficient dosage (low-dose) and measurements with insufficient projection angles (sparse-view), have been proposed to relieve these problems but are generally compromising imaging quality. Such a dilemma inspires the development of advanced tomographic imaging techniques, in particular, deep learning algorithms to improve reconstruction results with insufficient measurements. The overall aim of this thesis is to design efficient and robust data-driven algorithms with the help of prior knowledge from physics insights and measurement models. We first introduce a hierarchical synthesis CNN (HSCNN), which is a knowledge-incorporated data-driven tomographic reconstruction method for sparse-view and low-dose tomography with a split-and-synthesis approach. This proposed learning-based method informs the forward model biases based on data-driven learning but with reduced training data. The learning scheme is robust against sampling bias and aberrations introduced in the forward modeling. High-fidelity X-ray tomographic imaging reconstruction results are obtained with a very sparse number of projection angles for both numerical simulated and physics experiments. Comparison with both conventional non-learning-based algorithms and advanced learning-based approaches shows improved accuracy and reduced training data size. As a result of the split-and-synthesis strategy, the trained network could be transferable to new cases. We then present a deep learning-based enhancement method, HDrec (hybrid-dose reconstruction algorithm), for low-dose tomography reconstruction via a hybrid-dose acquisition strategy composed of textit{extremely sparse-view normal-dose measurements} and textit{full-view low-dose measurements}. The training is applied for each individual sample without the need of transferring the trained models for other samples. Evaluation of two experimental datasets under different hybrid-dose acquisition conditions shows significantly improved structural details and reduced noise levels compared to results with traditional analytical and regularization-based iterative reconstruction methods from uniform acquisitions under the same amount of total dosage. Our proposed approach is also more efficient in terms of single projection denoising and single image reconstruction. In addition, we provide a strategy to distribute dosage smartly with improved reconstruction quality. When the total dosage is limited, the strategy of combining a very few numbers of normal-dose projections and with not-too-low full-view low-dose measurements greatly outperforms the uniform distribution of the dosage throughout all projections. We finally apply the proposed data-driven X-ray tomographic imaging reconstruction techniques, HSCNN and HDrec, to the dynamic damage/defect characterization applications for the cellular materials and binder jetting additive manufacturing. These proposed algorithms improve data acquisition speeds to record internal dynamic structure changes. A quantitative comprehensive framework is proposed to study the dynamic internal behaviors of cellular structure, which contains four modules: (i) In-situ fast synchrotron X-ray tomography, which enables collection of 3D microstructure in a macroscopic volume; (ii) Automated 3D damage features detection to recognize damage behaviors in different scales; (iii) Quantitative 3D structural analysis of the cellular microstructure, by which key morphological descriptors of the structure are extracted and quantified; (iv) Automated multi-scale damage structure analysis, which provides a quantitative understanding of damage behaviors. In terms of binder jetting materials, we show a pathway toward the efficient acquisition of holistic defect information and robust morphological representation through the integration of (i) fast tomography algorithms, (ii) 3D morphological analysis, and (iii) machine learning-based big data analysis. The applications to two different 4D material characterization demonstrate the advantages of these proposed tomographic imaging techniques and provide quantitative insights into the global evolution of damage/defect beyond qualitative human observation. / Doctor of Philosophy / X-ray tomography is a nondestructive imaging technique to visualize interior structures of non-transparent objects, which has been widely applied to resolve implicit 3D structures, such as human organs and tissues for clinical diagnosis, contents of baggage for security check, internal defect evolution during additive manufacturing, observing fracturing accompanying mechanical tests, and etc. Multiple planar measurements with sufficient X-ray exposure time among different angles are desirable to reconstruct the unique high-quality 3D internal distribution. However, there are practical concerns about X-ray radiation damage to biology samples or long-time acquisition for dynamic experiments in real-life applications. Insufficient measurements by reducing the number of total measurements or the time for each measurement, are proposed to solve this problem but doing so usually leads to the sacrifice of the reconstruction quality. Computational algorithms are developed for tomographic imaging under these insufficient measurement conditions to obtain reconstructions with improved quality. Deep learning has been successfully applied to numerous areas, such as in recognizing speech, translating languages, detecting objects, and etc. It has also been applied to X-ray tomographic imaging to improve the reconstruction results by learning the features through thousands to millions of corrupted and ideal reconstruction pairs. The aim of this thesis to design efficient deep learning-based algorithms with the help of physical and measurement priors to reduce the number of training datasets. We propose two different deep learning-based tomographic imaging techniques to improve reconstruction results with reduced training data under different insufficient measurement conditions. One way is to incorporate prior knowledge of the physics models to reduce the required amount of ground truth data, from thousands to hundreds. The training data requirement is further simplified with another hybrid measurement strategy, which could be implemented on each individual sample with only several high-quality measurements. In the end, we apply these two proposed algorithms to different dynamic damage/defect behavior characterization applications. Our methods achieve improved reconstruction results with greatly enhanced experimental speeds, which become suitable for dynamic 3D recording. Final results demonstrate the advantages of the proposed tomographic imaging techniques and provide quantitative insights into the global dynamic evolution inside the material. This quantitative analysis also provides a much more comprehensive understanding than qualitative human observation.

Broadly this thesis looks into network and time-series mining problems pertaining to dynamics over networks in various domains. Which locations and staff should we monitor in order to detect C. Difficile outbreaks in hospitals? How do we predict the peak intensity of the influenza incidence in an interpretable fashion? How do we infer the states of all nodes in a critical infrastructure network where failures have occurred? Leveraging domain-based information should make it is possible to answer these questions. However, several new challenges arise, such as (a) presence of more complex dynamics. The dynamics over networks that we consider are complex. For example, C. Difficile spreads via both people-to-people and surface-to-people interactions and correlations between failures in critical infrastructures go beyond the network structure and depend on the geography as well. Traditional approaches either rely on models like Susceptible Infectious (SI) and Independent Cascade (IC) which are too restrictive because they focus only on single pathways or do not incorporate the model at all, resulting in sub-optimality. (b) data sparsity. Additionally, the data sparsity still persists in this space. Specifically, it is difficult to collect the exact state of each node in the network as it is high-dimensional and difficult to directly sample from. (c) mismatch between data and process. In many situations, the underlying dynamical process is unknown or depends on a mixture of several models. In such cases, there is a mismatch between the data collected and the model representing the dynamics. For example, the weighted influenza like illness (wILI) count released by the CDC, which is meant to represent the raw fraction of total population infected by influenza, actually depends on multiple factors like the number of health-care providers reporting the number and public tendency to seek medical advice. In such cases, methods which generalize well to unobserved (or unknown) models are required. Current approaches often fail in tackling these challenges as they either rely on restrictive models, require large volume of data, and/or work only for predefined models. In this thesis, we propose to leverage domain-based frameworks, which include novel models and analysis techniques, and domain-based low dimensional representation learning to tackle the challenges mentioned above for networks and time-series mining tasks. By developing novel frameworks, we can capture the complex dynamics accurately and analyze them more efficiently. For example, to detect C. Difficile outbreaks in a hospital setting, we use a two-mode disease model to capture multiple pathways of outbreaks and discrete lattice-based optimization framework. Similarly, we propose an information theoretic framework which includes geographically correlated failures in critical infrastructure networks to infer the status of the network components. Moreover, as we use more realistic frameworks to accurately capture and analyze the mechanistic processes themselves, our approaches are effective even with sparse data. At the same time, learning low-dimensional domain-aware embeddings capture domain specific properties (like incidence-based similarity between historical influenza seasons) more efficiently from sparse data, which is useful for subsequent tasks. Similarly, since the domain-aware embeddings capture the model information directly from the data without any modeling assumptions, they generalize better to new models. Our domain-aware frameworks and embeddings enable many applications in critical domains. For example, our domain-aware frameworks for C. Difficile allows different monitoring rates for people and locations, thus detecting more than 95% of outbreaks. Similarly, our framework for product recommendation in e-commerce for queries with sparse engagement data resulted in a 34% improvement over the current Walmart.com search engine. Similarly, our novel framework leads to a near optimal algorithms, with additive approximation guarantee, for inferring network states given a partial observation of the failures in networks. Additionally, by exploiting domain-aware embeddings, we outperform non-trivial competitors by up to 40% for influenza forecasting. Similarly, domain-aware representations of subgraphs helped us outperform non-trivial baselines by up to 68% in the graph classification task. We believe our techniques will be useful for variety of other applications in many areas like social networks, urban computing, and so on. / Doctor of Philosophy / Which locations and staff should we monitor to detect pathogen outbreaks in hospitals? How do we predict the peak intensity of the influenza incidence? How do we infer the failures in water distribution networks? These are some of the questions on dynamics over networks discussed in this thesis. Here, we leverage the domain knowledge to answer these questions. Specifically, we propose (a) novel optimization frameworks where we exploit domain knowledge for tractable formulations and near-optimal algorithms, and (b) low dimensional representation learning where we design novel neural architectures inspired by domain knowledge. Our frameworks capture the complex dynamics accurately and help analyze them more efficiently. At the same time, our low-dimensional embeddings capture domain specific properties more efficiently from sparse data, which is useful for subsequent tasks. Similarly, our domain-aware embeddings are inferred directly from the data without any modeling assumptions, hence they generalize better. The frameworks and embeddings we develop enable many applications in several domains. For example, our domain-aware framework for outbreak detection in hospitals has more than 95% accuracy. Similarly, our framework for product recommendation in e-commerce for queries with sparse data resulted in a 34% improvement over state-of-the-art e-commerce search engine. Additionally, our approach outperforms non-trivial competitors by up to 40% in influenza forecasting.

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.

Computational fluid dynamics (CFD) has been widely used to simulate turbulent flows. Although an increased availability of computational resources has enabled high-fidelity simulations (e.g. large eddy simulation and direct numerical simulation) of turbulent flows, the Reynolds-Averaged Navier-Stokes (RANS) equations based models are still the dominant tools for industrial applications. However, the predictive capability of RANS models is limited by potential inaccuracies driven by hypotheses in the Reynolds stress closure. With the ever-increasing use of RANS simulations in mission-critical applications, the estimation and reduction of model-form uncertainties in RANS models have attracted attention in the turbulence modeling community. In this work, I focus on estimating uncertainties stemming from the RANS turbulence closure and calibrating discrepancies in the modeled Reynolds stresses to improve the predictive capability of RANS models. Both on-line and off-line data are utilized to achieve this goal. The main contributions of this dissertation can be summarized as follows: First, a physics-based, data-driven Bayesian framework is developed for estimating and reducing model-form uncertainties in RANS simulations. An iterative ensemble Kalman method is employed to assimilate sparse on-line measurement data and empirical prior knowledge for a full-field inversion. The merits of incorporating prior knowledge and physical constraints in calibrating RANS model discrepancies are demonstrated and discussed. Second, a random matrix theoretic framework is proposed for estimating model-form uncertainties in RANS simulations. Maximum entropy principle is employed to identify the probability distribution that satisfies given constraints but without introducing artificial information. Objective prior perturbations of RANS-predicted Reynolds stresses in physical projections are provided based on comparisons between physics-based and random matrix theoretic approaches. Finally, a physics-informed, machine learning framework towards predictive RANS turbulence modeling is proposed. The functional forms of model discrepancies with respect to mean flow features are extracted from the off-line database of closely related flows based on machine learning algorithms. The RANS-modeled Reynolds stresses of prediction flows can be significantly improved by the trained discrepancy function, which is an important step towards the predictive turbulence modeling. / Ph. D.

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.

In this dissertation, I extend the analysis of human dynamics to human movements in online activities. My work starts with a discussion of the human information foraging process based on three large collections of empirical search click-through logs collected in different time periods. With the analogy of viewing the click-through on search engine result pages as a random walk, a variety of quantities like the distributions of step length and waiting time as well as mean-squared displacements, correlations and entropies are discussed. Notable differences between the different logs reveal an increased efficiency of the search engines, which is found to be related to the vanishing of the heavy-tailed characteristics of step lengths in newer logs as well as the switch from superdiffusion to normal diffusion in the diffusive processes of the random walks. In the language of foraging, the newer logs indicate that online searches overwhelmingly yield local searches, whereas for the older logs the foraging processes are a combination of local searches and relocation phases that are power-law distributed. The investigation highlights the presence of intermittent search processes in online searches, where phases of local explorations are separated by power-law distributed relocation jumps. In the second part of this dissertation I focus on an in-depth analysis of online gambling behaviors. For this analysis the collected empirical gambling logs reveal the wide existence of heavy-tailed statistics in various quantities in different online gambling games. For example, when players are allowed to choose arbitrary bet values, the bet values present log-normal distributions, meanwhile if they are restricted to use items as wagers, the distribution becomes truncated power laws. Under the analogy of viewing the net change of income of each player as a random walk, the mean-squared displacement and first-passage time distribution of these net income random walks both exhibit anomalous diffusion. In particular, in an online lottery game the mean-squared displacement presents a crossover from a superdiffusive to a normal diffusive regime, which is reproduced using simulations and explained analytically. This investigation also reveals the scaling characteristics and probability reweighting in risk attitude of online gamblers, which may help to interpret behaviors in economic systems. This work was supported by the US National Science Foundation through grants DMR-1205309 and DMR-1606814. / Ph. D. / Humans are complex, meanwhile understanding the complex human behaviors is of crucial importance in solving many social problems. In recent years, socio physicists have made substantial progress in human dynamics research. In this dissertation, I extend this type of analysis to human movements in online activities. My work starts with a discussion of the human information foraging process. This investigation is based on empirical search logs and an analogy of viewing the click-through on search engine result pages as a random walk. With an increased efficiency of the search engines, the heavy-tailed characteristics of step lengths disappear, and the diffusive processes of the random walkers switch from superdiffusion to normal diffusion. In the language of foraging, the newer logs indicate that online searches overwhelmingly yield local searches, whereas for the older logs the foraging processes are a combination of local searches and relocation phases that are power-law distributed. The investigation highlights the presence of intermittent search processes in online searches, where phases of local explorations are separated by power-law distributed relocation jumps. In the second part of this dissertation I focus on an in-depth analysis of online gambling behaviors, where the collected empirical gambling logs reveal the wide existence of heavy-tailed statistics in various quantities. Using an analogy of viewing the net change of income of each player as a random walk, the mean-squared displacement and first-passage time distribution of these net income random walks exhibit anomalous diffusion. This investigation also reveals the scaling characteristics and probability reweighting in risk attitude of online gamblers, which may help to interpret behaviors in economic systems. This work was supported by the US National Science Foundation through grants DMR-1205309 and DMR-1606814.

Reynolds-Averaged Navier-Stokes (RANS) simulations are widely used for engineering design and analysis involving turbulent flows. In RANS simulations, the Reynolds stress needs closure models and the existing models have large model-form uncertainties. Therefore, the RANS simulations are known to be unreliable in many flows of engineering relevance, including flows with three-dimensional structures, swirl, pressure gradients, or curvature. This lack of accuracy in complex flows has diminished the utility of RANS simulations as a predictive tool for engineering design, analysis, optimization, and reliability assessments. Recently, data-driven methods have emerged as a promising alternative to develop the model of Reynolds stress for RANS simulations. In this dissertation I explore two physics-informed, data-driven frameworks to improve RANS modeled Reynolds stresses. First, a Bayesian inference framework is proposed to quantify and reduce the model-form uncertainty of RANS modeled Reynolds stress by leveraging online sparse measurement data with empirical prior knowledge. Second, a machine-learning-assisted framework is proposed to utilize offline high-fidelity simulation databases. Numerical results show that the data-driven RANS models have better prediction of Reynolds stress and other quantities of interest for several canonical flows. Two metrics are also presented for an a priori assessment of the prediction confidence for the machine-learning-assisted RANS model. The proposed data-driven methods are also applicable to the computational study of other physical systems whose governing equations have some unresolved physics to be modeled. / Ph. D. / Reynolds-Averaged Navier–Stokes (RANS) simulations are widely used for engineering design and analysis involving turbulent flows. In RANS simulations, the Reynolds stress needs closure models and the existing models have large model-form uncertainties. Therefore, the RANS simulations are known to be unreliable in many flows of engineering relevance, including flows with three-dimensional structures, swirl, pressure gradients, or curvature. This lack of accuracy in complex flows has diminished the utility of RANS simulations as a predictive tool for engineering design, analysis, optimization, and reliability assessments. Recently, data-driven methods have emerged as a promising alternative to develop the model of Reynolds stress for RANS simulations. In this dissertation I explore two physics-informed, data-driven frameworks to improve RANS modeled Reynolds stresses. First, a Bayesian inference framework is proposed to quantify and reduce the model-form uncertainty of RANS modeled Reynolds stress by leveraging online sparse measurement data with empirical prior knowledge. Second, a machine-learning-assisted framework is proposed to utilize offline high fidelity simulation databases. Numerical results show that the data-driven RANS models have better prediction of Reynolds stress and other quantities of interest for several canonical flows. Two metrics are also presented for an a priori assessment of the prediction confidence for the machine-learning-assisted RANS model. The proposed data-driven methods are also applicable to the computational study of other physical systems whose governing equations have some unresolved physics to be modeled.

Modelling surface runoff can be beneficial to operations within many fields, such as agriculture planning, flood and drought risk assessment, and water resource management. In this study, we built a data-driven model that can reproduce monthly surface runoff at a 4-km grid network covering 13 watersheds in the Chesapeake Bay area. We used a random forest algorithm to build the model, where monthly precipitation, temperature, land cover, and topographic data were used as predictors, and monthly surface runoff generated by the SWAT hydrological model was used as the response. A sub-model was developed for each of 12 monthly surface runoff estimates, independent of one another. Accuracy statistics and variable importance measures from the random forest algorithm reveal that precipitation was the most important variable to the model, but including climatological data from multiple months as predictors significantly improves the model performance. Using 3-month climatological, land cover, and DEM derivatives from 40% of the 4-km grids as the training dataset, our model successfully predicted surface runoff for the remaining 60% of the grids (mean R2 (RMSE) for the 12 monthly models is 0.83 (6.60 mm)). The lowest R2 was associated with the model for August, when the surface runoff values are least in a year. In all studied watersheds, the highest predictive errors were found within the watershed with greatest topographic complexity, for which the model tended to underestimate surface runoff. For the other 12 watersheds studied, the data-driven model produced smaller and more spatially consistent predictive errors. / Master of Science / Surface runoff data can be valuable to many fields, such as agriculture planning, water resource management, and flood and drought risk assessment. The traditional approach to acquire the surface runoff data is by simulating hydrological models. However, running such models always requires advanced knowledge to watersheds and computation technologies. In this study, we build a statistical model that can reproduce monthly surface runoff at 4-km grid covering 13 watersheds in Chesapeake Bay area. This model uses publicly accessible climate, land cover, and topographic datasets as predictors, and monthly surface runoff from the SWAT model as the response. We develop 12 monthly models for each month, independent to each other. To test whether the model can be applied to generalize the surface runoff for the entire study area, we use 40% of grid data as the training sample and the remainder as validation. The accuracy statistics, the annual mean R2 and RMSE are 0.83 and 6.60 mm, show our model is capable to accurately reproduce monthly surface runoff of our study area. The statistics for August model are not as satisfying as other months’ models. The possible reason is the surface runoff in August is the lowest among the year, thus there is no enough variation for the algorithm to distinguish the minor difference of the response in model building process. When applying the model to watersheds in steep terrain conditions, we need to pay attention to the results in which the error may be relatively large.

We investigate the effect of spatial filtering on the recently proposed data-driven correction reduced order model (DDC-ROM). We compare two filters: the ROM projection, which was originally used to develop the DDC-ROM, and the ROM differential filter, which uses a Helmholtz operator to attenuate the small scales in the input signal. We focus on the following questions: ``Do filtering and differentiation with respect to space variable commute, when filtering is applied to the diffusion term?'' or in other words ``Do we have commutation error (CE) in the diffusion term?" and ``If so, is the commutation error data-driven correction ROM (CE-DDC-ROM) more accurate than the original DDC-ROM?'' If the CE exists, the DDC-ROM has two different correction terms: one comes from the diffusion term and the other from the nonlinear convection term. We investigate the DDC-ROM and the CE-DDC-ROM equipped with the two ROM spatial filters in the numerical simulation of the Burgers equation with different diffusion coefficients and two different initial conditions (smooth and non-smooth). / M.S. / We propose reduced order models (ROMs) for an efficient and relatively accurate numerical simulation of nonlinear systems. We use the ROM projection and the ROM differential filters to construct a novel data-driven correction ROM (DDC-ROM). We show that the ROM spatial filtering and differentiation do not commute for the diffusion operator. Furthermore, we show that the resulting commutation error has an important effect on the ROM, especially for low viscosity values. As a mathematical model for our numerical study, we use the one-dimensional Burgers equations with smooth and non-smooth initial conditions.

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.