Molecular dynamics (MD) simulations find their applications in fundamental understanding of molecular level mechanisms of physical processes. This assists in tuning the key features affecting the development of the novel hybrid materials. A certain application demanding the need for a desired function can be cherished through the hybrids with a blend of new properties by a combination of pure materials. However, to run MD simulations, an accurate representation of the interatomic potentials i.e. force-fields (FF) models remain a crucial aspect. This thesis intricately explores the fusion of MD simulations, uncertainty quantification, and data-driven methodologies to accelerate the computational design of innovative materials and models across the following interconnected chapters. Beginning with the development of force fields for atomic-level systems and coarse-grained models for FCC metals, the study progresses into exploring the intricate interfacial interactions between 2D materials like graphene, MoS2, and water. Current state-of-the-art model development faces the challenge of high dimensional input parameters' model and unknown robustness of developed model. The utilization of advanced optimization techniques such as particle swarm optimization (PSO) integrated with MD enhances the accuracy and precision of FF models. Moreover, the bayesian uncertainty quantification (BUQ) assists FF model development researchers in estimating the robustness of the model. Furthermore, the complex structure and dynamics of water confined between and around sheets was unraveled using 3D Convolutional Neural Networks (3D-CNN). Specifically, through classification and regression models, water molecule ordering/disordering and atomic density profiles were accurately predicted, thereby elucidating nuanced interplays between sheet compositions and confined water molecules. To further the computational design of hybrid materials, this thesis delves into designing and investigating polymer composites with functionalized MOFs shedding light on crucial factors governing their compatibility and performance. Therefore, this report includes the study of structure and dynamics of functionalized MOF in the polymer matrix. Additionally, it investigates the biomedical potential of porous MOFs as drug delivery vehicles (DDVs). Often overlooked is the pivotal role of solvents (used in MOF synthesis or found in relevant body fluids) in the drug adsorption and release process. This report underscores the solvent's impact on drug adsorption within MOFs by comparing results in its presence and absence. Building on these findings, the study delves into the effects of MOF functionalization on tuning the drug adsorption and release process. It further explores how different physical and chemical properties influence drug adsorption within MOFs. Furthermore, the research explores the potential of functionalized MOFs for improved carbon capture, considering their application in energy-related contexts. By harnessing machine learning and deep learning, the thesis introduces innovative pathways for material property prediction and design, emphasizing the pivotal fusion of computational methodologies with data-driven approaches to advance molecular-level understanding and propel future material design endeavors. / Doctor of Philosophy / Envision a world where scientific exploration reaches the microscopic scale, powered by advanced computational tools. In this frontier of materials science, researchers employ sophisticated computer simulations to delve into the intricate properties of materials, particularly focusing on Metal-Organic Frameworks (MOFs). These MOFs, equivalent to microscopic molecular sponges, exhibit remarkable abilities to capture gases or hold medicinal drug compounds. This thesis meticulously studies MOFs alongside materials like graphene, Boron Nitride and Molybdenum disulfide, investigating their interactions with water with unprecedented precision. Through these detailed explorations and the fusion of cutting-edge technologies, we aim to unlock a future featuring enhanced drug delivery systems, improved energy storage solutions, and innovative energy applications.

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Uncertainty quantification (UQ) is an increasingly important part of materials modeling. In this paper, we consider the problem of quantifying parametric uncertainty in classical empirical interatomic potentials (IPs). Previous work based on local sensitivity analysis using the Fisher Information has shown that IPs are sloppy, i.e., are insensitive to coordinated changes of many parameter combinations. We confirm these results and further explore the non-local statistics in the context of sloppy model analysis using both Bayesian (MCMC) and Frequentist (profile likelihood) methods. We interface these tools with the Knowledgebase of Interatomic Models (OpenKIM) and study three models based on the Lennard-Jones, Morse, and Stillinger-Weber potentials, respectively. We confirm that IPs have global properties similar to those of sloppy models from fields such as systems biology, power systems, and critical phenomena. These models exhibit a low effective dimensionality in which many of the parameters are unidentifiable, i.e., do not encode any information when fit to data. Because the inverse problem in such models is ill-conditioned, unidentifiable parameters present challenges for traditional statistical methods. In the Bayesian approach, Monte Carlo samples can depend on the choice of prior in subtle ways. In particular, they often "evaporate" parameters into high-entropy, sub-optimal regions of the parameter space. For profile likelihoods, confidence regions are extremely sensitive to the choice of confidence level. To get a better picture of the relationship between data and parametric uncertainty, we sample the Bayesian posterior at several sampling temperatures and compare the results with those of Frequentist analyses. In analogy to statistical mechanics, we classify samples as either energy-dominated, i.e., characterized by identifiable parameters in constrained (ground state) regions of parameter space, or entropy-dominated, i.e., characterized by unidentifiable (evaporated) parameters. We complement these two pictures with information geometry to illuminate the underlying cause of this phenomenon. In this approach, a parameterized model is interpreted as a manifold embedded in the space of possible data with parameters as coordinates. We calculate geodesics on the model manifold and find that IPs, like other sloppy models, have bounded manifolds with a hierarchy of widths, leading to low effective dimensionality in the model. We show how information geometry can motivate new, natural parameterizations that improve the stability and interpretation of UQ analysis and further suggest simplified, less-sloppy models.

Additive manufacturing (AM) is a novel fabrication technique capable of producing highly complex parts. Nevertheless, a major challenge is improving the quality of the fabricated parts. While there are several ways of approaching this problem, developing data-driven methods that use AM process signatures to identify these part anomalies can be rapidly applied to improve the overall part quality during the build. The objective of this dissertation is to model multiple processes within the AM to quantify the quality of the parts and reduced the uncertainty due to variation in input process parameters. The objective of first study is to build a new layer-wise process signature model to characterize the thermal-defect relationship. Based on melt pool images, we propose novel layer-wise key process signatures, which are calculated using multilinear principal component analysis (MPCA) and are directly correlated with layer-wise quality of the part. Second study broadens the spectrum of the dissertation to include mechanical properties, where a novel two-phase modeling methodology is proposed for fatigue life prediction based on in-situ monitoring of thermal history. In final study, our objective is to pave the way toward a better understanding of the uncertainty in the process-defect-structures relationship using an inverse robust design exploration method. The method involves two steps. In the first step, mathematical models are developed to characterize and model the forward flow of information in the intended additive manufacturing process. In the second step, inverse robust design exploration is carried out to investigate satisfying design solutions that meet multiple AM goals.

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