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Nanostructure describes the network of defective and distorted atomic structure existing on the nanoscale within materials. This nanostructure bridges the gap between idealised crys- talline structure and real materials, playing a deterministic role in tailoring physico-chemical properties, as well as providing a basis for mechanistic understanding of complex processes such as mechanical deformation and phase transformation. Characterising nanostructure, to develop understanding of materials, requires experimental techniques capable of probing the structure with spatial resolution on the order of nanometres and across regions of interest up to micrometres. Recent developments in electron microscopy, enabling the acquisition of numerous diffraction patterns in a spatially resolved manner, combined with modern computational power, provides a route to meet this need as developed in this work. Scanning electron diffraction (SED) involves the acquisition of a two-dimensional elec- tron diffraction pattern at each probe position in a two-dimensional scan of a specimen. An information rich 4-dimensional (4D-SED) dataset is obtained that can be analysed extensively post-facto using a wide-range of computational methods. The acquisition of such 4D-SED data from the specimen at numerous orientations may also enable the reconstruction of nanostructure in three-dimensions via tomographic methods. In this work, methods for the acquisition and analysis of 4D-SED data are developed and applied to reveal nanostructure in two and three-dimensions. These methods are applied to various prototypical characterisation challenges in materials science, particularly: strain mapping in two and three dimensions, revealing inter-phase crystallographic relationships, mapping grains in two-dimensional materials, and probing nanostructure in polyethylene.

Given a test input, not knowing the expected output of the software under test (SUT) is called the oracle problem. An emerging method of alleviating the oracle problem is metamorphic testing (MT). Rather than focusing on the correctness of output from a single execution of the SUT, MT exploits metamorphic relations (MRs) as derived oracles for checking the functional correctness of the code. Although researchers have argued that MT can be a simple and effective technique to help software developers, little is known about the actual cost of constructing MRs in real-world software and the relationship between MT and the already well-adopted method in software development. This research examines a series of practices to evaluate the effectiveness of MT during software development. Our investigation is conducted within the context of a real-world scientific software, the Storm Water Management Model (SWMM), developed and maintained by the U.S. Environmental Protection Agency (EPA). To ensure SWMM's accuracy in modeling stormwater runoff and executing hydraulic and water quality simulations, the development team continually evolves the software. Among the challenges they face, software testing stands out as one of the most technically complex tasks. Our research initially investigates the current testing practices and software quality assurance (QA) workflows in scientific software development, taking the SWMM as a case study. The value of our work resides in the qualitative characterizations and quantitative assessments of the tests that scientific software developers have independently written and released within the SWMM context. Our findings indicate that oracles indeed play a role in scientific software testing. Furthermore, by employing an empirical approach, we identified four critical requirements for the improved integration of MT into scientific software development. Constructing MRs is critical because without them, MT cannot be performed. Meanwhile, constructing MRs is typically a costly task. Therefore, we present an approach to classifying input and output (I/O) variables from scientific software's user manual, then mining these variables' associations from the user forum to reduce the cost of constructing MRs. On the other hand, regression testing has long been used by scientific software developers to tackle the oracle problem amid code changes. Although MT has the potential to complement regression testing by checking functional correctness more directly, the cost of constructing MRs and their added advantage in an evolving and highly specialized scientific software system are not yet understood. To further explore this, we conducted an exploratory case study focusing on MR construction by scientific software developers, enabling us to critically evaluate the value addition MT brings to software development. This dissertation offers significant contributions in three distinct areas: Firstly, it fosters a better understanding of the software QA workflow and existing test practices, which in turn aids in more effective support for MT adoption. Secondly, it provides automated support for enhancing the diversity of MRs and reducing the cost associated with MT. Lastly, it scrutinizes the feasibility of MT and its additional advantages compared to regression testing, demonstrated through a real-world system.

The ability to engineer the kinetic and thermodynamic processes by which nanoparticles and colloids form crystals would open new possibilities for materials design. Simulations, coupled with data science and machine learning, can open new frontiers towards obtaining this kind of control over matter at the nanoscale. We need novel approaches in theory and computation to bridge the perspectives of forward design (predicting the properties of a material from its components and their interactions) and inverse design (predicting components and interactions that produce a desired set of material properties). In Chapter I, I provide background about materials design via self-assembly and outline the questions I address in this dissertation. In Chapter II, I present mathematical and physical motivation for a new structural descriptor, the Continuous Topological Order Parameter (CTOP), for analyzing crystallization pathways during self-assembly from a microscopic (particle-local) perspective. The CTOP is comprised of Minkowski Structure Metrics and captures continuous deformations in particles' local environments, which we express as a high-dimensional feature space. This space is coupled with the topology-preserving Uniform Manifold Approximation and Projection (UMAP) dimensionality reduction algorithm to produce a continuous mapping from particles' local environments into interpretable self-assembly pathways. In Chapter III, I apply the CTOP method to a wide range of nanoparticle systems undergoing self-assembly. I directly investigate the CTOP manifold to illuminate aspects of the crystallization process in many types of simple and complex crystals. Hard Particle Monte Carlo and molecular dynamics simulations of pair potentials are analyzed, resulting in a diverse array of self-assembled crystal structures with unit cells ranging from one to 54 particles. I apply unsupervised learning methods to the pathways revealed by the CTOP method, enabling identification of particles' local environments in self-assembling systems including Frank-Kasper phases and decagonal quasicrystals. Next, I show comparisons of pathways with this method, including solid-solid phase transitions. The chapter closes with a discussion of this method's implications for the study of self-assembly, and an outlook on how continuous feature spaces may inspire future analyses and engineering applications. Chapter IV presents a study of machine learning applied to photonic crystals developed in an effort to accelerate photonic materials design. I discuss the development of convolutional neural networks and equivariant neural networks for predicting photonic properties. I conclude with a discussion of photonic densities of states and equivariance in physics-based machine learning, which may provide further insight on this challenging problem. Chapter V covers my contributions as a core developer and maintainer of the freud library, an open-source software package used for data analysis in this dissertation. I describe the use of the freud library in machine learning pipelines and data visualization, and summarize publications using freud (33 to date) across the fields of soft matter, statistical mechanics, and particle-based simulation. In Chapter VI, I discuss my contributions as a core developer and maintainer of the open-source signac data management framework, which helps researchers execute reproducible computational studies, scaling from laptops to supercomputers and emphasizing portability and fast prototyping. I describe the framework's data model, HDF5 data stores for large numerical arrays, enhancements to performance and scalability, and the signac-dashboard application for data visualization. Finally, I conclude with a summary of the work presented in this dissertation and insights for future research in the field of self-assembly pathways, photonics, and software designed for computational researchers.

The ability to produce particles on the nano-scale that self-assemble into soft materials with specifically targeted properties is a promising avenue for a completely new class of materials with novel applications. New synthesis routes and increased computational resources have led to the proposition, modeling, simulation, and experimental realization of a whole plethora of new particle types, including but not limited to faceted polyhedra, Janus particles, lock-and- key particles, and self-propelled particles. The inverse design problem of engineering particles for targeted self-assembly is challenging because of the large available design space. Unlike atoms which are more easily classified by their composition and energy state, nanoparticles can be almost arbitrarily shaped and interactions between particles can be further modulated to various degrees, for example with complete or partial surface coatings. One of the main determinants of material properties is the breaking of symmetries manifested in the formation of crystal structures. In Chapter II of this dissertation, I present a computational method for the optimization of isotropic pair potentials (IPPs) as a general model for the effective interaction between colloidal particles. Using this method, which is based on the minimization of the relative entropy, I optimize IPPs for various simple and complex crystal structures, including simple cubic (cP1), body-centered cubic (cI2), face-centered cubic (cF4), β-tin tI4-Sn (tI4), diamond (cF8), A15-type cP8-Cr3Si (cP8), σ-phase tP30-CrFe (tP30), and clathrate-I cP54-K4Si23 (cP54). Reducing the design space to IPPs allows us to explore it more effectively, however solutions found in this way still need to be mapped to a physical model for experimental synthesis. Chapter III is a study of crystallization pathways, including pathways of some of the models presented in Chapter II. I developed and applied an unsupervised machine learning (ML) workflow for the analysis of self-assembly pathways, which allows us to make observations about the general mechanism of, as well as identify local particle environments that play a role in, the nucleation and growth of the crystal structure. I observe two-step nucleation for all tested crystal structures at moderate supercooling and can demonstrate that random fluctuations of local order play a crucial role in mediating nucleation and growth. 
 In Chapter IV, I present signac, a software framework that assists researchers in managing their computational data and implementing workflows that operate on that data. The signac framework was originally designed and implemented by me and has since its early inception matured into an open-source project with a team of core maintainers and many internal and external contributors and users. Recent work has been focused on enabling the implementation of more complex workflows and increasing the user base, which is facilitated by an affiliation of the project with the NumFOCUS organization. 
Chapter V provides guidelines on how to efficiently develop robust and reusable software within an academic research environment. These guidelines are presented in the form of a heuristic named lazy refactoring, which in essence priorities the incremental development of working solutions over general complete solutions. Determining the correct scope and Application Program Interface (API) for general solutions from scratch is typically much more difficult compared to refactoring existing partial solutions. I conclude this dissertation with a general summary of the presented work and provide a brief outlook on potential future research directions.

Due to the increasing level of knowledge and complexity, scientific software is written by specialists who need to integrate software systems developed by different groups of experts. We describe the faced challenges and our solution when attempting to automate the calibration process of Storm Water Management Model (SWMM) by integrating a Parameter ESTimation (PEST++) tool. Our approach is to integrate only the essential modules of PEST++ into SWMM. Of the many challenges, tight coupling between modules of PEST++ turns out to be our main roadblock. While trying to decouple these modules, a novel coupling pattern is identified, which we name Implicit Class Coupling (ICC). We describe ICC in detail and show the complexity of identifying and resolving it. We propose our heuristic to detect and decouple the implicitly coupled classes. Our solution not only helps achieve integration but can also potentially improve the reusability of PEST++.

Vespucci is a software application developed for imaging and analysis of hyperspectral datasets. Vespucci offers several advantages over other software packages, including a simple user interface, no cost, and less restrictive licensing. Vespucci incorporates several analysis techniques including univariate imaging, principal components analysis, partial-least-squares regression, vertex components analysis and k- means clustering. Additionally, Vespucci can perform a number of useful data-processing operations, including filtering, normalization, baseline correction, and background subtraction. Datasets that consist of spatial or temporal data with a corresponding digital signal, including spectroscopic images, mass spectrometric images, and X-ray diffraction data can be processed in this software. The use of Vespucci in Raman and surface- enhanced Raman spectroscopies has been successfully demonstrated to examine the interaction of silver nanoparticles with corundum and Dengue virus virions. A manuscript detailing Vespucci has been published in the Journal of Open Research Software (http://openresearchsoftware.metajnl.com/articles/10.5334/jors.91/). More information about Vespucci will be available at http://vespucciproject.org.

The demands placed on scientific software are different from those placed on general purpose software, and as a result, creating software for science and for scientists requires a specialized approach. Much of software engineering practices have developed in situations in which a tool is desired to perform some definable task, with measurable and verifiable outcomes. The users and the developers know what the tool "should" do. Scientific software often uses unproven or experimental techniques to address unsolved problems. The software is often run on "experimental" High Performance Computing hardware, adding another layer of complexity. It may not be possible to say what the software should do, or what the results should be, as these may be connected to very scientific questions for which the software is being developed. Software development in this realm requires a deep understanding of the relevent scientific domain area. The present work describes applications resulting from a scientific software development process that builds upon detailed understanding of the scientific domain area. YODA is an application primarily for selecting microarray probe sequences for measuring gene expression. At the time of its development, none of the existing programs for this task satisfied the best-known requirements for microarray probe selection. The question of what makes a good microarray probe was a research area at the time, and YODA was developed to incorporate the latest understanding of these requirements, drawn from the research literature, into a tool that can be used by a research biologist. An appendix examines the response and use in the years since YODA was released. PEPR is a software system for inferring highly resolved whole-genome phylogenies for hundreds of genomes. It encodes a process developed through years of research and collaboration to produce some of the highest quality phylogenies available for large sets of bacterial genomes, with no manual intervention required. This process is described in detail, and results are compared with high quality results from the literature to show that the process is at least as successful as more labor-intensive manual efforts. An appendix presents additional results, including high quality phylogenies for many bacterial Orders.