<div>Data scarcity is intrinsic to many problems in chemical engineering due to physical constraints or cost. This challenge is acute in chemical and materials design applications, where a lack of data is the norm when trying to develop something new for an emerging application. Addressing novel chemical design under these scarcity constraints takes one of two routes: the traditional forward approach, where properties are predicted based on chemical structure, and the recent inverse approach, where structures are predicted based on required properties. Statistical methods such as machine learning (ML) could greatly accelerate chemical design under both frameworks; however, in contrast to the modeling of continuous data types, molecular prediction has many unique obstacles (e.g., spatial and causal relationships, featurization difficulties) that require further ML methods development. Despite these challenges, this work demonstrates how transfer learning and active learning strategies can be used to create successful chemical ML models in data scarce situations.<br></div><div>Transfer learning is a domain of machine learning under which information learned in solving one task is transferred to help in another, more difficult task. Consider the case of a forward design problem involving the search for a molecule with a particular property target with limited existing data, a situation not typically amenable to ML. In these situations, there are often correlated properties that are computationally accessible. As all chemical properties are fundamentally tied to the underlying chemical topology, and because related properties arise due to related moieties, the information contained in the correlated property can be leveraged during model training to help improve the prediction of the data scarce property. Transfer learning is thus a favorable strategy for facilitating high throughput characterization of low-data design spaces.</div><div>Generative chemical models invert the structure-function paradigm, and instead directly suggest new chemical structures that should display the desired application properties. This inversion process is fraught with difficulties but can be improved by training these models with strategically selected chemical information. Structural information contained within this chemical property data is thus transferred to support the generation of new, feasible compounds. Moreover, transfer learning approach helps ensure that the proposed structures exhibit the specified property targets. Recent extensions also utilize thermodynamic reaction data to help promote the synthesizability of suggested compounds. These transfer learning strategies are well-suited for explorative scenarios where the property values being sought are well outside the range of available training data.</div><div>There are situations where property data is so limited that obtaining additional training data is unavoidable. By improving both the predictive and generative qualities of chemical ML models, a fully closed-loop computational search can be conducted using active learning. New molecules in underrepresented property spaces may be iteratively generated by the network, characterized by the network, and used for retraining the network. This allows the model to gradually learn the unknown chemistries required to explore the target regions of chemical space by actively suggesting the new training data it needs. By utilizing active learning, the create-test-refine pathway can be addressed purely in silico. This approach is particularly suitable for multi-target chemical design, where the high dimensionality of the desired property targets exacerbates data scarcity concerns.</div><div>The techniques presented herein can be used to improve both predictive and generative performance of chemical ML models. Transfer learning is demonstrated as a powerful technique for improving the predictive performance of chemical models in situations where a correlated property can be leveraged alongside scarce experimental or computational properties. Inverse design may also be facilitated through the use of transfer learning, where property values can be connected with stable structural features to generate new compounds with targeted properties beyond those observed in the training data. Thus, when the necessary chemical structures are not known, generative networks can directly propose them based on function-structure relationships learned from domain data, and this domain data can even be generated and characterized by the model itself for closed-loop chemical searches in an active learning framework. With recent extensions, these models are compelling techniques for looking at chemical reactions and other data types beyond the individual molecule. Furthermore, the approaches are not limited by choice of model architecture or chemical representation and are expected to be helpful in a variety of data scarce chemical applications.</div>

Recent advances in linear quantum optics have involved the development of unbiased, multi-port optical elements for use with pairs of identical photons, or biphotons, for the design of novel quantum devices. The unbiased counterpart of a conventional 50:50 beam-splitter is a particularly useful multiport, thanks to its unique algebraic properties when acting on both classical and quantum states of light. Dubbed the “Grover coin” due to its utility in the Grover’s Search quantum algorithm, the unbiased four-port behaves as a conventional beam splitter, but with two additional ports to provide a photon amplitude with four, equally-probable, spatially distinct paths through which it may propagate. While the Grover coin has been realized in the laboratory in the form of bulk optical elements, the formation of a network of Grover coins is impractical due to the meticulous alignment and large number of elements required for a single component. Therefore, the development of a small, chip-integrated embodiment of the unbiased four-port would enable experimentation with novel quantum optics theories, through the interconnection of multiple Grover coins over a small footprint. This thesis details the design and fabrication of photonic waveguide-based integrated circuit elements through numerical simulation, topology optimization and CMOS-compatible manufacturing processes. / 2025-06-08T00:00:00Z

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"Inverse design" formulates the design process as an inverse problem; optimal values of a parameterized design space are sought so to best reproduce quantitative outcomes from the forwards dynamics of the design's intended environment. Arguably, two subtasks are necessary to iteratively solve such a design problem; the generation and evaluation of designs. This thesis work documents two experiments leveraging machine learning (ML) to facilitate each subtask. Included first is a review of relevant physics and machine learning theory. Then, analysis on the theoretical foundations of ensemble methods realizes a novel equation describing the effect of Bagging and Random Forests on the expected mean squared error of a base model. Complex models of design evaluation may capture environmental dynamics beyond those that are useful for a design optimization. These constitute unnecessary time and computational costs. The first experiment attempts to avoid these by replacing EGSnrc, a Monte Carlo simulation of coupled electron-photon transport, with an efficient ML "surrogate model". To investigate the benefits of surrogate models, a simulated annealing design optimization is twice conducted to reproduce an arbitrary target design, once using EGSnrc and once using a random forest regressor as a surrogate model. It is found that using the surrogate model produced approximately an 100x speed-up, and converged upon an effective design in fewer iterations. In conclusion, using a surrogate model is faster and (in this case) also more effective per-iteration. The second experiment of this thesis work leveraged machine learning for design generation. As a proof-of-concept design objective, the work seeks to efficiently sample 2D Ising spin model configurations from an optimized design space with a uniform distribution of internal energies. Randomly sampling configurations yields a narrow Gaussian distribution of internal energies. Convolutional neural networks (CNN) trained with NeuroEvolution, a mutation-only genetic algorithm, were used to statistically shape the design space. Networks contribute to sampling by processing random inputs, their outputs are then regularized into acceptable configurations. Samples produced with CNNs had more uniform distribution of internal energies, and ranged across the entire space of possible values. In combination with conventional sampling methods, these CNNs can facilitate the sampling of configurations with uniformly distributed internal energies.

Due to the ever-increasing demands of highly integrated optical devices in imaging, spectroscopy, communications, and so on, there is a compelling need to design and characterize novel compact photonic components. The traditional approaches to realizing compact optical devices typically result in large footprints and sizable optical thicknesses. Moreover, they offer few degrees of freedom (DOF), hampering on-demand functionalities, on-chip integration, and scalability. This thesis will address the design and development of ultracompact diffractive devices for imaging and spectroscopy, utilizing advanced machine learning techniques and optimization algorithms. I first present the inverse design of ultracompact dual-focusing lenses and broad-band focusing spectrometers based on adaptive diffractive optical networks (a-DONs), which combine optical diffraction physics and deep learning capabilities for the inverse design of multi-layered diffractive devices. I designed two-layer diffractive devices that can selectively focus incident radiation over well-separated spectral bands at desired distances and also optimized a-DON-based focusing spectrometers with engineered angular dispersion for desired bandwidth and nanometer spectral resolution. Furthermore, I introduced a new approach based on a-DONs for the engineering of diffractive devices with arbitrary k-space, which produces improved imaging performances compared to contour-PSF approaches to lens-less computational imaging. Moreover, my method enables control of sparsity and isotropic k-space in pixelated screens of dielectric scatterers that are compatible with large-scale photolithographic fabrication techniques. Finally, by combining adjoint optimization with the rigorous generalized Mie theory, I developed and characterize functionalized compact devices, which I called "photonic patches," consisting of ~100 dielectric nanocylinders that achieve predefined functionalities such as beam steering, Fresnel zone focusing, local density of states (LDOS) enhancement, etc. My method enables the inverse design of ultracompact focusing spectrometers for on-chip planar integration. Leveraging multiple scattering of light in disordered random media, I additionally demonstrated a novel approach to on-chip spectroscopy driven by high-throughput multifractal (i.e., multiscale) media, resulting in sub-nanometer spectral resolution at the 50×50 µm²-scale footprint.

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The automation of airfoil design process is an ongoing effort within the field of turbo-machinery design, with significant focus on developing new reliable and consistent methods that can meet the needs of the engineers. A wide variety of approaches has been in use for inverse airfoil design process which benefit from theoretical inverse design, statistical methods, empirical discoveries and many other ways to solve the design problem. This thesis work also develops a tool in Python to be used in airfoil aerodynamic design process that is simple, fast and accurate enough for initial design of turbo-machinery blades with focus on turbine airfoils used for operation in aircraft engines. To convey the decision-making process during development a simplified case is presented. The underlying considerations are discussed. Other available methods in the literature used for similar problems, are also evaluated and compared to demonstrate the advantages and limitations of the methods used within the tool. The inverse design problem is formulated as a multi-objective optimization problem to handle various different objectives that are relevant for aerodynamic design of turbo-machinery airfoils. Test runs are made and the results are discussed to assess how robust the tool is and how the current capabilities can be modified or extended. After the development process, the tool is verified to be a suitable option for real-life design optimization tasks and can be used as a building block for a much more comprehensive tool that may be developed in the future. / Automatisering av processen för design av vingprofiler kräver fortlöpande insatser inom området turbomaskindesign, med stort fokus på att utveckla nya tillförlitliga och konsekventa metoder som kan tillgodose ingenjörernas behov. Ett stort antal olika tillvägagångssätt har provats för omvänd design av vingprofiler såsom teoretisk invers design, statistiska metoder, empiriska upptäckter och många andra sätt att lösa designproblemet. Detta avhandlingsarbete är också ett lyckat försök att utveckla ett verktyg i Python som ska användas i den aerodynamiska designprocessen; det är enkelt, snabbt och noggrant för den initiala designen av turbomaskinblad med fokus på turbinblad som för användning i flygmotorer. För att förmedla beslutsprocessen under utvecklingen presenteras ett förenklat fall. De underliggande övervägandena diskuteras. Andra tillgängliga metoder i litteraturen som används för liknande problem utvärderas och jämförs för att visa fördelarna och begränsningarna med de metoder som används i verktyget. Det omvända designproblemet formuleras som ett multi-objektivt optimeringsproblem för att hantera olika mål som är relevanta för aerodynamisk design av turbomaskiner. Testkörningar görs och resultaten diskuteras för att bedöma hur robust verktyget är och hur de nuvarande funktionerna kan modifieras eller utökas. Efter utvecklingsprocessen verifieras verktyget som ett lämpligt alternativ för verkliga designoptimeringsuppgifter och kan användas som en byggsten för ett mycket mer omfattande verktyg som kan utvecklas i framtiden.

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.

The Flux Jacobian matrices, the elements of which are the derivatives of the flux vectors with respect to the flow variables, are needed to be evaluated in implicit flow solutions and in analytical sensitivity analyzing methods. The main motivation behind this thesis study is to explore the accuracy of the numerically evaluated flux Jacobian matrices and the effects of the errors in those matrices on the convergence of the flow solver, on the accuracy of the sensitivities and on the performance of the design optimization cycle. To perform these objectives a flow solver, which uses exact Newton&rsquo / s method with direct sparse matrix solution technique, is developed for the Euler flow equations. Flux Jacobian is evaluated both numerically and analytically for different upwind flux discretization schemes with second order MUSCL face interpolation. Numerical flux Jacobian matrices that are derived with wide range of finite difference perturbation magnitudes were compared with analytically derived ones and the optimum perturbation magnitude, which minimizes the error in the numerical evaluation, is searched. The factors that impede the accuracy are analyzed and a simple formulation for optimum perturbation magnitude is derived. The sensitivity derivatives are evaluated by direct-differentiation method with discrete approach. The reuse of the LU factors of the flux Jacobian that are evaluated in the flow solution enabled efficient sensitivity analysis. The sensitivities calculated by the analytical Jacobian are compared with the ones that are calculated by numerically evaluated Jacobian matrices. Both internal and external flow problems with varying flow speeds, varying grid types and sizes are solved with different discretization schemes. In these problems, when the optimum perturbation magnitude is used for numerical Jacobian evaluation, the errors in Jacobian matrix and the sensitivities are minimized. Finally, the effect of the accuracy of the sensitivities on the design optimization cycle is analyzed for an inverse airfoil design performed with least squares minimization.