Metal additive manufacturing (AM) is an emerging technology for producing parts with virtually no constraint on the geometry. AM builds a part by depositing materials in a layer-by-layer fashion. Despite the benefits in several critical applications, quality issues are one of the primary concerns for the widespread adoption of metal AM. Addressing these issues starts with a better understanding of the underlying physics and includes monitoring and controlling the process in a real-world manufacturing environment. Digital Twins (DTs) are virtual representations of physical systems that enable fast and accurate decision-making. DTs rely on Artificial Intelligence (AI) to process complex information from multiple sources in a manufacturing system at multiple levels. This information typically comes from partially known process physics, in-situ sensor data, and ex-situ quality measurements for a metal AM process. Most current AI models cannot handle ill-structured information from metal AM. Thus, this work proposes three novel machine-learning methods for improving the quality of metal AM processes. These methods enable DTs to control quality in several processes, including laser powder bed fusion (LPBF) and additive friction stir deposition (AFSD). The proposed three methods are as follows 1. Process improvement requires mapping the process parameters with ex-situ quality measurements. These mappings often tend to be non-stationary, with limited experimental data. This work utilizes a novel Deep Gaussian Process-based Bayesian optimization (DGP-SI-BO) method for sequential process design. DGP can model non-stationarity better than a traditional Gaussian Process (GP), but it is challenging for BO. The proposed DGP-SI-BO provides a bagging procedure for acquisition function with a DGP surrogate model inferred via Stochastic Imputation (SI). For a fixed time budget, the proposed method gives 10% better quality for the LPBF process than the widely used BO method while being three times faster than the state-of-the-art method. 2. For metal AM, the process physics information is usually in the form of Partial Differential Equations (PDEs). Though the PDEs, along with in-situ data, can be handled through Physics-informed Neural Networks (PINNs), the activation function in NNs is traditionally not designed to handle multi-scale PDEs. This work proposes a novel activation function Self-scalable tanh (Stan) function for PINNs. The proposed activation function modifies the traditional tanh function. Stan function is smooth, non-saturating, and has a trainable parameter. It can allow an easy flow of gradients and enable systematic scaling of the input-output mapping during training. Apart from solving the heat transfer equations for LPBF and AFSD, this work provides applications in areas including quantum physics and solid and fluid mechanics. Stan function also accelerates notoriously hard and ill-posed inverse discovery of process physics. 3. PDE-based simulations typically need to be much faster for in-situ process control. This work proposes to use a Fourier Neural Operator (FNO) for instantaneous predictions (1000 times speed up) of quality in metal AM. FNO is a data-driven method that maps the process parameters with a high dimensional quality tensor (like thermal distribution in LPBF). Training the FNO with simulated data from PINN ensures a quick response to alter the course of the manufacturing process. Once trained, a DT can readily deploy the model for real-time process monitoring. The proposed methods combine complex information to provide reliable machine-learning models and improve understanding of metal AM processes. Though these models can be independent, they complement each other to build DTs and achieve quality assurance in metal AM. / Doctor of Philosophy / Metal 3D printing, technically known as metal additive manufacturing (AM), is an emerging technology for making virtually any physical part with a click of a button. For instance, one of the most common AM processes, Laser Powder Bed Fusion (L-PBF), melts metal powder using a laser to build into any desired shape. Despite the attractiveness, the quality of the built part is often not satisfactory for its intended usage. For example, a metal plate built for a fractured bone may not adhere to the required dimensions. Improving the quality of metal AM parts starts with a better understanding the underlying mechanisms at a fine length scale (size of the powder or even smaller). Collecting data during the process and leveraging the known physics can help adjust the AM process to improve quality. Digital Twins (DTs) are exactly suited for the task, as they combine the process physics and the data obtained from sensors on metal AM machines to inform an AM machine on process settings and adjustments. This work develops three specific methods to utilize the known information from metal AM to improve the quality of the parts built from metal AM machines. These methods combine different types of known information to alter the process setting for metal AM machines that produce high-quality parts.

Laminar-turbulent transition has a strong impact on aerodynamic performance in many practical applications. Hence, there is a practical need for developing reliable and efficient transition prediction models, which form a critical element of the CFD process for aerospace vehicles across multiple flow regimes. This dissertation explores machine learning approaches to develop transition models using data from computations based on linear stability theory. Such data provide strong correlation with the underlying physics governed by linearized disturbance equations. In the proposed transition model, a convolutional neural network-based model encodes information from boundary layer profiles into integral quantities. Such automated feature extraction capability enables generalization of the proposed model to multiple instability mechanisms, even for those where physically defined shape factor parameters cannot be defined/determined in a consistent manner. Furthermore, sequence-to-sequence mapping is used to predict the transition location based on the mean boundary layer profiles. Such an end-to-end transition model provides a significantly simplified workflow. Although the proposed model has been analyzed for two-dimensional boundary layer flows, the embedded feature extraction capability enables their generalization to other flows as well. Neural network-based nonlinear functional approximation has also been presented in the context of transport equation-based closure models. Such models have been examined for their computational complexity and invariance properties based on the transport equation of a general scalar quantity. The data-driven approaches explored here demonstrate the potential for improved transition prediction models. / Doctor of Philosophy / Surface skin friction and aerodynamic heating caused by the flow over a body significantly increases due to the transition from laminar to turbulent flow. Hence, efficient and reliable prediction of transition onset location is a critical component of simulating fluid flows in engineering applications. Currently available transition prediction tools do not provide a good balance between computational efficiency and accuracy. This dissertation explores machine learning approach to develop efficient and reliable models for predicting transition in a significantly simplified manner. Convolutional neural network is used to extract features from the state of boundary layer flow at each location along the body. These extracted features are then processed sequentially using recurrent neural network to predict the amplification of instabilities in the flow, which is directly correlated to the onset of transition. Such an automated nature of feature extraction enables the generalization of this model to multiple transition mechanisms associated with different flow conditions and geometries. Furthermore, an end-to-end mapping from flow data to transition prediction requires no user expertise in stability theory and provides a significantly simplified workflow as compared to traditional stability-based computations. Another category of neural network-based models (known as neural operators) is also examined which can learn functional mapping from input variable field to output quantities. Such models can learn directly from data for complex set of problems, without the knowledge of underlying governing equations. Such attribute can be leveraged to develop a transition prediction model which can be integrated seamlessly in flow solvers. While further development is needed, such data-driven models demonstrate the potential for improved transition prediction models.

Une grande variété d'information se prête bien à être interprétée comme signal; à peu près toute quantité fluctuant continuellement dans l'espace se trouve inclue. La vie quotidienne abonde d'exemples; les images peuvent être vues comme une variation de couleur à travers l'espace bidimensionnel; le son, la pression à travers le temps; les environnements physiques, la matière à travers l'espace tridimensionnel. Les calculs sur ce type d'information requièrent nécessairement une transformation de la forme continue vers la forme discrète, ce qui est accompli par le processus de discrétisation, où seules quelques valeurs du signal continu sous-jacent sont observées et compilées en un signal discret. Sous certaines conditions, à l'aide seulement d'un nombre fini de valeurs observées, le signal discret capture la totalité de l'information comprise dans le signal continu, et permet de le reconstruire parfaitement. Les divers systèmes de senseurs permettant d'acquérir des signaux effectuent tous ce processus jusqu'à un certain niveau de fidélité, qu'il s'agisse d'une caméra, d'un enregistreur audio, ou d'un système de capture tridimensionnelle. Le processus de discrétisation n'est pas unique par contre. Pour un seul signal continu, il existe une infinité de signaux discrets qui lui sont équivalents, et entre lesquels les différences sont contingentes. Ces différences correspondent étroitement aux différences entre systèmes de senseurs, qui ont chacun leur niveau de fidélité et leurs particularités techniques. Les réseaux de neurones profonds sont fréquemment spécialisés pour le type de données spécifiques sur lesquels ils opèrent. Cette spécialisation se traduit souvent par des biais inductifs qui supportent des symétries intrinsèques au type de donnée. Quand le comportement d'une architecture neuronale reste inchangé par une certaine opération, l'architecture est dite invariante sous cette opération. Quand le comportement est affecté d'une manière identique, l'architecture est dite équivariante sous cette opération. Nous explorons en détail l'idée que les architectures neuronales puissent être formulées de façon plus générale si nous abstrayions les spécificités contingentes des signaux discrets, qui dépendent généralement de particularités de systèmes de senseurs, et considérions plutôt l'unique signal continu représenté, qui est la réelle information d'importance. Cette idée correspond au biais inductif de l'invariance à la discrétisation, qui reconnaît que les signaux ont une forme de symétrie à la discrétisation. Nous formulons une architecture très générale qui respecte ce biais inductif. Du fait même, l'architecture gagne la capacité d'être évaluée sur des discrétisations de taille arbitraire avec une grande robustesse, à l'entraînement et à l'inférence. Cela permet d'accéder à de plus grands corpus de données pour l'entraînement, qui peuvent être formés à partir de discrétisations hétérogènes. Cela permet aussi de déployer l'architecture dans un plus grand nombre de contextes où des systèmes de senseurs produisent des discrétisations variées. Nous formulons aussi cette architecture de façon à se généraliser à n'importe quel nombre de dimensions, ce qui la rend idéale pour une grande variété de signaux. Nous notons aussi que son coût d'évaluation diminue avec la taille de la discrétisation, ce qui est peu commun d'architectures conçues pour les signaux, qui ont généralement une discrétisation fixe. Nous remarquons qu'il existe un lien entre l'invariance à la discrétisation, et la distinction séparant l'équivariance à la translation discrète et l'équivariance à la translation continue. Ces deux propriétés reflètent la même symétrie à la translation, mais l'une est plus diluée que l'autre. Nous notons que la plus grande part de la littérature entourant les architectures motivées par l'algèbre générale omettent cette distinction, ce qui affaiblit la force des biais inductifs implémentés. Nous incorporons aussi dans notre méthode la capacité d'implémenter d'autres invariances and equivariances plus générales à l'aide de couches formulées à partir de l'opérateur de dérivée partielle. La symétrie à la translation, la rotation, la réflexion, et la mise à l'échelle peuvent être adoptées, et l'expressivité et l'efficacité en paramètres de la couche résultante sont excellentes. Nous introduisons aussi un nouveau bloc résiduel Laplacien, qui permet de compresser l'architecture sans perte en fonction de la densité de la discrétisation. À mesure que le nombre d'échantillons de la discrétisation réduit, le nombre de couches requises pour l'évaluation diminue aussi. Le coût de calcul de l'architecture diminue ainsi à mesure que certaines de ses couches sont retirées, mais elle se comporte de façon virtuellement identique; c'est ainsi une forme de compression sans perte qui est appliquée. La validité de cette compression sans perte est prouvée théoriquement, et démontrée empiriquement. Cette capacité est absente de la littérature antérieure, au meilleur de notre savoir. Nous greffons à ce mécanisme une forme de décrochage Laplacien, qui applique effectivement une augmentation spectrale aux données pendant l'entraînement. Cela mène à une grande augmentation de la robustesse de l'architecture à des dégradations de qualité de la discrétisation, sans toutefois compromettre sa capacité à performer optimalement sur des discrétisations de haute qualité. Nous n'observons pas cette capacité dans les méthodes comparées. Nous introduisons aussi un algorithme d'initialisation des poids qui ne dépend pas de dérivations analytiques, ce qui permet un prototypage rapide de couches plus exotiques. Nous introduisons finalement une méthode qui généralise notre architecture de l'application à des signaux échantillonnés uniformément vers des signaux échantillonnés non uniformément. Les garanties théoriques que nous fournissons sur son efficacité d'échantillonnage sont positives, mais la complexité ajoutée par la méthode limite malheureusement sa viabilité. / Signals are a useful representation for many types of information that consist of continuously changing quantities. Examples from everyday life are abundant: images are fluctuations of colour over two-dimensional space; sounds are fluctuations of air pressure over time; physical environments are fluctuations of material qualities over three-dimensional space. Computation over this information requires that we reduce its continuous form to some discrete form. This is done through the process of discretization, where only a few values of the underlying continuous signal are observed and compiled into a discrete signal. This process incurs no loss of information and is reversible under some conditions. Sensor systems, such as cameras, sound recorders, and laser scanners all effectively perform discretization when they capture signals, and they preserve them up to a certain degree. This process is not unique, however. Given a single continuous signal, there are countless discrete signals that correspond to it, and the specific choice of discrete signal is generally contingent. Sensor systems all have different technical characteristics that lead to different discretizations. Deep neural network architectures are often tailored to respect the fundamental properties of the specific data type they operate on. Their behaviour often implements inductive biases that respect some fundamental symmetry of the data. When behaviour is unchanged by some operation, the architecture is invariant under it. When behaviour transparently reproduces some operation, the architecture is equivariant under it. We explore in great detail the idea that neural network architectures can be formulated in a more general way if we abstract away the contingent details of the discrete signal, which generally depend on the implementation details of a sensor system, and only consider the underlying continuous signal, which is the true information of interest. This is the intuitive idea behind discretization invariance. We formulate a very general architecture that implements this inductive bias. This allows handling discretizations of various sizes with much greater robustness, both during training and inference. We find that training can leverage more data by allowing heterogeneous discretizations, and that inference can apply to discretizations produced by a broader range of sensor systems. The architecture is agnostic to dimensionality, which makes it widely applicable to different types of signals. The architecture also lowers its computational cost proportionally to the sample count, which is unusual and highly desirable. We find that discretization invariance is also key to the distinction between discrete shift equivariance and continuous shift equivariance. We underline the fact that the majority of previous work on architecture design motivated by abstract algebra fails to consider this distinction. This nuance impacts the robustness of convolutional neural network architectures to translations on signals, weakening their inductive biases if unaddressed. We also incorporate the ability to implement more general invariances and equivariances by formulating steerable layers based on the partial derivative operator, and a set of other compatible architectural blocks. The framework we propose supports shift, rotation, reflection, and scale. We find that this results in excellent expressivity and parameter efficiency. We further improve computational efficiency with a novel Laplacian residual structure that allows lossless compression of the whole network depending on the sample density of the discretization. As the number of samples reduces, the number of layers required for evaluation also reduces. Pruning these layers reduces computational cost and has virtually no effect on the behaviour of the architecture. This is proven theoretically and demonstrated empirically. This capability is absent from any prior work to our knowledge. We also incorporate a novel form of Laplacian dropout within this structure, which performs a spectral augmentation to the data during training. This leads to greatly improved robustness to changes in spectral volume, meaning the architecture has a much greater tolerance to low-quality discretizations without compromising its performance on high-quality discretization. We do not observe this phenomenon in competing methods. We also provide a simple data-driven weight initialization scheme that allows quickly prototyping exotic layer types without analytically deriving weight initialization. We finally provide a method that generalizes our architecture from uniformly sampled signals to nonuniformly sampled signals. While the best-case theoretical guarantees it provides for sample efficiency are excellent, we find it is not viable in practice because of the complications it brings to the discretization of the architecture.