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Emulation of complex computer simulations have become an effective tool in the exploration of the behaviour of the simulated processes. Agriculture is one such area where the simulation of crop growth, nutrition, soil condition and pollution could be invaluable in any land management decisions. In this paper, we study output from the EPIC simulation model to investigate the behaviour of crop yield in response to changes in inputs such as fertilizer levels, soil, steepness, and other environmental covariates. We build a model for crop yield around a non-linear Mitscherlich Baule growth model to make inferences about the response of crop yield to changes continuous input variables (fertiliser levels), as well as exploring the impact of categorical factor inputs such as land steepness and soil type. A Bayesian hierarchical approach to the modelling was taking for mixed inputs, requiring Markov Chain Monte Carlo simulations to obtain samples from the posterior distributions, to validate and illustrate the results, and to carry out model selection. Our results highlight a strong response of yield to nitrogen, but surprisingly a weak response to phosphorus and also shows the substantial improvement of the model after adding factor effects response to maximum yield for this particular simulator configuration and catchment.

We present a novel hybrid algorithm for training Deep Neural Networks that combines the state-of-the-art Gradient Descent (GD) method with a Mixed Integer Linear Programming (MILP) solver, outperforming GD and variants in terms of accuracy, as well as resource and data efficiency for both regression and classification tasks. Our GD+Solver hybrid algorithm, called GDSolver, works as follows: given a DNN $D$ as input, GDSolver invokes GD to partially train $D$ until it gets stuck in a local minima, at which point GDSolver invokes an MILP solver to exhaustively search a region of the loss landscape around the weight assignments of $D$'s final layer parameters with the goal of tunnelling through and escaping the local minima. The process is repeated until desired accuracy is achieved. In our experiments, we find that GDSolver not only scales well to additional data and very large model sizes, but also outperforms all other competing methods in terms of rates of convergence and data efficiency. For regression tasks, GDSolver produced models that, on average, had 31.5% lower MSE in 48% less time, and for classification tasks on MNIST and CIFAR10, GDSolver was able to achieve the highest accuracy over all competing methods, using only 50% of the training data that GD baselines required.

Process synthesis experiences a disruptive transformation accelerated by digitization and artificial intelligence. We propose a reinforcement learning algorithm for chemical process design based on a state-of-the-art actor-critic logic. Our proposed algorithm represents chemical processes as graphs and uses graph convolutional neural networks to learn from process graphs. In particular, the graph neural networks are implemented within the agent architecture to process the states and make decisions. Moreover, we implement a hierarchical and hybrid decision-making process to generate flowsheets, where unit operations are placed iteratively as discrete decisions and corresponding design variables are selected as continuous decisions. We demonstrate the potential of our method to design economically viable flowsheets in an illustrative case study comprising equilibrium reactions, azeotropic separation, and recycles. The results show quick learning in discrete, continuous, and hybrid action spaces. Due to the flexible architecture of the proposed reinforcement learning agent, the method is predestined to include large action-state spaces and an interface to process simulators in future research.

In the pursuit of explaining implicit regularization in deep learning, prominent focus was given to matrix and tensor factorizations, which correspond to simplified neural networks. It was shown that these models exhibit an implicit tendency towards low matrix and tensor ranks, respectively. Drawing closer to practical deep learning, the current paper theoretically analyzes the implicit regularization in hierarchical tensor factorization, a model equivalent to certain deep convolutional neural networks. Through a dynamical systems lens, we overcome challenges associated with hierarchy, and establish implicit regularization towards low hierarchical tensor rank. This translates to an implicit regularization towards locality for the associated convolutional networks. Inspired by our theory, we design explicit regularization discouraging locality, and demonstrate its ability to improve the performance of modern convolutional networks on non-local tasks, in defiance of conventional wisdom by which architectural changes are needed. Our work highlights the potential of enhancing neural networks via theoretical analysis of their implicit regularization.

There will be a fast-paced shift from conventional network systems to novel quantum networks that are supported by the quantum entanglement and teleportation, key technologies of the quantum era, to enable secured data transmissions in the next-generation of the Internet. Despite this prospect, migration to quantum networks cannot be done at once, especially on the aspect of quantum routing. In this paper, we study the maximizing entangled routing rate (MERR) problem. In particular, given a set of demands, we try to determine entangled routing paths for the maximum number of demands in the quantum network while meeting the network's fidelity. We first formulate the MERR problem using an integer linear programming (ILP) model to capture the traffic patent for all demands in the network. We then leverage the theory of relaxation of ILP to devise two efficient algorithms including HBRA and RRA with provable approximation ratios for the objective function. To deal with the challenge of the combinatorial optimization problem in big scale networks, we also propose the path-length-based approach (PLBA) to solve the MERR problem. Using both simulations and an open quantum network simulator platform to conduct experiments with real-world topologies and traffic matrices, we evaluate the performance of our algorithms and show up the success of maximizing entangled routing rate.

The adaptive processing of structured data is a long-standing research topic in machine learning that investigates how to automatically learn a mapping from a structured input to outputs of various nature. Recently, there has been an increasing interest in the adaptive processing of graphs, which led to the development of different neural network-based methodologies. In this thesis, we take a different route and develop a Bayesian Deep Learning framework for graph learning. The dissertation begins with a review of the principles over which most of the methods in the field are built, followed by a study on graph classification reproducibility issues. We then proceed to bridge the basic ideas of deep learning for graphs with the Bayesian world, by building our deep architectures in an incremental fashion. This framework allows us to consider graphs with discrete and continuous edge features, producing unsupervised embeddings rich enough to reach the state of the art on several classification tasks. Our approach is also amenable to a Bayesian nonparametric extension that automatizes the choice of almost all model's hyper-parameters. Two real-world applications demonstrate the efficacy of deep learning for graphs. The first concerns the prediction of information-theoretic quantities for molecular simulations with supervised neural models. After that, we exploit our Bayesian models to solve a malware-classification task while being robust to intra-procedural code obfuscation techniques. We conclude the dissertation with an attempt to blend the best of the neural and Bayesian worlds together. The resulting hybrid model is able to predict multimodal distributions conditioned on input graphs, with the consequent ability to model stochasticity and uncertainty better than most works. Overall, we aim to provide a Bayesian perspective into the articulated research field of deep learning for graphs.

The conjoining of dynamical systems and deep learning has become a topic of great interest. In particular, neural differential equations (NDEs) demonstrate that neural networks and differential equation are two sides of the same coin. Traditional parameterised differential equations are a special case. Many popular neural network architectures, such as residual networks and recurrent networks, are discretisations. NDEs are suitable for tackling generative problems, dynamical systems, and time series (particularly in physics, finance, ...) and are thus of interest to both modern machine learning and traditional mathematical modelling. NDEs offer high-capacity function approximation, strong priors on model space, the ability to handle irregular data, memory efficiency, and a wealth of available theory on both sides. This doctoral thesis provides an in-depth survey of the field. Topics include: neural ordinary differential equations (e.g. for hybrid neural/mechanistic modelling of physical systems); neural controlled differential equations (e.g. for learning functions of irregular time series); and neural stochastic differential equations (e.g. to produce generative models capable of representing complex stochastic dynamics, or sampling from complex high-dimensional distributions). Further topics include: numerical methods for NDEs (e.g. reversible differential equations solvers, backpropagation through differential equations, Brownian reconstruction); symbolic regression for dynamical systems (e.g. via regularised evolution); and deep implicit models (e.g. deep equilibrium models, differentiable optimisation). We anticipate this thesis will be of interest to anyone interested in the marriage of deep learning with dynamical systems, and hope it will provide a useful reference for the current state of the art.

Sampling methods (e.g., node-wise, layer-wise, or subgraph) has become an indispensable strategy to speed up training large-scale Graph Neural Networks (GNNs). However, existing sampling methods are mostly based on the graph structural information and ignore the dynamicity of optimization, which leads to high variance in estimating the stochastic gradients. The high variance issue can be very pronounced in extremely large graphs, where it results in slow convergence and poor generalization. In this paper, we theoretically analyze the variance of sampling methods and show that, due to the composite structure of empirical risk, the variance of any sampling method can be decomposed into \textit{embedding approximation variance} in the forward stage and \textit{stochastic gradient variance} in the backward stage that necessities mitigating both types of variance to obtain faster convergence rate. We propose a decoupled variance reduction strategy that employs (approximate) gradient information to adaptively sample nodes with minimal variance, and explicitly reduces the variance introduced by embedding approximation. We show theoretically and empirically that the proposed method, even with smaller mini-batch sizes, enjoys a faster convergence rate and entails a better generalization compared to the existing methods.

We propose a Bayesian convolutional neural network built upon Bayes by Backprop and elaborate how this known method can serve as the fundamental construct of our novel, reliable variational inference method for convolutional neural networks. First, we show how Bayes by Backprop can be applied to convolutional layers where weights in filters have probability distributions instead of point-estimates; and second, how our proposed framework leads with various network architectures to performances comparable to convolutional neural networks with point-estimates weights. In the past, Bayes by Backprop has been successfully utilised in feedforward and recurrent neural networks, but not in convolutional ones. This work symbolises the extension of the group of Bayesian neural networks which encompasses all three aforementioned types of network architectures now.

Traditional methods for link prediction can be categorized into three main types: graph structure feature-based, latent feature-based, and explicit feature-based. Graph structure feature methods leverage some handcrafted node proximity scores, e.g., common neighbors, to estimate the likelihood of links. Latent feature methods rely on factorizing networks' matrix representations to learn an embedding for each node. Explicit feature methods train a machine learning model on two nodes' explicit attributes. Each of the three types of methods has its unique merits. In this paper, we propose SEAL (learning from Subgraphs, Embeddings, and Attributes for Link prediction), a new framework for link prediction which combines the power of all the three types into a single graph neural network (GNN). GNN is a new type of neural network which directly accepts graphs as input and outputs their labels. In SEAL, the input to the GNN is a local subgraph around each target link. We prove theoretically that our local subgraphs also reserve a great deal of high-order graph structure features related to link existence. Another key feature is that our GNN can naturally incorporate latent features and explicit features. It is achieved by concatenating node embeddings (latent features) and node attributes (explicit features) in the node information matrix for each subgraph, thus combining the three types of features to enhance GNN learning. Through extensive experiments, SEAL shows unprecedentedly strong performance against a wide range of baseline methods, including various link prediction heuristics and network embedding methods.