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Simulated Moving Bed (SMB) chromatography is a well-known technique for the resolution of several high-value-added compounds. Parameters identification and model topology definition are arduous when one is dealing with complex systems such as a Simulated Moving Bed unit. Moreover, the large number of experiments necessary might be an expansive-long process. Hence, this work proposes a novel methodology for parameter estimation, screening the most suitable topology of the models sink-source (defined by the adsorption isotherm equation) and defining the minimum number of experiments necessary to identify the model. Therefore, a nested loop optimization problem is proposed with three levels considering the three main goals of the work: parameters estimation; topology screening by isotherm definition; minimum number of experiments necessary to yield a precise model. The proposed methodology emulated a real scenario by introducing noise in the data and using a Software-in-the-Loop (SIL) approach. Data reconciliation and uncertainty evaluation add robustness to the parameter estimation adding precision and reliability to the model. The methodology is validated considering experimental data from literature apart from the samples applied for parameter estimation, following a cross-validation. The results corroborate that it is possible to carry out trustworthy parameter estimation directly from an SMB unit with minimal system knowledge.

The staple of human intelligence is the capability of acquiring knowledge in a continuous fashion. In stark contrast, Deep Networks forget catastrophically and, for this reason, the sub-field of Class-Incremental Continual Learning fosters methods that learn a sequence of tasks incrementally, blending sequentially-gained knowledge into a comprehensive prediction. This work aims at assessing and overcoming the pitfalls of our previous proposal Dark Experience Replay (DER), a simple and effective approach that combines rehearsal and Knowledge Distillation. Inspired by the way our minds constantly rewrite past recollections and set expectations for the future, we endow our model with the abilities to i) revise its replay memory to welcome novel information regarding past data ii) pave the way for learning yet unseen classes. We show that the application of these strategies leads to remarkable improvements; indeed, the resulting method - termed eXtended-DER (X-DER) - outperforms the state of the art on both standard benchmarks (such as CIFAR-100 and miniImagenet) and a novel one here introduced. To gain a better understanding, we further provide extensive ablation studies that corroborate and extend the findings of our previous research (e.g. the value of Knowledge Distillation and flatter minima in continual learning setups).

Using information-theoretic principles, we consider the generalization error (gen-error) of iterative semi-supervised learning (SSL) algorithms that iteratively generate pseudo-labels for a large amount of unlabelled data to progressively refine the model parameters. In contrast to most previous works that {\em bound} the gen-error, we provide an {\em exact} expression for the gen-error and particularize it to the binary Gaussian mixture model. Our theoretical results suggest that when the class conditional variances are not too large, the gen-error decreases with the number of iterations, but quickly saturates. On the flip side, if the class conditional variances (and so amount of overlap between the classes) are large, the gen-error increases with the number of iterations. To mitigate this undesirable effect, we show that regularization can reduce the gen-error. The theoretical results are corroborated by extensive experiments on the MNIST and CIFAR datasets in which we notice that for easy-to-distinguish classes, the gen-error improves after several pseudo-labelling iterations, but saturates afterwards, and for more difficult-to-distinguish classes, regularization improves the generalization performance.

Decentralised Finance (DeFi) applications constitute an entire financial ecosystem deployed on blockchains. Such applications are based on complex protocols and incentive mechanisms whose financial safety is hard to determine. Besides, their adoption is rapidly growing, hence imperilling an increasingly higher amount of assets. Therefore, accurate formalisation and verification of DeFi applications is essential to assess their safety. We have developed a tool for the formal analysis of one of the most widespread DeFi applications: Lending Pools (LP). This was achieved by leveraging an existing formal model for LPs, the Maude verification environment and the MultiVeStA statistical analyser. The tool supports several analyses including reachability analysis, LTL model checking and statistical model checking. In this paper we show how the tool can be used to analyse several parameters of LPs that are fundamental to assess and predict their behaviour. In particular, we use statistical analysis to search for threshold and reward parameters that minimize the risk of unrecoverable loans.

Inferring the timing and amplitude of perturbations in epidemiological systems from their stochastically spread low-resolution outcomes is as relevant as challenging. It is a requirement for current approaches to overcome the need to know the details of the perturbations to proceed with the analyses. However, the general problem of connecting epidemiological curves with the underlying incidence lacks the highly effective methodology present in other inverse problems, such as super-resolution and dehazing from computer vision. Here, we develop an unsupervised physics-informed convolutional neural network approach in reverse to connect death records with incidence that allows the identification of regime changes at single-day resolution. Applied to COVID-19 data with proper regularization and model-selection criteria, the approach can identify the implementation and removal of lockdowns and other nonpharmaceutical interventions with 0.93-day accuracy over the time span of a year.

We develop a new formulation of deep learning based on the Mori-Zwanzig (MZ) formalism of irreversible statistical mechanics. The new formulation is built upon the well-known duality between deep neural networks and discrete stochastic dynamical systems, and it allows us to directly propagate quantities of interest (conditional expectations and probability density functions) forward and backward through the network by means of exact linear operator equations. Such new equations can be used as a starting point to develop new effective parameterizations of deep neural networks, and provide a new framework to study deep-learning via operator theoretic methods. The proposed MZ formulation of deep learning naturally introduces a new concept, i.e., the memory of the neural network, which plays a fundamental role in low-dimensional modeling and parameterization. By using the theory of contraction mappings, we develop sufficient conditions for the memory of the neural network to decay with the number of layers. This allows us to rigorously transform deep networks into shallow ones, e.g., by reducing the number of neurons per layer (using projection operators), or by reducing the total number of layers (using the decay property of the memory operator).

Facial 3D Morphable Models are a main computer vision subject with countless applications and have been highly optimized in the last two decades. The tremendous improvements of deep generative networks have created various possibilities for improving such models and have attracted wide interest. Moreover, the recent advances in neural radiance fields, are revolutionising novel-view synthesis of known scenes. In this work, we present a facial 3D Morphable Model, which exploits both of the above, and can accurately model a subject's identity, pose and expression and render it in arbitrary illumination. This is achieved by utilizing a powerful deep style-based generator to overcome two main weaknesses of neural radiance fields, their rigidity and rendering speed. We introduce a style-based generative network that synthesizes in one pass all and only the required rendering samples of a neural radiance field. We create a vast labelled synthetic dataset of facial renders, and train the network on these data, so that it can accurately model and generalize on facial identity, pose and appearance. Finally, we show that this model can accurately be fit to "in-the-wild" facial images of arbitrary pose and illumination, extract the facial characteristics, and be used to re-render the face in controllable conditions.

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.

This book develops an effective theory approach to understanding deep neural networks of practical relevance. Beginning from a first-principles component-level picture of networks, we explain how to determine an accurate description of the output of trained networks by solving layer-to-layer iteration equations and nonlinear learning dynamics. A main result is that the predictions of networks are described by nearly-Gaussian distributions, with the depth-to-width aspect ratio of the network controlling the deviations from the infinite-width Gaussian description. We explain how these effectively-deep networks learn nontrivial representations from training and more broadly analyze the mechanism of representation learning for nonlinear models. From a nearly-kernel-methods perspective, we find that the dependence of such models' predictions on the underlying learning algorithm can be expressed in a simple and universal way. To obtain these results, we develop the notion of representation group flow (RG flow) to characterize the propagation of signals through the network. By tuning networks to criticality, we give a practical solution to the exploding and vanishing gradient problem. We further explain how RG flow leads to near-universal behavior and lets us categorize networks built from different activation functions into universality classes. Altogether, we show that the depth-to-width ratio governs the effective model complexity of the ensemble of trained networks. By using information-theoretic techniques, we estimate the optimal aspect ratio at which we expect the network to be practically most useful and show how residual connections can be used to push this scale to arbitrary depths. With these tools, we can learn in detail about the inductive bias of architectures, hyperparameters, and optimizers.

In this paper, we propose the joint learning attention and recurrent neural network (RNN) models for multi-label classification. While approaches based on the use of either model exist (e.g., for the task of image captioning), training such existing network architectures typically require pre-defined label sequences. For multi-label classification, it would be desirable to have a robust inference process, so that the prediction error would not propagate and thus affect the performance. Our proposed model uniquely integrates attention and Long Short Term Memory (LSTM) models, which not only addresses the above problem but also allows one to identify visual objects of interests with varying sizes without the prior knowledge of particular label ordering. More importantly, label co-occurrence information can be jointly exploited by our LSTM model. Finally, by advancing the technique of beam search, prediction of multiple labels can be efficiently achieved by our proposed network model.