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Despite the growing availability of sensing and data in general, we remain unable to fully characterise many in-service engineering systems and structures from a purely data-driven approach. The vast data and resources available to capture human activity are unmatched in our engineered world, and, even in cases where data could be referred to as ``big,'' they will rarely hold information across operational windows or life spans. This paper pursues the combination of machine learning technology and physics-based reasoning to enhance our ability to make predictive models with limited data. By explicitly linking the physics-based view of stochastic processes with a data-based regression approach, a spectrum of possible Gaussian process models are introduced that enable the incorporation of different levels of expert knowledge of a system. Examples illustrate how these approaches can significantly reduce reliance on data collection whilst also increasing the interpretability of the model, another important consideration in this context.

Introduction: Covert tobacco advertisements often raise regulatory measures. This paper presents that artificial intelligence, particularly deep learning, has great potential for detecting hidden advertising and allows unbiased, reproducible, and fair quantification of tobacco-related media content. Methods: We propose an integrated text and image processing model based on deep learning, generative methods, and human reinforcement, which can detect smoking cases in both textual and visual formats, even with little available training data. Results: Our model can achieve 74\% accuracy for images and 98\% for text. Furthermore, our system integrates the possibility of expert intervention in the form of human reinforcement. Conclusions: Using the pre-trained multimodal, image, and text processing models available through deep learning makes it possible to detect smoking in different media even with few training data.

Quantum neural networks (QNNs) and quantum kernels stand as prominent figures in the realm of quantum machine learning, poised to leverage the nascent capabilities of near-term quantum computers to surmount classical machine learning challenges. Nonetheless, the training efficiency challenge poses a limitation on both QNNs and quantum kernels, curbing their efficacy when applied to extensive datasets. To confront this concern, we present a unified approach: coreset selection, aimed at expediting the training of QNNs and quantum kernels by distilling a judicious subset from the original training dataset. Furthermore, we analyze the generalization error bounds of QNNs and quantum kernels when trained on such coresets, unveiling the comparable performance with those training on the complete original dataset. Through systematic numerical simulations, we illuminate the potential of coreset selection in expediting tasks encompassing synthetic data classification, identification of quantum correlations, and quantum compiling. Our work offers a useful way to improve diverse quantum machine learning models with a theoretical guarantee while reducing the training cost.

This work proposes to measure the scope of a patent claim as the reciprocal of the self-information contained in this claim. Grounded in information theory, this approach is based on the assumption that a rare concept is more informative than a usual concept, inasmuch as it is more surprising. The self-information is calculated from the probability of occurrence of that claim, where the probability is calculated in accordance with a language model. Five language models are considered, ranging from the simplest models (each word or character is drawn from a uniform distribution) to intermediate models (using average word or character frequencies), to a large language model (GPT2). Interestingly, the simplest language models reduce the scope measure to the reciprocal of the word or character count, a metric already used in previous works. Application is made to nine series of patent claims directed to distinct inventions, where the claims in each series have a gradually decreasing scope. The performance of the language models is then assessed with respect to several ad hoc tests. The more sophisticated the model, the better the results. The GPT2 model outperforms models based on word and character frequencies, which are themselves ahead of models based on word and character counts.

We study an optimal control problem governed by elliptic PDEs with interface, which the control acts on the interface. Due to the jump of the coefficient across the interface and the control acting on the interface, the regularity of solution of the control problem is limited on the whole domain, but smoother on subdomains. The control function with pointwise inequality constraints is served as the flux jump condition which we called Neumann interface control. We use a simple uniform mesh that is independent of the interface. The standard linear finite element method can not achieve optimal convergence when the uniform mesh is used. Therefore the state and adjoint state equations are discretized by piecewise linear immersed finite element method (IFEM). While the accuracy of the piecewise constant approximation of the optimal control on the interface is improved by a postprocessing step which possesses superconvergence properties; as well as the variational discretization concept for the optimal control is used to improve the error estimates. Optimal error estimates for the control, suboptimal error estimates for state and adjoint state are derived. Numerical examples with and without constraints are provided to illustrate the effectiveness of the proposed scheme and correctness of the theoretical analysis.

Complex networks are used to model many real-world systems. However, the dimensionality of these systems can make them challenging to analyze. Dimensionality reduction techniques like POD can be used in such cases. However, these models are susceptible to perturbations in the input data. We propose an algorithmic framework that combines techniques from pattern recognition (PR) and stochastic filtering theory to enhance the output of such models. The results of our study show that our method can improve the accuracy of the surrogate model under perturbed inputs. Deep Neural Networks (DNNs) are susceptible to adversarial attacks. However, recent research has revealed that Neural Ordinary Differential Equations (neural ODEs) exhibit robustness in specific applications. We benchmark our algorithmic framework with the neural ODE-based approach as a reference.

We consider the weighted least squares spline approximation of a noisy dataset. By interpreting the weights as a probability distribution, we maximize the associated entropy subject to the constraint that the mean squared error is prescribed to a desired (small) value. Acting on this error yields a robust regression method that automatically detects and removes outliers from the data during the fitting procedure, by assigning them a very small weight. We discuss the use of both spline functions and spline curves. A number of numerical illustrations have been included to disclose the potentialities of the maximal-entropy approach in different application fields.

Conventional neural network elastoplasticity models are often perceived as lacking interpretability. This paper introduces a two-step machine-learning approach that returns mathematical models interpretable by human experts. In particular, we introduce a surrogate model where yield surfaces are expressed in terms of a set of single-variable feature mappings obtained from supervised learning. A postprocessing step is then used to re-interpret the set of single-variable neural network mapping functions into mathematical form through symbolic regression. This divide-and-conquer approach provides several important advantages. First, it enables us to overcome the scaling issue of symbolic regression algorithms. From a practical perspective, it enhances the portability of learned models for partial differential equation solvers written in different programming languages. Finally, it enables us to have a concrete understanding of the attributes of the materials, such as convexity and symmetries of models, through automated derivations and reasoning. Numerical examples have been provided, along with an open-source code to enable third-party validation.

This work uses the entropy-regularised relaxed stochastic control perspective as a principled framework for designing reinforcement learning (RL) algorithms. Herein agent interacts with the environment by generating noisy controls distributed according to the optimal relaxed policy. The noisy policies on the one hand, explore the space and hence facilitate learning but, on the other hand, introduce bias by assigning a positive probability to non-optimal actions. This exploration-exploitation trade-off is determined by the strength of entropy regularisation. We study algorithms resulting from two entropy regularisation formulations: the exploratory control approach, where entropy is added to the cost objective, and the proximal policy update approach, where entropy penalises policy divergence between consecutive episodes. We focus on the finite horizon continuous-time linear-quadratic (LQ) RL problem, where a linear dynamics with unknown drift coefficients is controlled subject to quadratic costs. In this setting, both algorithms yield a Gaussian relaxed policy. We quantify the precise difference between the value functions of a Gaussian policy and its noisy evaluation and show that the execution noise must be independent across time. By tuning the frequency of sampling from relaxed policies and the parameter governing the strength of entropy regularisation, we prove that the regret, for both learning algorithms, is of the order $\mathcal{O}(\sqrt{N}) $ (up to a logarithmic factor) over $N$ episodes, matching the best known result from the literature.

Women are at increased risk of bone loss during the menopausal transition; in fact, nearly 50\% of women's lifetime bone loss occurs during this time. The longitudinal relationships between estradiol (E2) and follicle-stimulating hormone (FSH), two hormones that change have characteristic changes during the menopausal transition, and bone health outcomes are complex. However, in addition to level and rate of change in E2 and FSH, variability in these hormones across the menopausal transition may be an important predictor of bone health, but this question has yet to be well explored. We introduce a joint model that characterizes individual mean estradiol (E2) trajectories and the individual residual variances and links these variances to bone health trajectories. In our application, we found that higher FSH variability was associated with declines in bone mineral density (BMD) before menopause, but this association was moderated over time after the menopausal transition. Additionally, higher mean E2, but not E2 variability, was associated with slower decreases in during the menopausal transition. We also include a simulation study that shows that naive two-stage methods often fail to propagate uncertainty in the individual-level variance estimates, resulting in estimation bias and invalid interval coverage