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An extremely schematic model of the forces acting an a sailing yacht equipped with a system of foils is here presented and discussed. The role of the foils is to raise the hull from the water in order to reduce the total resistance and then increase the speed. Some CFD simulations are providing the total resistance of the bare hull at some values of speed and displacement, as well as the characteristics (drag and lift coefficients) of the 2D foil sections used for the appendages. A parametric study has been performed for the characterization of a foil of finite dimensions. The equilibrium of the vertical forces and longitudinal moments, as well as a reduced displacement, is obtained by controlling the pitch angle of the foils. The value of the total resistance of the yacht with foils is then compared with the case without foils, evidencing the speed regime where an advantage is obtained, if any.

In this paper we describe a general approach to optimal imperfect maintenance activities of a repairable equipment with independent components. Most of the existing works on optimal imperfect maintenance activities of a repairable equipment with independent components. In addition, it is assumed that all the components of the equipment share the same model and the same maintenance intervals and that effectiveness of maintenance is known. In this paper we take a different approach. In order to formalize the uncertainty on the occurrence of failures and on the effect of maintenance activities we consider, for each component, a class of candidate models obtained combining models for failure rate with models for imperfect maintenance and let the data select the best model (that might be different for the different components). All the parameters are assumed to be unknown and are jointly estimated via maximum likelihood. Model selection is performed, separately for each component, using standard selection criteria that take into account the problem of over-parametrization. The selected models are used to derive the cost per unit time and the average reliability of the equipment, the objective functions of a Multi-Objective Optimization Problem with maintenance intervals of each single component as decision variables. The proposed procedure is illustrated using a real data example.

Many optimization problems require hyperparameters, i.e., parameters that must be pre-specified in advance, such as regularization parameters and parametric regularizers in variational regularization methods for inverse problems, and dictionaries in compressed sensing. A data-driven approach to determine appropriate hyperparameter values is via a nested optimization framework known as bilevel learning. Even when it is possible to employ a gradient-based solver to the bilevel optimization problem, construction of the gradients, known as hypergradients, is computationally challenging, each one requiring both a solution of a minimization problem and a linear system solve. These systems do not change much during the iterations, which motivates us to apply recycling Krylov subspace methods, wherein information from one linear system solve is re-used to solve the next linear system. Existing recycling strategies often employ eigenvector approximations called Ritz vectors. In this work we propose a novel recycling strategy based on a new concept, Ritz generalized singular vectors, which acknowledge the bilevel setting. Additionally, while existing iterative methods primarily terminate according to the residual norm, this new concept allows us to define a new stopping criterion that directly approximates the error of the associated hypergradient. The proposed approach is validated through extensive numerical testing in the context of an inverse problem in imaging.

We present a novel computational framework to assess the structural integrity of welds. In the first stage of the simulation framework, local fractions of microstructural constituents within weld regions are predicted based on steel composition and welding parameters. The resulting phase fraction maps are used to define heterogeneous properties that are subsequently employed in structural integrity assessments using an elastoplastic phase field fracture model. The framework is particularised to predicting failure in hydrogen pipelines, demonstrating its potential to assess the feasibility of repurposing existing pipeline infrastructure to transport hydrogen. First, the process model is validated against experimental microhardness maps for vintage and modern pipeline welds. Additionally, the influence of welding conditions on hardness and residual stresses is investigated, demonstrating that variations in heat input, filler material composition, and weld bead order can significantly affect the properties within the weld region. Coupled hydrogen diffusion-fracture simulations are then conducted to determine the critical pressure at which hydrogen transport pipelines will fail. To this end, the model is enriched with a microstructure-sensitive description of hydrogen transport and hydrogen-dependent fracture resistance. The analysis of an X52 pipeline reveals that even 2 mm defects in a hard heat-affected zone can drastically reduce the critical failure pressure.

This paper explores the utility of diffusion-based models for anomaly detection, focusing on their efficacy in identifying deviations in both compact and high-resolution datasets. Diffusion-based architectures, including Denoising Diffusion Probabilistic Models (DDPMs) and Diffusion Transformers (DiTs), are evaluated for their performance using reconstruction objectives. By leveraging the strengths of these models, this study benchmarks their performance against traditional anomaly detection methods such as Isolation Forests, One-Class SVMs, and COPOD. The results demonstrate the superior adaptability, scalability, and robustness of diffusion-based methods in handling complex real-world anomaly detection tasks. Key findings highlight the role of reconstruction error in enhancing detection accuracy and underscore the scalability of these models to high-dimensional datasets. Future directions include optimizing encoder-decoder architectures and exploring multi-modal datasets to further advance diffusion-based anomaly detection.

This paper presents a loss-based generalized Bayesian methodology for high-dimensional robust regression with serially correlated errors and predictors. The proposed framework employs a novel scaled pseudo-Huber (SPH) loss function, which smooths the well-known Huber loss, achieving a balance between quadratic and absolute linear loss behaviors. This flexibility enables the framework to accommodate both thin-tailed and heavy-tailed data effectively. The generalized Bayesian approach constructs a working likelihood utilizing the SPH loss that facilitates efficient and stable estimation while providing rigorous estimation uncertainty quantification for all model parameters. Notably, this allows formal statistical inference without requiring ad hoc tuning parameter selection while adaptively addressing a wide range of tail behavior in the errors. By specifying appropriate prior distributions for the regression coefficients -- e.g., ridge priors for small or moderate-dimensional settings and spike-and-slab priors for high-dimensional settings -- the framework ensures principled inference. We establish rigorous theoretical guarantees for the accurate estimation of underlying model parameters and the correct selection of predictor variables under sparsity assumptions for a wide range of data generating setups. Extensive simulation studies demonstrate the superiority of our approach compared to traditional quadratic and absolute linear loss-based Bayesian regression methods, highlighting its flexibility and robustness in high-dimensional and challenging data contexts.

In this work, we present a novel variant of the stochastic gradient descent method termed as iteratively regularized stochastic gradient descent (IRSGD) method to solve nonlinear ill-posed problems in Hilbert spaces. Under standard assumptions, we demonstrate that the mean square iteration error of the method converges to zero for exact data. In the presence of noisy data, we first propose a heuristic parameter choice rule (HPCR) based on the method suggested by Hanke and Raus, and then apply the IRSGD method in combination with HPCR. Precisely, HPCR selects the regularization parameter without requiring any a-priori knowledge of the noise level. We show that the method terminates in finitely many steps in case of noisy data and has regularizing features. Further, we discuss the convergence rates of the method using well-known source and other related conditions under HPCR as well as discrepancy principle. To the best of our knowledge, this is the first work that establishes both the regularization properties and convergence rates of a stochastic gradient method using a heuristic type rule in the setting of infinite-dimensional Hilbert spaces. Finally, we provide the numerical experiments to showcase the practical efficacy of the proposed method.

In this work, we develop a novel neural operator, the Solute Transport Operator Network (STONet), to efficiently model contaminant transport in micro-cracked reservoirs. The model combines different networks to encode heterogeneous properties effectively. By predicting the concentration rate, we are able to accurately model the transport process. Numerical experiments demonstrate that our neural operator approach achieves accuracy comparable to that of the finite element method. The previously introduced Enriched DeepONet architecture has been revised, motivated by the architecture of the popular multi-head attention of transformers, to improve its performance without increasing the compute cost. The computational efficiency of the proposed model enables rapid and accurate predictions of solute transport, facilitating the optimization of reservoir management strategies and the assessment of environmental impacts. The data and code for the paper will be published at //github.com/ehsanhaghighat/STONet.

We consider an unknown multivariate function representing a system-such as a complex numerical simulator-taking both deterministic and uncertain inputs. Our objective is to estimate the set of deterministic inputs leading to outputs whose probability (with respect to the distribution of the uncertain inputs) of belonging to a given set is less than a given threshold. This problem, which we call Quantile Set Inversion (QSI), occurs for instance in the context of robust (reliability-based) optimization problems, when looking for the set of solutions that satisfy the constraints with sufficiently large probability. To solve the QSI problem we propose a Bayesian strategy, based on Gaussian process modeling and the Stepwise Uncertainty Reduction (SUR) principle, to sequentially choose the points at which the function should be evaluated to efficiently approximate the set of interest. We illustrate the performance and interest of the proposed SUR strategy through several numerical experiments.

Motivated by the increasing demand for multi-source data integration in various scientific fields, in this paper we study matrix completion in scenarios where the data exhibits certain block-wise missing structures -- specifically, where only a few noisy submatrices representing (overlapping) parts of the full matrix are available. We propose the Chain-linked Multiple Matrix Integration (CMMI) procedure to efficiently combine the information that can be extracted from these individual noisy submatrices. CMMI begins by deriving entity embeddings for each observed submatrix, then aligns these embeddings using overlapping entities between pairs of submatrices, and finally aggregates them to reconstruct the entire matrix of interest. We establish, under mild regularity conditions, entrywise error bounds and normal approximations for the CMMI estimates. Simulation studies and real data applications show that CMMI is computationally efficient and effective in recovering the full matrix, even when overlaps between the observed submatrices are minimal.