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We propose a new reduced order modeling strategy for tackling parametrized Partial Differential Equations (PDEs) with linear constraints, in particular Darcy flow systems in which the constraint is given by mass conservation. Our approach employs classical neural network architectures and supervised learning, but it is constructed in such a way that the resulting Reduced Order Model (ROM) is guaranteed to satisfy the linear constraints exactly. The procedure is based on a splitting of the PDE solution into a particular solution satisfying the constraint and a homogenous solution. The homogeneous solution is approximated by mapping a suitable potential function, generated by a neural network model, onto the kernel of the constraint operator; for the particular solution, instead, we propose an efficient spanning tree algorithm. Starting from this paradigm, we present three approaches that follow this methodology, obtained by exploring different choices of the potential spaces: from empirical ones, derived via Proper Orthogonal Decomposition (POD), to more abstract ones based on differential complexes. All proposed approaches combine computational efficiency with rigorous mathematical interpretation, thus guaranteeing the explainability of the model outputs. To demonstrate the efficacy of the proposed strategies and to emphasize their advantages over vanilla black-box approaches, we present a series of numerical experiments on fluid flows in porous media, ranging from mixed-dimensional problems to nonlinear systems. This research lays the foundation for further exploration and development in the realm of model order reduction, potentially unlocking new capabilities and solutions in computational geosciences and beyond.

We address the problem of testing conditional mean and conditional variance for non-stationary data. We build e-values and p-values for four types of non-parametric composite hypotheses with specified mean and variance as well as other conditions on the shape of the data-generating distribution. These shape conditions include symmetry, unimodality, and their combination. Using the obtained e-values and p-values, we construct tests via e-processes, also known as testing by betting, as well as some tests based on combining p-values for comparison. Although we mainly focus on one-sided tests, the two-sided test for the mean is also studied. Simulation and empirical studies are conducted under a few settings, and they illustrate features of the methods based on e-processes.

This document defines a method for FIR system modelling which is very trivial as it only depends on phase introduction and removal (allpass filters). As magnitude is not altered, the processing is numerically stable. It is limited to phase alteration which maintains the time domain magnitude to force a system within its linear limits.

We present a new Krylov subspace recycling method for solving a linear system of equations, or a sequence of slowly changing linear systems. Our new method, named GMRES-SDR, combines randomized sketching and deflated restarting in a way that avoids orthogononalizing a full Krylov basis. We provide new theory which characterizes sketched GMRES with and without augmentation as a projection method using a semi-inner product. We present results of numerical experiments demonstrating the effectiveness of GMRES-SDR over competitor methods such as GMRES-DR and GCRO-DR.

Many time-dependent differential equations are equipped with invariants. Preserving such invariants under discretization can be important, e.g., to improve the qualitative and quantitative properties of numerical solutions. Recently, relaxation methods have been proposed as small modifications of standard time integration schemes guaranteeing the correct evolution of functionals of the solution. Here, we investigate how to combine these relaxation techniques with efficient step size control mechanisms based on local error estimates for explicit Runge-Kutta methods. We demonstrate our results in several numerical experiments including ordinary and partial differential equations.

We address the communication overhead of distributed sparse matrix-(multiple)-vector multiplication in the context of large-scale eigensolvers, using filter diagonalization as an example. The basis of our study is a performance model which includes a communication metric that is computed directly from the matrix sparsity pattern without running any code. The performance model quantifies to which extent scalability and parallel efficiency are lost due to communication overhead. To restore scalability, we identify two orthogonal layers of parallelism in the filter diagonalization technique. In the horizontal layer the rows of the sparse matrix are distributed across individual processes. In the vertical layer bundles of multiple vectors are distributed across separate process groups. An analysis in terms of the communication metric predicts that scalability can be restored if, and only if, one implements the two orthogonal layers of parallelism via different distributed vector layouts. Our theoretical analysis is corroborated by benchmarks for application matrices from quantum and solid state physics, road networks, and nonlinear programming. We finally demonstrate the benefits of using orthogonal layers of parallelism with two exemplary application cases -- an exciton and a strongly correlated electron system -- which incur either small or large communication overhead.

We consider the task of estimating functions belonging to a specific class of nonsmooth functions, namely so-called tame functions. These functions appear in a wide range of applications: training deep learning, value functions of mixed-integer programs, or wave functions of small molecules. We show that tame functions are approximable by piecewise polynomials on any full-dimensional cube. We then present the first ever mixed-integer programming formulation of piecewise polynomial regression. Together, these can be used to estimate tame functions. We demonstrate promising computational results.

Navigating the challenges of data-driven speech processing, one of the primary hurdles is accessing reliable pathological speech data. While public datasets appear to offer solutions, they come with inherent risks of potential unintended exposure of patient health information via re-identification attacks. Using a comprehensive real-world pathological speech corpus, with over n=3,800 test subjects spanning various age groups and speech disorders, we employed a deep-learning-driven automatic speaker verification (ASV) approach. This resulted in a notable mean equal error rate (EER) of 0.89% with a standard deviation of 0.06%, outstripping traditional benchmarks. Our comprehensive assessments demonstrate that pathological speech overall faces heightened privacy breach risks compared to healthy speech. Specifically, adults with dysphonia are at heightened re-identification risks, whereas conditions like dysarthria yield results comparable to those of healthy speakers. Crucially, speech intelligibility does not influence the ASV system's performance metrics. In pediatric cases, particularly those with cleft lip and palate, the recording environment plays a decisive role in re-identification. Merging data across pathological types led to a marked EER decrease, suggesting the potential benefits of pathological diversity in ASV, accompanied by a logarithmic boost in ASV effectiveness. In essence, this research sheds light on the dynamics between pathological speech and speaker verification, emphasizing its crucial role in safeguarding patient confidentiality in our increasingly digitized healthcare era.

Robotic capacities in object manipulation are incomparable to those of humans. Besides years of learning, humans rely heavily on the richness of information from physical interaction with the environment. In particular, tactile sensing is crucial in providing such rich feedback. Despite its potential contributions to robotic manipulation, tactile sensing is less exploited; mainly due to the complexity of the time series provided by tactile sensors. In this work, we propose a method for assessing grasp stability using tactile sensing. More specifically, we propose a methodology to extract task-relevant features and design efficient classifiers to detect object slippage with respect to individual fingertips. We compare two classification models: support vector machine and logistic regression. We use highly sensitive Uskin tactile sensors mounted on an Allegro hand to test and validate our method. Our results demonstrate that the proposed method is effective in slippage detection in an online fashion.

An enriched hybrid high-order method is designed for the Stokes equations of fluid flow and is fully applicable to generic curved meshes. Minimal regularity requirements of the enrichment spaces are given, and an abstract error analysis of the scheme is provided. The method achieves consistency in the enrichment space and is proven to converge optimally in energy error. The scheme is applied to 2D flow around circular cylinders, for which the local behaviour of the velocity and pressure fields are known. By enriching the local spaces with these solutions, superior numerical results near the submerged cylinders are achieved.