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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.

We evaluate using Julia as a single language and ecosystem paradigm powered by LLVM to develop workflow components for high-performance computing. We run a Gray-Scott, 2-variable diffusion-reaction application using a memory-bound, 7-point stencil kernel on Frontier, the US Department of Energy's first exascale supercomputer. We evaluate the feasibility, performance, scaling, and trade-offs of (i) the computational kernel on AMD's MI250x GPUs, (ii) weak scaling up to 4,096 MPI processes/GPUs or 512 nodes, (iii) parallel I/O writes using the ADIOS2 library bindings, and (iv) Jupyter Notebooks for interactive data analysis. Our results suggest that although Julia generates a reasonable LLVM-IR kernel, a nearly 50\% performance difference exists vs. native AMD HIP stencil codes when running on the GPUs. As expected, we observed near-zero overhead when using MPI and parallel I/O bindings for system-wide installed implementations. Consequently, Julia emerges as a compelling high-performance and high-productivity workflow composition strategy, as measured on the fastest supercomputer in the world.

We introduce new discrete best approximation problems, formulated and solved in the framework of tropical algebra, which deals with semirings and semifields with idempotent addition. Given a set of samples, each consisting of the input and output of an unknown function defined on an idempotent semifield, the problem is to find a best approximation of the function, by tropical Puiseux polynomial and rational functions. A new solution approach is proposed, which involves the reduction of the problem of polynomial approximation to the best approximate solution of a tropical linear vector equation with an unknown vector on one side (a one-sided equation). We derive a best approximate solution to the one-sided equation, and we evaluate the inherent approximation error in a direct analytical form. Furthermore, we reduce the rational approximation problem to the best approximate solution of an equation with unknown vectors on both sides (a two-sided equation). A best approximate solution to the two-sided equation is obtained in numerical form, by using an iterative alternating algorithm. To illustrate the new technique developed, we solve example approximation problems in terms of a real semifield, where addition is defined as maximum and multiplication as arithmetic addition (max-plus algebra), which corresponds to the best Chebyshev approximation by piecewise linear functions.

The possibility of dynamically modifying the computational load of neural models at inference time is crucial for on-device processing, where computational power is limited and time-varying. Established approaches for neural model compression exist, but they provide architecturally static models. In this paper, we investigate the use of early-exit architectures, that rely on intermediate exit branches, applied to large-vocabulary speech recognition. This allows for the development of dynamic models that adjust their computational cost to the available resources and recognition performance. Unlike previous works, besides using pre-trained backbones we also train the model from scratch with an early-exit architecture. Experiments on public datasets show that early-exit architectures from scratch not only preserve performance levels when using fewer encoder layers, but also improve task accuracy as compared to using single-exit models or using pre-trained models. Additionally, we investigate an exit selection strategy based on posterior probabilities as an alternative to frame-based entropy.

This paper presents a reduced algorithm to the classical projection method for the solution of $d$-dimensional quasiperiodic problems, particularly Schr\"{o}dinger eigenvalue problems. Using the properties of the Schr\"{o}dinger operator in higher-dimensional space via a projection matrix of size $d\times n$, we rigorously prove that the generalized Fourier coefficients of the eigenfunctions decay exponentially along a fixed direction associated with the projection matrix. An efficient reduction strategy of the basis space is then proposed to reduce the degrees of freedom from $O(N^{n})$ to $O(N^{n-d}D^d)$, where $N$ is the number of Fourier grids in one dimension and the truncation coefficient $D$ is much less than $N$. Correspondingly, the computational complexity of the proposed algorithm for solving the first $k$ eigenpairs using the Krylov subspace method decreases from $O(kN^{2n})$ to $O(kN^{2(n-d)}D^{2d})$. Rigorous error estimates of the proposed reduced projection method are provided, indicating that a small $D$ is sufficient to achieve the same level of accuracy as the classical projection method. We present numerical examples of quasiperiodic Schr\"{o}dinger eigenvalue problems in one and two dimensions to demonstrate the accuracy and efficiency of our proposed method.

Testing cross-sectional independence in panel data models is of fundamental importance in econometric analysis with high-dimensional panels. Recently, econometricians began to turn their attention to the problem in the presence of serial dependence. The existing procedure for testing cross-sectional independence with serial correlation is based on the sum of the sample cross-sectional correlations, which generally performs well when the alternative has dense cross-sectional correlations, but suffers from low power against sparse alternatives. To deal with sparse alternatives, we propose a test based on the maximum of the squared sample cross-sectional correlations. Furthermore, we propose a combined test to combine the p-values of the max based and sum based tests, which performs well under both dense and sparse alternatives. The combined test relies on the asymptotic independence of the max based and sum based test statistics, which we show rigorously. We show that the proposed max based and combined tests have attractive theoretical properties and demonstrate the superior performance via extensive simulation results. We apply the two new tests to analyze the weekly returns on the securities in the S\&P 500 index under the Fama-French three-factor model, and confirm the usefulness of the proposed combined test in detecting cross-sectional independence.

We present a novel computational model for the dynamics of alveolar recruitment/derecruitment (RD), which reproduces the underlying characteristics typically observed in injured lungs. The basic idea is a pressure- and time-dependent variation of the stress-free reference volume in reduced dimensional viscoelastic elements representing the acinar tissue. We choose a variable reference volume triggered by critical opening and closing pressures in a time-dependent manner from a straightforward mechanical point of view. In the case of (partially and progressively) collapsing alveolar structures, the volume available for expansion during breathing reduces and vice versa, eventually enabling consideration of alveolar collapse and reopening in our model. We further introduce a method for patient-specific determination of the underlying critical parameters of the new alveolar RD dynamics when integrated into the tissue elements, referred to as terminal units, of a spatially resolved physics-based lung model that simulates the human respiratory system in an anatomically correct manner. Relevant patient-specific parameters of the terminal units are herein determined based on medical image data and the macromechanical behavior of the lung during artificial ventilation. We test the whole modeling approach for a real-life scenario by applying it to the clinical data of a mechanically ventilated patient. The generated lung model is capable of reproducing clinical measurements such as tidal volume and pleural pressure during various ventilation maneuvers. We conclude that this new model is an important step toward personalized treatment of ARDS patients by considering potentially harmful mechanisms - such as cyclic RD and overdistension - and might help in the development of relevant protective ventilation strategies to reduce ventilator-induced lung injury (VILI).

This article proposes a novel high-performance computing approach for the prediction of the temperature field in powder bed fusion (PBF) additive manufacturing processes. In contrast to many existing approaches to part-scale simulations, the underlying computational model consistently resolves physical scan tracks without additional heat source scaling, agglomeration strategies or any other heuristic modeling assumptions. A growing, adaptively refined mesh accurately captures all details of the laser beam motion. Critically, the fine spatial resolution required for resolved scan tracks in combination with the high scan velocities underlying these processes mandates the use of comparatively small time steps to resolve the underlying physics. Explicit time integration schemes are well-suited for this setting, while unconditionally stable implicit time integration schemes are employed for the interlayer cool down phase governed by significantly larger time scales. These two schemes are combined and implemented in an efficient fast operator evaluation framework providing significant performance gains and optimization opportunities. The capabilities of the novel framework are demonstrated through realistic AM examples on the centimeter scale including the first scan-resolved simulation of the entire NIST AM Benchmark cantilever specimen, with a computation time of less than one day. Apart from physical insights gained through these simulation examples, also numerical aspects are thoroughly studied on basis of weak and strong parallel scaling tests. As potential applications, the proposed thermal PBF simulation framework can serve as a basis for microstructure and thermo-mechanical predictions on the part-scale, but also to assess the influence of scan pattern and part geometry on melt pool shape and temperature, which are important indicators for well-known process instabilities.

Solving multiphysics-based inverse problems for geological carbon storage monitoring can be challenging when multimodal time-lapse data are expensive to collect and costly to simulate numerically. We overcome these challenges by combining computationally cheap learned surrogates with learned constraints. Not only does this combination lead to vastly improved inversions for the important fluid-flow property, permeability, it also provides a natural platform for inverting multimodal data including well measurements and active-source time-lapse seismic data. By adding a learned constraint, we arrive at a computationally feasible inversion approach that remains accurate. This is accomplished by including a trained deep neural network, known as a normalizing flow, which forces the model iterates to remain in-distribution, thereby safeguarding the accuracy of trained Fourier neural operators that act as surrogates for the computationally expensive multiphase flow simulations involving partial differential equation solves. By means of carefully selected experiments, centered around the problem of geological carbon storage, we demonstrate the efficacy of the proposed constrained optimization method on two different data modalities, namely time-lapse well and time-lapse seismic data. While permeability inversions from both these two modalities have their pluses and minuses, their joint inversion benefits from either, yielding valuable superior permeability inversions and CO2 plume predictions near, and far away, from the monitoring wells.

We propose a decoder-only language model, VoxtLM, that can perform four tasks: speech recognition, speech synthesis, text generation, and speech continuation. VoxtLM integrates text vocabulary with discrete speech tokens from self-supervised speech features and uses special tokens to enable multitask learning. Compared to a single-task model, VoxtLM exhibits a significant improvement in speech synthesis, with improvements in both speech intelligibility from 28.9 to 5.6 and objective quality from 2.68 to 3.90. VoxtLM also improves speech generation and speech recognition performance over the single-task counterpart. VoxtLM is trained with publicly available data and training recipes and model checkpoints will be open-sourced to make fully reproducible work.