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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 post-processing 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.

We propose a new numerical domain decomposition method for solving elliptic equations on compact Riemannian manifolds. One advantage of this method is its ability to bypass the need for global triangulations or grids on the manifolds. Additionally, it features a highly parallel iterative scheme. To verify its efficacy, we conduct numerical experiments on some $4$-dimensional manifolds without and with boundary.

The emergence of industrial-scale speech recognition (ASR) models such as Whisper and USM, trained on 1M hours of weakly labelled and 12M hours of audio only proprietary data respectively, has led to a stronger need for large scale public ASR corpora and competitive open source pipelines. Unlike the said models, large language models are typically based on Transformer decoders, and it remains unclear if decoder-only models trained on public data alone can deliver competitive performance. In this work, we investigate factors such as choice of training datasets and modeling components necessary for obtaining the best performance using public English ASR corpora alone. Our Decoder-Only Transformer for ASR (DOTA) model comprehensively outperforms the encoder-decoder open source replication of Whisper (OWSM) on nearly all English ASR benchmarks and outperforms Whisper large-v3 on 7 out of 15 test sets. We release our codebase and model checkpoints under permissive license.

This review article focuses on regularised estimation procedures applicable to geostatistical and spatial econometric models. These methods are particularly relevant in the case of big geospatial data for dimensionality reduction or model selection. To structure the review, we initially consider the most general case of multivariate spatiotemporal processes (i.e., $g > 1$ dimensions of the spatial domain, a one-dimensional temporal domain, and $q \geq 1$ random variables). Then, the idea of regularised/penalised estimation procedures and different choices of shrinkage targets are discussed. Finally, guided by the elements of a mixed-effects model, which allows for a variety of spatiotemporal models, we show different regularisation procedures and how they can be used for the analysis of geo-referenced data, e.g. for selection of relevant regressors, dimensionality reduction of the covariance matrices, detection of conditionally independent locations, or the estimation of a full spatial interaction matrix.

Data generation remains a bottleneck in training surrogate models to predict molecular properties. We demonstrate that multitask Gaussian process regression overcomes this limitation by leveraging both expensive and cheap data sources. In particular, we consider training sets constructed from coupled-cluster (CC) and density function theory (DFT) data. We report that multitask surrogates can predict at CC level accuracy with a reduction to data generation cost by over an order of magnitude. Of note, our approach allows the training set to include DFT data generated by a heterogeneous mix of exchange-correlation functionals without imposing any artificial hierarchy on functional accuracy. More generally, the multitask framework can accommodate a wider range of training set structures -- including full disparity between the different levels of fidelity -- than existing kernel approaches based on $\Delta$-learning, though we show that the accuracy of the two approaches can be similar. Consequently, multitask regression can be a tool for reducing data generation costs even further by opportunistically exploiting existing data sources.

In instrumental variable (IV) settings, such as in imperfect randomized trials and observational studies with Mendelian randomization, one may encounter a continuous exposure, the causal effect of which is not of true interest. Instead, scientific interest may lie in a coarsened version of this exposure. Although there is a lengthy literature on the impact of coarsening of an exposure with several works focusing specifically on IV settings, all methods proposed in this literature require parametric assumptions. Instead, just as in the standard IV setting, one can consider partial identification via bounds making no parametric assumptions. This was first pointed out in Alexander Balke's PhD dissertation. We extend and clarify his work and derive novel bounds in several settings, including for a three-level IV, which will most likely be the case in Mendelian randomization. We demonstrate our findings in two real data examples, a randomized trial for peanut allergy in infants and a Mendelian randomization setting investigating the effect of homocysteine on cardiovascular disease.

Attention is the brain's mechanism for selectively processing specific stimuli while filtering out irrelevant information. Characterizing changes in attention following long-term interventions (such as transcranial direct current stimulation (tDCS)) has seldom been emphasized in the literature. To classify attention performance post-tDCS, this study uses functional connectivity and machine learning algorithms. Fifty individuals were split into experimental and control conditions. On Day 1, EEG data was obtained as subjects executed an attention task. From Day 2 through Day 8, the experimental group was administered 1mA tDCS, while the control group received sham tDCS. On Day 10, subjects repeated the task mentioned on Day 1. Functional connectivity metrics were used to classify attention performance using various machine learning methods. Results revealed that combining the Adaboost model and recursive feature elimination yielded a classification accuracy of 91.84%. We discuss the implications of our results in developing neurofeedback frameworks to assess attention.

Stepped wedge cluster randomized experiments represent a class of unidirectional crossover designs increasingly adopted for comparative effectiveness and implementation science research. Although stepped wedge cluster randomized experiments have become popular, definitions of estimands and robust methods to target clearly-defined estimands remain insufficient. To address this gap, we describe a class of estimands that explicitly acknowledge the multilevel data structure in stepped wedge cluster randomized experiments, and highlight three typical members of the estimand class that are interpretable and are of practical interest. We then introduce four possible formulations of analysis of covariance (ANCOVA) working models to achieve estimand-aligned analyses. By exploiting baseline covariates, each ANCOVA model can potentially improve the estimation efficiency over the unadjusted estimators. In addition, each ANCOVA estimator is model-assisted in the sense that its point estimator is consistent with the target estimand even when the working model is misspecified. Under the stepped wedge randomization scheme, we establish the finite population Central Limit Theorem for each estimator, which motivates design-based variance estimators. Through simulations, we study the finite-sample operating characteristics of the ANCOVA estimators under different data-generating processes. We illustrate their applications via the analysis of the Washington State Expedited Partner Therapy study.

Environmental data science for spatial extremes has traditionally relied heavily on max-stable processes. Even though the popularity of these models has perhaps peaked with statisticians, they are still perceived and considered as the `state-of-the-art' in many applied fields. However, while the asymptotic theory supporting the use of max-stable processes is mathematically rigorous and comprehensive, we think that it has also been overused, if not misused, in environmental applications, to the detriment of more purposeful and meticulously validated models. In this paper, we review the main limitations of max-stable process models, and strongly argue against their systematic use in environmental studies. Alternative solutions based on more flexible frameworks using the exceedances of variables above appropriately chosen high thresholds are discussed, and an outlook on future research is given, highlighting recommendations moving forward and the opportunities offered by hybridizing machine learning with extreme-value statistics.

Lattices are architected metamaterials whose properties strongly depend on their geometrical design. The analogy between lattices and graphs enables the use of graph neural networks (GNNs) as a faster surrogate model compared to traditional methods such as finite element modelling. In this work we present a higher-order GNN model trained to predict the fourth-order stiffness tensor of periodic strut-based lattices. The key features of the model are (i) SE(3) equivariance, and (ii) consistency with the thermodynamic law of conservation of energy. We compare the model to non-equivariant models based on a number of error metrics and demonstrate the benefits of the encoded equivariance and energy conservation in terms of predictive performance and reduced training requirements.