Knowing the actual precipitation in space and time is critical in hydrological modelling applications, yet the spatial coverage with rain gauge stations is limited due to economic constraints. Gridded satellite precipitation datasets offer an alternative option for estimating the actual precipitation by covering uniformly large areas, albeit related estimates are not accurate. To improve precipitation estimates, machine learning is applied to merge rain gauge-based measurements and gridded satellite precipitation products. In this context, observed precipitation plays the role of the dependent variable, while satellite data play the role of predictor variables. Random forests is the dominant machine learning algorithm in relevant applications. In those spatial predictions settings, point predictions (mostly the mean or the median of the conditional distribution) of the dependent variable are issued. The aim of the manuscript is to solve the problem of probabilistic prediction of precipitation with an emphasis on extreme quantiles in spatial interpolation settings. Here we propose, issuing probabilistic spatial predictions of precipitation using Light Gradient Boosting Machine (LightGBM). LightGBM is a boosting algorithm, highlighted by prize-winning entries in prediction and forecasting competitions. To assess LightGBM, we contribute a large-scale application that includes merging daily precipitation measurements in contiguous US with PERSIANN and GPM-IMERG satellite precipitation data. We focus on extreme quantiles of the probability distribution of the dependent variable, where LightGBM outperforms quantile regression forests (QRF, a variant of random forests) in terms of quantile score at extreme quantiles. Our study offers understanding of probabilistic predictions in spatial settings using machine learning.
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In this work, a recently proposed high-cycle fatigue cohesive zone model, which covers crack initiation and propagation with limited input parameters, is embedded in a robust and efficient numerical framework for simulating progressive failure in composite laminates under fatigue loading. The fatigue cohesive zone model is enhanced with an implicit time integration scheme of the fatigue damage variable which allows for larger cycle increments and more efficient analyses. The method is combined with an adaptive strategy for determining the cycle increment based on global convergence rates. Moreover, a consistent material tangent stiffness matrix has been derived by fully linearizing the underlying mixed-mode quasi-static model and the fatigue damage update. The enhanced fatigue cohesive zone model is used to describe matrix cracking and delamination in laminates. In order to allow for matrix cracks to initiate at arbitrary locations and to avoid complex and costly mesh generation, the phantom node version of the eXtended finite element method (XFEM) is employed. For the insertion of new crack segments, an XFEM fatigue crack insertion criterion is presented, which is consistent with the fatigue cohesive zone formulation. It is shown with numerical examples that the improved fatigue damage update enhances the accuracy, efficiency and robustness of the numerical simulations significantly. The numerical framework is applied to the simulation of progressive fatigue failure in an open-hole [$\pm$45]-laminate. It is demonstrated that the numerical model is capable of accurately and efficiently simulating the complete failure process from distributed damage to localized failure.
Discovering causal relationships from observational data is a fundamental yet challenging task. In some applications, it may suffice to learn the causal features of a given response variable, instead of learning the entire underlying causal structure. Invariant causal prediction (ICP, Peters et al., 2016) is a method for causal feature selection which requires data from heterogeneous settings. ICP assumes that the mechanism for generating the response from its direct causes is the same in all settings and exploits this invariance to output a subset of the causal features. The framework of ICP has been extended to general additive noise models and to nonparametric settings using conditional independence testing. However, nonparametric conditional independence testing often suffers from low power (or poor type I error control) and the aforementioned parametric models are not suitable for applications in which the response is not measured on a continuous scale, but rather reflects categories or counts. To bridge this gap, we develop ICP in the context of transformation models (TRAMs), allowing for continuous, categorical, count-type, and uninformatively censored responses (we show that, in general, these model classes do not allow for identifiability when there is no exogenous heterogeneity). We propose TRAM-GCM, a test for invariance of a subset of covariates, based on the expected conditional covariance between environments and score residuals which satisfies uniform asymptotic level guarantees. For the special case of linear shift TRAMs, we propose an additional invariance test, TRAM-Wald, based on the Wald statistic. We implement both proposed methods in the open-source R package "tramicp" and show in simulations that under the correct model specification, our approach empirically yields higher power than nonparametric ICP based on conditional independence testing.
Dual-path is a popular architecture for speech separation models (e.g. Sepformer) which splits long sequences into overlapping chunks for its intra- and inter-blocks that separately model intra-chunk local features and inter-chunk global relationships. However, it has been found that inter-blocks, which comprise half a dual-path model's parameters, contribute minimally to performance. Thus, we propose the Single-Path Global Modulation (SPGM) block to replace inter-blocks. SPGM is named after its structure consisting of a parameter-free global pooling module followed by a modulation module comprising only 2% of the model's total parameters. The SPGM block allows all transformer layers in the model to be dedicated to local feature modelling, making the overall model single-path. SPGM achieves 22.1 dB SI-SDRi on WSJ0-2Mix and 20.4 dB SI-SDRi on Libri2Mix, exceeding the performance of Sepformer by 0.5 dB and 0.3 dB respectively and matches the performance of recent SOTA models with up to 8 times fewer parameters.
Trace finite element methods have become a popular option for solving surface partial differential equations, especially in problems where surface and bulk effects are coupled. In such methods a surface mesh is formed by approximately intersecting the continuous surface on which the PDE is posed with a three-dimensional (bulk) tetrahedral mesh. In classical $H^1$-conforming trace methods, the surface finite element space is obtained by restricting a bulk finite element space to the surface mesh. It is not clear how to carry out a similar procedure in order to obtain other important types of finite element spaces such as $H({\rm div})$-conforming spaces. Following previous work of Olshanskii, Reusken, and Xu on $H^1$-conforming methods, we develop a ``quasi-trace'' mixed method for the Laplace-Beltrami problem. The finite element mesh is taken to be the intersection of the surface with a regular tetrahedral bulk mesh as previously described, resulting in a surface triangulation that is highly unstructured and anisotropic but satisfies a classical maximum angle condition. The mixed method is then employed on this mesh. Optimal error estimates with respect to the bulk mesh size are proved along with superconvergent estimates for the projection of the scalar error and a postprocessed scalar approximation.
Offline model-based optimization aims to find a design that maximizes a property of interest using only an offline dataset, with applications in robot, protein, and molecule design, among others. A prevalent approach is gradient ascent, where a proxy model is trained on the offline dataset and then used to optimize the design. This method suffers from an out-of-distribution issue, where the proxy is not accurate for unseen designs. To mitigate this issue, we explore using a pseudo-labeler to generate valuable data for fine-tuning the proxy. Specifically, we propose \textit{\textbf{I}mportance-aware \textbf{C}o-\textbf{T}eaching for Offline Model-based Optimization}~(\textbf{ICT}). This method maintains three symmetric proxies with their mean ensemble as the final proxy, and comprises two steps. The first step is \textit{pseudo-label-driven co-teaching}. In this step, one proxy is iteratively selected as the pseudo-labeler for designs near the current optimization point, generating pseudo-labeled data. Subsequently, a co-teaching process identifies small-loss samples as valuable data and exchanges them between the other two proxies for fine-tuning, promoting knowledge transfer. This procedure is repeated three times, with a different proxy chosen as the pseudo-labeler each time, ultimately enhancing the ensemble performance. To further improve accuracy of pseudo-labels, we perform a secondary step of \textit{meta-learning-based sample reweighting}, which assigns importance weights to samples in the pseudo-labeled dataset and updates them via meta-learning. ICT achieves state-of-the-art results across multiple design-bench tasks, achieving the best mean rank of $3.1$ and median rank of $2$, among $15$ methods. Our source code can be found here.
Neuromorphic computing is one of the few current approaches that have the potential to significantly reduce power consumption in Machine Learning and Artificial Intelligence. Imam & Cleland presented an odour-learning algorithm that runs on a neuromorphic architecture and is inspired by circuits described in the mammalian olfactory bulb. They assess the algorithm's performance in "rapid online learning and identification" of gaseous odorants and odorless gases (short "gases") using a set of gas sensor recordings of different odour presentations and corrupting them by impulse noise. We replicated parts of the study and discovered limitations that affect some of the conclusions drawn. First, the dataset used suffers from sensor drift and a non-randomised measurement protocol, rendering it of limited use for odour identification benchmarks. Second, we found that the model is restricted in its ability to generalise over repeated presentations of the same gas. We demonstrate that the task the study refers to can be solved with a simple hash table approach, matching or exceeding the reported results in accuracy and runtime. Therefore, a validation of the model that goes beyond restoring a learned data sample remains to be shown, in particular its suitability to odour identification tasks.
Neuro-evolutionary methods have proven effective in addressing a wide range of tasks. However, the study of the robustness and generalisability of evolved artificial neural networks (ANNs) has remained limited. This has immense implications in the fields like robotics where such controllers are used in control tasks. Unexpected morphological or environmental changes during operation can risk failure if the ANN controllers are unable to handle these changes. This paper proposes an algorithm that aims to enhance the robustness and generalisability of the controllers. This is achieved by introducing morphological variations during the evolutionary process. As a results, it is possible to discover generalist controllers that can handle a wide range of morphological variations sufficiently without the need of the information regarding their morphologies or adaptation of their parameters. We perform an extensive experimental analysis on simulation that demonstrates the trade-off between specialist and generalist controllers. The results show that generalists are able to control a range of morphological variations with a cost of underperforming on a specific morphology relative to a specialist. This research contributes to the field by addressing the limited understanding of robustness and generalisability in neuro-evolutionary methods and proposes a method by which to improve these properties.
Geographical and Temporal Weighted Regression (GTWR) model is an important local technique for exploring spatial heterogeneity in data relationships, as well as temporal dependence due to its high fitting capacity when it comes to real data. In this article, we consider a GTWR model driven by a spatio-temporal noise, colored in space and fractional in time. Concerning the covariates, we consider that they are correlated, taking into account two interaction types between covariates, weak and strong interaction. Under these assumptions, Weighted Least Squares Estimator (WLS) is obtained, as well as its rate of convergence. In order to evidence the good performance of the estimator studied, it is provided a simulation study of four different scenarios, where it is observed that the residuals oscillate with small variation around zero. The STARMA package of the R software allows obtaining a variant of the $R^{2}$ coefficient, with values very close to 1, which means that most of the variability is explained by the model.
Ordinary state-based peridynamic (OSB-PD) models have an unparalleled capability to simulate crack propagation phenomena in solids with arbitrary Poisson's ratio. However, their non-locality also leads to prohibitively high computational cost. In this paper, a fast solution scheme for OSB-PD models based on matrix operation is introduced, with which, the graphics processing units (GPUs) are used to accelerate the computation. For the purpose of comparison and verification, a commonly used solution scheme based on loop operation is also presented. An in-house software is developed in MATLAB. Firstly, the vibration of a cantilever beam is solved for validating the loop- and matrix-based schemes by comparing the numerical solutions to those produced by a FEM software. Subsequently, two typical dynamic crack propagation problems are simulated to illustrate the effectiveness of the proposed schemes in solving dynamic fracture problems. Finally, the simulation of the Brokenshire torsion experiment is carried out by using the matrix-based scheme, and the similarity in the shapes of the experimental and numerical broken specimens further demonstrates the ability of the proposed approach to deal with 3D non-planar fracture problems. In addition, the speed-up of the matrix-based scheme with respect to the loop-based scheme and the performance of the GPU acceleration are investigated. The results emphasize the high computational efficiency of the matrix-based implementation scheme.
We propose an approach to compute inner and outer-approximations of the sets of values satisfying constraints expressed as arbitrarily quantified formulas. Such formulas arise for instance when specifying important problems in control such as robustness, motion planning or controllers comparison. We propose an interval-based method which allows for tractable but tight approximations. We demonstrate its applicability through a series of examples and benchmarks using a prototype implementation.
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