Many-query computations, in which a computational model for an engineering system must be evaluated many times, are crucial in design and control. For systems governed by partial differential equations (PDEs), typical high-fidelity numerical models are high-dimensional and too computationally expensive for the many-query setting. Thus, efficient surrogate models are required to enable low-cost computations in design and control. This work presents a physics-preserving reduced model learning approach that targets PDEs whose quadratic operators preserve energy, such as those arising in governing equations in many fluids problems. The approach is based on the Operator Inference method, which fits reduced model operators to state snapshot and time derivative data in a least-squares sense. However, Operator Inference does not generally learn a reduced quadratic operator with the energy-preserving property of the original PDE. Thus, we propose a new energy-preserving Operator Inference (EP-OpInf) approach, which imposes this structure on the learned reduced model via constrained optimization. Numerical results using the viscous Burgers' and Kuramoto-Sivashinksy equation (KSE) demonstrate that EP-OpInf learns efficient and accurate reduced models that retain this energy-preserving structure.
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In many applications, a combinatorial problem must be repeatedly solved with similar, but distinct parameters. Yet, the parameters $w$ are not directly observed; only contextual data $d$ that correlates with $w$ is available. It is tempting to use a neural network to predict $w$ given $d$. However, training such a model requires reconciling the discrete nature of combinatorial optimization with the gradient-based frameworks used to train neural networks. When the problem in question is an Integer Linear Program (ILP), one approach to overcome this training issue is to consider a continuous relaxation of the combinatorial problem. While existing methods utilizing this approach have shown to be highly effective on small problems, they do not always scale well to large problems. In this work, we draw on ideas from modern convex optimization to design a network and training scheme which scales effortlessly to problems with thousands of variables. Our experiments verify the computational advantage our proposed method enjoys on two representative problems, namely the shortest path problem and the knapsack problem.
Meshfree simulation methods are emerging as compelling alternatives to conventional mesh-based approaches, particularly in the fields of Computational Fluid Dynamics (CFD) and continuum mechanics. In this publication, we provide a comprehensive overview of our research combining Machine Learning (ML) and Fraunhofer's MESHFREE software (www.meshfree.eu), a powerful tool utilizing a numerical point cloud in a Generalized Finite Difference Method (GFDM). This tool enables the effective handling of complex flow domains, moving geometries, and free surfaces, while allowing users to finely tune local refinement and quality parameters for an optimal balance between computation time and results accuracy. However, manually determining the optimal parameter combination poses challenges, especially for less experienced users. We introduce a novel ML-optimized approach, using active learning, regression trees, and visualization on MESHFREE simulation data, demonstrating the impact of input combinations on results quality and computation time. This research contributes valuable insights into parameter optimization in meshfree simulations, enhancing accessibility and usability for a broader user base in scientific and engineering applications.
Mediation analysis is an important statistical tool in many research fields. Its aim is to investigate the mechanism along the causal pathway between an exposure and an outcome. The joint significance test is widely utilized as a prominent statistical approach for examining mediation effects in practical applications. Nevertheless, the limitation of this mediation testing method stems from its conservative Type I error, which reduces its statistical power and imposes certain constraints on its popularity and utility. The proposed solution to address this gap is the adaptive joint significance test for one mediator, a novel data-adaptive test for mediation effect that exhibits significant advancements compared to traditional joint significance test. The proposed method is designed to be user-friendly, eliminating the need for complicated procedures. We have derived explicit expressions for size and power, ensuring the theoretical validity of our approach. Furthermore, we extend the proposed adaptive joint significance tests for small-scale mediation hypotheses with family-wise error rate (FWER) control. Additionally, a novel adaptive Sobel-type approach is proposed for the estimation of confidence intervals for the mediation effects, demonstrating significant advancements over conventional Sobel's confidence intervals in terms of achieving desirable coverage probabilities. Our mediation testing and confidence intervals procedure is evaluated through comprehensive simulations, and compared with numerous existing approaches. Finally, we illustrate the usefulness of our method by analysing three real-world datasets with continuous, binary and time-to-event outcomes, respectively.
With the development of multimedia applications, multimodal recommendations are playing an essential role, as they can leverage rich contexts beyond user interactions. Existing methods mainly regard multimodal information as an auxiliary, using them to help learn ID features; however, there exist semantic gaps among multimodal content features and ID features, for which directly using multimodal information as an auxiliary would lead to misalignment in representations of users and items. In this paper, we first systematically investigate the misalignment issue in multimodal recommendations, and propose a solution named AlignRec. In AlignRec, the recommendation objective is decomposed into three alignments, namely alignment within contents, alignment between content and categorical ID, and alignment between users and items. Each alignment is characterized by a specific objective function and is integrated into our multimodal recommendation framework. To effectively train our AlignRec, we propose starting from pre-training the first alignment to obtain unified multimodal features and subsequently training the following two alignments together with these features as input. As it is essential to analyze whether each multimodal feature helps in training, we design three new classes of metrics to evaluate intermediate performance. Our extensive experiments on three real-world datasets consistently verify the superiority of AlignRec compared to nine baselines. We also find that the multimodal features generated by AlignRec are better than currently used ones, which are to be open-sourced.
Advances in modern technology have enabled the simultaneous recording of neural spiking activity, which statistically can be represented by a multivariate point process. We characterise the second order structure of this process via the spectral density matrix, a frequency domain equivalent of the covariance matrix. In the context of neuronal analysis, statistics based on the spectral density matrix can be used to infer connectivity in the brain network between individual neurons. However, the high-dimensional nature of spike train data mean that it is often difficult, or at times impossible, to compute these statistics. In this work, we discuss the importance of regularisation-based methods for spectral estimation, and propose novel methodology for use in the point process setting. We establish asymptotic properties for our proposed estimators and evaluate their performance on synthetic data simulated from multivariate Hawkes processes. Finally, we apply our methodology to neuroscience spike train data in order to illustrate its ability to infer connectivity in the brain network.
Electromagnetic information theory (EIT) is one of the important topics for 6G communication due to its potential to reveal the performance limit of wireless communication systems. For EIT, the research foundation is reasonable and accurate channel modeling. Existing channel modeling works for EIT in non-line-of-sight (NLoS) scenario focus on far-field modeling, which can not accurately capture the characteristics of the channel in near-field. In this paper, we propose the near-field channel model for EIT based on electromagnetic scattering theory. We model the channel by using non-stationary Gaussian random fields and derive the analytical expression of the correlation function of the fields. Furthermore, we analyze the characteristics of the proposed channel model, e.g., the sparsity of the model in wavenumber domain. Based on the sparsity of the model, we design a channel estimation scheme for near-field scenario. Numerical analysis verifies the correctness of the proposed scheme and shows that it can outperform existing schemes like least square (LS) and orthogonal matching pursuit (OMP).
Data augmentation, the artificial creation of training data for machine learning by transformations, is a widely studied research field across machine learning disciplines. While it is useful for increasing the generalization capabilities of a model, it can also address many other challenges and problems, from overcoming a limited amount of training data over regularizing the objective to limiting the amount data used to protect privacy. Based on a precise description of the goals and applications of data augmentation (C1) and a taxonomy for existing works (C2), this survey is concerned with data augmentation methods for textual classification and aims to achieve a concise and comprehensive overview for researchers and practitioners (C3). Derived from the taxonomy, we divided more than 100 methods into 12 different groupings and provide state-of-the-art references expounding which methods are highly promising (C4). Finally, research perspectives that may constitute a building block for future work are given (C5).
With the advances of data-driven machine learning research, a wide variety of prediction problems have been tackled. It has become critical to explore how machine learning and specifically deep learning methods can be exploited to analyse healthcare data. A major limitation of existing methods has been the focus on grid-like data; however, the structure of physiological recordings are often irregular and unordered which makes it difficult to conceptualise them as a matrix. As such, graph neural networks have attracted significant attention by exploiting implicit information that resides in a biological system, with interactive nodes connected by edges whose weights can be either temporal associations or anatomical junctions. In this survey, we thoroughly review the different types of graph architectures and their applications in healthcare. We provide an overview of these methods in a systematic manner, organized by their domain of application including functional connectivity, anatomical structure and electrical-based analysis. We also outline the limitations of existing techniques and discuss potential directions for future research.
We consider the problem of referring image segmentation. Given an input image and a natural language expression, the goal is to segment the object referred by the language expression in the image. Existing works in this area treat the language expression and the input image separately in their representations. They do not sufficiently capture long-range correlations between these two modalities. In this paper, we propose a cross-modal self-attention (CMSA) module that effectively captures the long-range dependencies between linguistic and visual features. Our model can adaptively focus on informative words in the referring expression and important regions in the input image. In addition, we propose a gated multi-level fusion module to selectively integrate self-attentive cross-modal features corresponding to different levels in the image. This module controls the information flow of features at different levels. We validate the proposed approach on four evaluation datasets. Our proposed approach consistently outperforms existing state-of-the-art methods.
Dynamic programming (DP) solves a variety of structured combinatorial problems by iteratively breaking them down into smaller subproblems. In spite of their versatility, DP algorithms are usually non-differentiable, which hampers their use as a layer in neural networks trained by backpropagation. To address this issue, we propose to smooth the max operator in the dynamic programming recursion, using a strongly convex regularizer. This allows to relax both the optimal value and solution of the original combinatorial problem, and turns a broad class of DP algorithms into differentiable operators. Theoretically, we provide a new probabilistic perspective on backpropagating through these DP operators, and relate them to inference in graphical models. We derive two particular instantiations of our framework, a smoothed Viterbi algorithm for sequence prediction and a smoothed DTW algorithm for time-series alignment. We showcase these instantiations on two structured prediction tasks and on structured and sparse attention for neural machine translation.
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