The immersed interface method (IIM) for models of fluid flow and fluid-structure interaction imposes jump conditions that capture stress discontinuities generated by forces that are concentrated along immersed boundaries. Most prior work using the IIM for fluid dynamic applications has focused on smooth interfaces, but boundaries with sharp features such as corners and edges can appear in practical analyses, particularly on engineered structures. The present study builds on our work to integrate finite element-type representations of interface geometries with the IIM. Initial realizations of this approach used a continuous Galerkin (CG) finite element discretization for the boundary, but as we show herein, these approaches generate large errors near sharp geometrical features. To overcome this difficulty, this study introduces an IIM approach using discontinuous Galerkin (DG) representation of the jump conditions. Numerical examples explore the impacts of different interface representations on accuracy for both smooth and sharp boundaries, particularly flows interacting with fixed interface configurations. We demonstrate that using a DG approach provides accuracy that is comparable to the CG method for smooth cases. Further, we identify a time step size restriction for the CG representation that is directly related to the sharpness of the geometry. In contrast, time step size restrictions imposed by DG representations are demonstrated to be insensitive to the presence of sharp features.
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The opaque nature of transformer-based models, particularly in applications susceptible to unethical practices such as dark-patterns in user interfaces, requires models that integrate uncertainty quantification to enhance trust in predictions. This study focuses on dark-pattern detection, deceptive design choices that manipulate user decisions, undermining autonomy and consent. We propose a differential fine-tuning approach implemented at the final classification head via uncertainty quantification with transformer-based pre-trained models. Employing a dense neural network (DNN) head architecture as a baseline, we examine two methods capable of quantifying uncertainty: Spectral-normalized Neural Gaussian Processes (SNGPs) and Bayesian Neural Networks (BNNs). These methods are evaluated on a set of open-source foundational models across multiple dimensions: model performance, variance in certainty of predictions and environmental impact during training and inference phases. Results demonstrate that integrating uncertainty quantification maintains performance while providing insights into challenging instances within the models. Moreover, the study reveals that the environmental impact does not uniformly increase with the incorporation of uncertainty quantification techniques. The study's findings demonstrate that uncertainty quantification enhances transparency and provides measurable confidence in predictions, improving the explainability and clarity of black-box models. This facilitates informed decision-making and mitigates the influence of dark-patterns on user interfaces. These results highlight the importance of incorporating uncertainty quantification techniques in developing machine learning models, particularly in domains where interpretability and trustworthiness are critical.
Latent Gaussian process (GP) models are flexible probabilistic non-parametric function models. Vecchia approximations are accurate approximations for GPs to overcome computational bottlenecks for large data, and the Laplace approximation is a fast method with asymptotic convergence guarantees to approximate marginal likelihoods and posterior predictive distributions for non-Gaussian likelihoods. Unfortunately, the computational complexity of combined Vecchia-Laplace approximations grows faster than linearly in the sample size when used in combination with direct solver methods such as the Cholesky decomposition. Computations with Vecchia-Laplace approximations can thus become prohibitively slow precisely when the approximations are usually the most accurate, i.e., on large data sets. In this article, we present iterative methods to overcome this drawback. Among other things, we introduce and analyze several preconditioners, derive new convergence results, and propose novel methods for accurately approximating predictive variances. We analyze our proposed methods theoretically and in experiments with simulated and real-world data. In particular, we obtain a speed-up of an order of magnitude compared to Cholesky-based calculations and a threefold increase in prediction accuracy in terms of the continuous ranked probability score compared to a state-of-the-art method on a large satellite data set. All methods are implemented in a free C++ software library with high-level Python and R packages.
A multichannel extension to the RVQGAN neural coding method is proposed, and realized for data-driven compression of third-order Ambisonics audio. The input- and output layers of the generator and discriminator models are modified to accept multiple (16) channels without increasing the model bitrate. We also propose a loss function for accounting for spatial perception in immersive reproduction, and transfer learning from single-channel models. Listening test results with 7.1.4 immersive playback show that the proposed extension is suitable for coding scene-based, 16-channel Ambisonics content with good quality at 16 kbps.
Intelligent reflecting surface (IRS)-assisted mobile edge computing (MEC) systems have shown notable improvements in efficiency, such as reduced latency, higher data rates, and better energy efficiency. However, the resource competition among users will lead to uneven allocation, increased latency, and lower throughput. Fortunately, the rate-splitting multiple access (RSMA) technique has emerged as a promising solution for managing interference and optimizing resource allocation in MEC systems. This paper studies an IRS-assisted MEC system with RSMA, aiming to jointly optimize the passive beamforming of the IRS, the active beamforming of the base station, the task offloading allocation, the transmit power of users, the ratios of public and private information allocation, and the decoding order of the RSMA to minimize the average delay from a novel uplink transmission perspective. Since the formulated problem is non-convex and the optimization variables are highly coupled, we propose a hierarchical deep reinforcement learning-based algorithm to optimize both continuous and discrete variables of the problem. Additionally, to better extract channel features, we design a novel network architecture within the policy and evaluation networks of the proposed algorithm, combining convolutional neural networks and densely connected convolutional network for feature extraction. Simulation results indicate that the proposed algorithm not only exhibits excellent convergence performance but also outperforms various benchmarks.
Diversity in demonstration selection is crucial for enhancing model generalization, as it enables a broader coverage of structures and concepts. However, constructing an appropriate set of demonstrations has remained a focal point of research. This paper presents the Relevance-Diversity Enhanced Selection (RDES), an innovative approach that leverages reinforcement learning to optimize the selection of diverse reference demonstrations for text classification tasks using Large Language Models (LLMs), especially in few-shot prompting scenarios. RDES employs a Q-learning framework to dynamically identify demonstrations that maximize both diversity and relevance to the classification objective by calculating a diversity score based on label distribution among selected demonstrations. This method ensures a balanced representation of reference data, leading to improved classification accuracy. Through extensive experiments on four benchmark datasets and involving 12 closed-source and open-source LLMs, we demonstrate that RDES significantly enhances classification accuracy compared to ten established baselines. Furthermore, we investigate the incorporation of Chain-of-Thought (CoT) reasoning in the reasoning process, which further enhances the model's predictive performance. The results underscore the potential of reinforcement learning to facilitate adaptive demonstration selection and deepen the understanding of classification challenges.
Uncertainty quantification in text-to-image (T2I) generative models is crucial for understanding model behavior and improving output reliability. In this paper, we are the first to quantify and evaluate the uncertainty of T2I models with respect to the prompt. Alongside adapting existing approaches designed to measure uncertainty in the image space, we also introduce Prompt-based UNCertainty Estimation for T2I models (PUNC), a novel method leveraging Large Vision-Language Models (LVLMs) to better address uncertainties arising from the semantics of the prompt and generated images. PUNC utilizes a LVLM to caption a generated image, and then compares the caption with the original prompt in the more semantically meaningful text space. PUNC also enables the disentanglement of both aleatoric and epistemic uncertainties via precision and recall, which image-space approaches are unable to do. Extensive experiments demonstrate that PUNC outperforms state-of-the-art uncertainty estimation techniques across various settings. Uncertainty quantification in text-to-image generation models can be used on various applications including bias detection, copyright protection, and OOD detection. We also introduce a comprehensive dataset of text prompts and generation pairs to foster further research in uncertainty quantification for generative models. Our findings illustrate that PUNC not only achieves competitive performance but also enables novel applications in evaluating and improving the trustworthiness of text-to-image models.
We consider the problem of classifying trajectories on a discrete or discretised 2-dimensional manifold modelled by a simplicial complex. Previous works have proposed to project the trajectories into the harmonic eigenspace of the Hodge Laplacian, and then cluster the resulting embeddings. However, if the considered space has vanishing homology (i.e., no "holes"), then the harmonic space of the 1-Hodge Laplacian is trivial and thus the approach fails. Here we propose to view this issue akin to a sensor placement problem and present an algorithm that aims to learn "optimal holes" to distinguish a set of given trajectory classes. Specifically, given a set of labelled trajectories, which we interpret as edge-flows on the underlying simplicial complex, we search for 2-simplices whose deletion results in an optimal separation of the trajectory labels according to the corresponding spectral embedding of the trajectories into the harmonic space. Finally, we generalise this approach to the unsupervised setting.
Molecular design and synthesis planning are two critical steps in the process of molecular discovery that we propose to formulate as a single shared task of conditional synthetic pathway generation. We report an amortized approach to generate synthetic pathways as a Markov decision process conditioned on a target molecular embedding. This approach allows us to conduct synthesis planning in a bottom-up manner and design synthesizable molecules by decoding from optimized conditional codes, demonstrating the potential to solve both problems of design and synthesis simultaneously. The approach leverages neural networks to probabilistically model the synthetic trees, one reaction step at a time, according to reactivity rules encoded in a discrete action space of reaction templates. We train these networks on hundreds of thousands of artificial pathways generated from a pool of purchasable compounds and a list of expert-curated templates. We validate our method with (a) the recovery of molecules using conditional generation, (b) the identification of synthesizable structural analogs, and (c) the optimization of molecular structures given oracle functions relevant to drug discovery.
We introduce a multi-task setup of identifying and classifying entities, relations, and coreference clusters in scientific articles. We create SciERC, a dataset that includes annotations for all three tasks and develop a unified framework called Scientific Information Extractor (SciIE) for with shared span representations. The multi-task setup reduces cascading errors between tasks and leverages cross-sentence relations through coreference links. Experiments show that our multi-task model outperforms previous models in scientific information extraction without using any domain-specific features. We further show that the framework supports construction of a scientific knowledge graph, which we use to analyze information in scientific literature.
High spectral dimensionality and the shortage of annotations make hyperspectral image (HSI) classification a challenging problem. Recent studies suggest that convolutional neural networks can learn discriminative spatial features, which play a paramount role in HSI interpretation. However, most of these methods ignore the distinctive spectral-spatial characteristic of hyperspectral data. In addition, a large amount of unlabeled data remains an unexploited gold mine for efficient data use. Therefore, we proposed an integration of generative adversarial networks (GANs) and probabilistic graphical models for HSI classification. Specifically, we used a spectral-spatial generator and a discriminator to identify land cover categories of hyperspectral cubes. Moreover, to take advantage of a large amount of unlabeled data, we adopted a conditional random field to refine the preliminary classification results generated by GANs. Experimental results obtained using two commonly studied datasets demonstrate that the proposed framework achieved encouraging classification accuracy using a small number of data for training.
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