Outflow boundaries play an important role in multiphase fluid dynamics simulations that involve transition between liquid and vapor phases. These flows are dominated by low Weber numbers and a sharp jump in pressure, velocity, and temperature. Inadequate treatment of these jumps at the outlet generates undesirable fluid disturbances that propagate upstream and lead to instabilities within the computational domain. To mitigate these disturbances, we introduce a forcing term that can be applied to incompressible Navier-Stokes equations to enforce stability in the numerical solution. The forcing term acts as a damping mechanism to control vortices that are generated by droplet/bubbles in multiphase flows, and is designed to be a general formulation that can be coupled with a fixed pressure outflow boundary condition to simulate a variety of multiphase flow problems. We demonstrate its applicability to simulate pool and flow boiling problems, where bubble-induced vortices during evaporation and condensation present a challenge at the outflow. Validation and verification cases are chosen to quantify accuracy and stability of the proposed method in comparison to established benchmarks and reference solutions, along with detailed performance analysis for three-dimensional simulations on leadership supercomputing platforms. Computational experiments are performed using Flash-X, which is a composable open-source software instrument designed for multiscale fluid dynamics simulations on heterogeneous architectures.
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Collaborative filtering (CF) is an essential technique in recommender systems that provides personalized recommendations by only leveraging user-item interactions. However, most CF methods represent users and items as fixed points in the latent space, lacking the ability to capture uncertainty. While probabilistic embedding is proposed to intergrate uncertainty, they suffer from several limitations when introduced to graph-based recommender systems. Graph convolutional network framework would confuse the semantic of uncertainty in the nodes, and similarity measured by Kullback-Leibler (KL) divergence suffers from degradation problem and demands an exponential number of samples. To address these challenges, we propose a novel approach, called the Wasserstein dependent Graph Attention network (W-GAT), for collaborative filtering with uncertainty. We utilize graph attention network and Wasserstein distance to learn Gaussian embedding for each user and item. Additionally, our method incorporates Wasserstein-dependent mutual information further to increase the similarity between positive pairs. Experimental results on three benchmark datasets show the superiority of W-GAT compared to several representative baselines. Extensive experimental analysis validates the effectiveness of W-GAT in capturing uncertainty by modeling the range of user preferences and categories associated with items.
Brain-inspired Spiking Neural Networks (SNNs) have attracted much attention due to their event-based computing and energy-efficient features. However, the spiking all-or-none nature has prevented direct training of SNNs for various applications. The surrogate gradient (SG) algorithm has recently enabled spiking neural networks to shine in neuromorphic hardware. However, introducing surrogate gradients has caused SNNs to lose their original sparsity, thus leading to the potential performance loss. In this paper, we first analyze the current problem of direct training using SGs and then propose Masked Surrogate Gradients (MSGs) to balance the effectiveness of training and the sparseness of the gradient, thereby improving the generalization ability of SNNs. Moreover, we introduce a temporally weighted output (TWO) method to decode the network output, reinforcing the importance of correct timesteps. Extensive experiments on diverse network structures and datasets show that training with MSG and TWO surpasses the SOTA technique.
We propose a novel approach to mitigate biases in computer vision models by utilizing counterfactual generation and fine-tuning. While counterfactuals have been used to analyze and address biases in DNN models, the counterfactuals themselves are often generated from biased generative models, which can introduce additional biases or spurious correlations. To address this issue, we propose using adversarial images, that is images that deceive a deep neural network but not humans, as counterfactuals for fair model training. Our approach leverages a curriculum learning framework combined with a fine-grained adversarial loss to fine-tune the model using adversarial examples. By incorporating adversarial images into the training data, we aim to prevent biases from propagating through the pipeline. We validate our approach through both qualitative and quantitative assessments, demonstrating improved bias mitigation and accuracy compared to existing methods. Qualitatively, our results indicate that post-training, the decisions made by the model are less dependent on the sensitive attribute and our model better disentangles the relationship between sensitive attributes and classification variables.
High order accurate Hermite methods for the wave equation on curvilinear domains are presented. Boundaries are treated using centered compatibility conditions rather than more standard one-sided approximations. Both first-order-in-time (FOT) and second-order-in-time (SOT) Hermite schemes are developed. Hermite methods use the solution and multiple derivatives as unknowns and achieve space-time orders of accuracy $2m-1$ (FOT) and $2m$ (SOT) for methods using $(m+1)^d$ degree of freedom per node in $d$ dimensions. The compatibility boundary conditions (CBCs) are based on taking time derivatives of the boundary conditions and using the governing equations to replace the time derivatives with spatial derivatives. These resulting constraint equations augment the Hermite scheme on the boundary. The solvability of the equations resulting from the compatibility conditions are analyzed. Numerical examples demonstrate the accuracy and stability of the new schemes in two dimensions.
We consider the problem of selecting an optimal subset of information sources for a hypothesis testing/classification task where the goal is to identify the true state of the world from a finite set of hypotheses, based on finite observation samples from the sources. In order to characterize the learning performance, we propose a misclassification penalty framework, which enables non-uniform treatment of different misclassification errors. In a centralized Bayesian learning setting, we study two variants of the subset selection problem: (i) selecting a minimum cost information set to ensure that the maximum penalty of misclassifying the true hypothesis remains bounded and (ii) selecting an optimal information set under a limited budget to minimize the maximum penalty of misclassifying the true hypothesis. Under certain assumptions, we prove that the objective (or constraints) of these combinatorial optimization problems are weak (or approximate) submodular, and establish high-probability performance guarantees for greedy algorithms. Further, we propose an alternate metric for information set selection which is based on the total penalty of misclassification. We prove that this metric is submodular and establish near-optimal guarantees for the greedy algorithms for both the information set selection problems. Finally, we present numerical simulations to validate our theoretical results over several randomly generated instances.
We discuss the advantages of a spline-based freeform shape optimization approach using the example of a multi-tapered coaxial balun connected to a spiral antenna. The underlying simulation model is given in terms of a recently proposed isogeometric integral equation formulation, which can be interpreted as a high-order generalization of the partial element equivalent circuit method. We demonstrate a significant improvement in the optimized design, i.e., a reduction in the magnitude of the scattering parameter over a wide frequency range.
Randomized subspace approximation with "matrix sketching" is an effective approach for constructing approximate partial singular value decompositions (SVDs) of large matrices. The performance of such techniques has been extensively analyzed, and very precise estimates on the distribution of the residual errors have been derived. However, our understanding of the accuracy of the computed singular vectors (measured in terms of the canonical angles between the spaces spanned by the exact and the computed singular vectors, respectively) remains relatively limited. In this work, we present practical bounds and estimates for canonical angles of randomized subspace approximation that can be computed efficiently either a priori or a posteriori, without assuming prior knowledge of the true singular subspaces. Under moderate oversampling in the randomized SVD, our prior probabilistic bounds are asymptotically tight and can be computed efficiently, while bringing a clear insight into the balance between oversampling and power iterations given a fixed budget on the number of matrix-vector multiplications. The numerical experiments demonstrate the empirical effectiveness of these canonical angle bounds and estimates on different matrices under various algorithmic choices for the randomized SVD.
Retrieval-Augmented Generation (RAG) merges retrieval methods with deep learning advancements to address the static limitations of large language models (LLMs) by enabling the dynamic integration of up-to-date external information. This methodology, focusing primarily on the text domain, provides a cost-effective solution to the generation of plausible but incorrect responses by LLMs, thereby enhancing the accuracy and reliability of their outputs through the use of real-world data. As RAG grows in complexity and incorporates multiple concepts that can influence its performance, this paper organizes the RAG paradigm into four categories: pre-retrieval, retrieval, post-retrieval, and generation, offering a detailed perspective from the retrieval viewpoint. It outlines RAG's evolution and discusses the field's progression through the analysis of significant studies. Additionally, the paper introduces evaluation methods for RAG, addressing the challenges faced and proposing future research directions. By offering an organized framework and categorization, the study aims to consolidate existing research on RAG, clarify its technological underpinnings, and highlight its potential to broaden the adaptability and applications of LLMs.
Graph Convolutional Networks (GCNs) have been widely applied in various fields due to their significant power on processing graph-structured data. Typical GCN and its variants work under a homophily assumption (i.e., nodes with same class are prone to connect to each other), while ignoring the heterophily which exists in many real-world networks (i.e., nodes with different classes tend to form edges). Existing methods deal with heterophily by mainly aggregating higher-order neighborhoods or combing the immediate representations, which leads to noise and irrelevant information in the result. But these methods did not change the propagation mechanism which works under homophily assumption (that is a fundamental part of GCNs). This makes it difficult to distinguish the representation of nodes from different classes. To address this problem, in this paper we design a novel propagation mechanism, which can automatically change the propagation and aggregation process according to homophily or heterophily between node pairs. To adaptively learn the propagation process, we introduce two measurements of homophily degree between node pairs, which is learned based on topological and attribute information, respectively. Then we incorporate the learnable homophily degree into the graph convolution framework, which is trained in an end-to-end schema, enabling it to go beyond the assumption of homophily. More importantly, we theoretically prove that our model can constrain the similarity of representations between nodes according to their homophily degree. Experiments on seven real-world datasets demonstrate that this new approach outperforms the state-of-the-art methods under heterophily or low homophily, and gains competitive performance under homophily.
Object detection typically assumes that training and test data are drawn from an identical distribution, which, however, does not always hold in practice. Such a distribution mismatch will lead to a significant performance drop. In this work, we aim to improve the cross-domain robustness of object detection. We tackle the domain shift on two levels: 1) the image-level shift, such as image style, illumination, etc, and 2) the instance-level shift, such as object appearance, size, etc. We build our approach based on the recent state-of-the-art Faster R-CNN model, and design two domain adaptation components, on image level and instance level, to reduce the domain discrepancy. The two domain adaptation components are based on H-divergence theory, and are implemented by learning a domain classifier in adversarial training manner. The domain classifiers on different levels are further reinforced with a consistency regularization to learn a domain-invariant region proposal network (RPN) in the Faster R-CNN model. We evaluate our newly proposed approach using multiple datasets including Cityscapes, KITTI, SIM10K, etc. The results demonstrate the effectiveness of our proposed approach for robust object detection in various domain shift scenarios.
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