Zhu Wang

Hongfei Fu, Hong Wang, Zhu Wang

In this paper, a reduced-order model (ROM) based on the proper orthogonal decomposition and the discrete empirical interpolation method is proposed for efficiently simulating time-fractional partial differential equations (TFPDEs). Both linear and nonlinear equations are considered. We demonstrate the effectiveness of the ROM by several numerical examples, in which the ROM achieves the same accuracy of the full-order model (FOM) over a long-term simulation while greatly reducing the computational cost. The proposed ROM is then regarded as a surrogate of FOM and is applied to an inverse problem for identifying the order of the time-fractional derivative of the TFPDE model. Based on the Levenberg--Marquardt regularization iterative method with the Armijo rule, we develop a ROM-based algorithm for solving the inverse problem. For cases in which the observation data is either uncontaminated or contaminated by random noise, the proposed approach is able to achieve accurate parameter estimation efficiently.

Traian Iliescu, Zhu Wang

We develop a variational multiscale proper orthogonal decomposition reduced-order model for turbulent incompressible Navier-Stokes equations. The error analysis of the full discretization of the model is presented. All error contributions are considered: the spatial discretization error (due to the finite element discretization), the temporal discretization error (due to the backward Euler method), and the proper orthogonal decomposition truncation error. Numerical tests for a three-dimensional turbulent flow past a cylinder at Reynolds number Re=1000 show the improved physical accuracy of the new model over the standard Galerkin and mixing-length proper orthogonal decomposition reduced-order models. The high computational efficiency of the new model is also showcased. Finally, the theoretical error estimates are confirmed by numerical simulations of a two-dimensional Navier-Stokes problem.

Traian Iliescu, Zhu Wang

This paper presents a theoretical and numerical investigation of the following practical question: Should the time difference quotients of the snapshots be used to generate the proper orthogonal decomposition basis functions? The answer to this question is important, since some published numerical studies use the time difference quotients, whereas other numerical studies do not. The criterion used in this paper to answer this question is the rate of convergence of the error of the reduced order model with respect to the number of proper orthogonal decomposition basis functions. Two cases are considered: the no_DQ case, in which the snapshot difference quotients are not used, and the DQ case, in which the snapshot difference quotients are used. The error estimates suggest that the convergence rates in the $C^0(L^2)$-norm and in the $C^0(H^1)$-norm are optimal for the DQ case, but suboptimal for the no_DQ case. The convergence rates in the $L^2(H^1)$-norm are optimal for both the DQ case and the no_DQ case. Numerical tests are conducted on the heat equation and on the Burgers equation. The numerical results support the conclusions drawn from the theoretical error estimates. Overall, the theoretical and numerical results strongly suggest that, in order to achieve optimal pointwise in time rates of convergence with respect to the number of proper orthogonal decomposition basis functions, one should use the snapshot difference quotients.

Xuping Xie, David Wells, Zhu Wang et al.

Standard ROMs generally yield spurious numerical oscillations in the simulation of convection-dominated flows. Regularized ROMs use explicit ROM spatial filtering to decrease these spurious numerical oscillations. The Leray ROM is a recently introduced regularized ROM that utilizes explicit ROM spatial filtering of the convective term in the Navier-Stokes equations. This paper presents the numerical analysis of the finite element discretization of the Leray ROM. Error estimates for the ROM differential filter, which is the explicit ROM spatial filter used in the Leray ROM, are proved. These ROM filtering error estimates are then used to prove error estimates for the Leray ROM. Finally, both the ROM filtering error estimates and the Leray ROM error estimates are numerically investigated in the simulation of the two-dimensional Navier-Stokes equations with an analytic solution.

Erich L Foster, Traian Iliescu, Zhu Wang

This paper presents a conforming finite element discretization of the streamfunction formulation of the one-layer stationary quasi-geostrophic equations, which are a commonly used model for the large scale wind- driven ocean circulation. Optimal error estimates for this finite element discretization with the Argyris element are derived. Numerical tests for the finite element discretization of the quasi-geostrophic equations and two of its standard simplifications (the linear Stommel model and the linear Stommel-Munk model) are carried out. By benchmarking the numerical results against those in the published literature, we conclude that our finite element discretization is accurate. Furthermore, the numerical results have the same convergence rates as those predicted by the theoretical error estimates.

Chang Yang, Chuang Zhou, Yilin Xiao et al.

Memory emerges as the core module in the Large Language Model (LLM)-based agents for long-horizon complex tasks (e.g., multi-turn dialogue, game playing, scientific discovery), where memory can enable knowledge accumulation, iterative reasoning and self-evolution. Among diverse paradigms, graph stands out as a powerful structure for agent memory due to the intrinsic capabilities to model relational dependencies, organize hierarchical information, and support efficient retrieval. This survey presents a comprehensive review of agent memory from the graph-based perspective. First, we introduce a taxonomy of agent memory, including short-term vs. long-term memory, knowledge vs. experience memory, non-structural vs. structural memory, with an implementation view of graph-based memory. Second, according to the life cycle of agent memory, we systematically analyze the key techniques in graph-based agent memory, covering memory extraction for transforming the data into the contents, storage for organizing the data efficiently, retrieval for retrieving the relevant contents from memory to support reasoning, and evolution for updating the contents in the memory. Third, we summarize the open-sourced libraries and benchmarks that support the development and evaluation of self-evolving agent memory. We also explore diverse application scenarios. Finally, we identify critical challenges and future research directions. This survey aims to offer actionable insights to advance the development of more efficient and reliable graph-based agent memory systems. All the related resources, including research papers, open-source data, and projects, are collected for the community in https://github.com/DEEP-PolyU/Awesome-GraphMemory.

Traian iliescu, Zhu Wang

We introduce a variational multiscale closure modeling strategy for the numerical stabilization of proper orthogonal decomposition reduced-order models of convection-dominated equations. As a first step, the new model is analyzed and tested for convection-dominated convection-diffusion equations. The numerical analysis of the finite element discretization of the model is presented. Numerical tests show the increased numerical accuracy over the standard reduced-order model and illustrate the theoretical convergence rates.

Thi-Thao-Phuong Hoang, Lili Ju, Zhu Wang

The paper is concerned with overlapping domain decomposition and exponential time differencing for the diffusion equation discretized in space by cell-centered finite differences. Two localized exponential time differencing methods are proposed to solve the fully discrete problem: the first method is based on Schwarz iteration applied at each time step and involves solving stationary problems in the subdomains at each iteration, while the second method is based on the Schwarz waveform relaxation algorithm in which time-dependent subdomain problems are solved at each iteration. The convergence of the associated iterative solutions to the corresponding fully discrete multidomain solution and to the exact semi-discrete solution is rigorously proved. Numerical experiments are carried out to confirm theoretical results and to compare the performance of the two methods.

Yan Luo, Zhu Wang

In this paper, we develop an ensemble-based time-stepping algorithm to efficiently find numerical solutions to a group of linear, second-order parabolic partial differential equations (PDEs). Particularly, the PDE models in the group could be subject to different diffusion coefficients, initial conditions, boundary conditions, and body forces. The proposed algorithm leads to a single discrete system for the group with multiple right-hand-side vectors by introducing an ensemble average of the diffusion coefficient functions and using a new semi-implicit time integration method. The system could be solved more efficiently than multiple linear systems with a single right-hand-side vector. We first apply the algorithm to deterministic parabolic PDEs and derive a rigorous error estimate that shows the scheme is first-order accurate in time and is optimally accurate in space. We then extend it to find stochastic solutions of parabolic PDEs with random coefficients and put forth an ensemble-based Monte Carlo method. The effectiveness of the new approach is demonstrated through theoretical analysis. Several numerical experiments are presented to illustrate our theoretical results.

Jun Liu, Zhu Wang

In this paper, we analyze the convergence of several discretize-then-optimize algorithms, based on either a second-order or a fourth-order finite difference discretization, for solving elliptic PDE-constrained optimization or optimal control problems. To ensure the convergence of a discretize-then-optimize algorithm, one well-accepted criterion is to choose or redesign the discretization scheme such that the resultant discretize-then-optimize algorithm commutes with the corresponding optimize-then-discretize algorithm. In other words, both types of algorithms would give rise to exactly the same discrete optimality system. However, such an approach is not trivial. In this work, by investigating a simple distributed elliptic optimal control problem, we first show that enforcing such a stringent condition of commutative property is only sufficient but not necessary for achieving the desired convergence. We then propose to add some suitable $H_1$ semi-norm penalty/regularization terms to recover the lost convergence due to the inconsistency caused by the loss of commutativity. Numerical experiments are carried out to verify our theoretical analysis and also validate the effectiveness of our proposed regularization techniques.

Zhu Wang

For nonlinear reduced-order models, especially for those with non-polynomial nonlinearities, the computational complexity still depends on the dimension of the original dynamical system. As a result, the reduced-order model loses its computational efficiency, which, however, is its the most significant advantage. Nonlinear dimensional reduction methods, such as the discrete empirical interpolation method, have been widely used to evaluate the nonlinear terms at a low cost. But when the finite element method is utilized for the spatial discretization, nonlinear snapshot generation requires inner products to be fulfilled, which costs lots of off-line time. Numerical integrations are also needed over elements sharing the selected interpolation points during the simulation, which keeps on-line time high. In this paper, we extend the finite element method with interpolated coefficients to nonlinear reduced-order models. It approximates the nonlinear function in the reduced-order model by its finite element interpolation, which makes coefficient matrices of the nonlinear terms pre-computable and, thus, leads to great savings in the computational efforts. Due to the separation of spatial and temporal variables in the finite element interpolation, the discrete empirical interpolation method can be directly applied on the nonlinear functions. Therefore, the main computational hurdles when applying the discrete empirical interpolation method in the finite element context are conquered. We also establish a rigorous asymptotic error estimation, which shows that the proposed approach achieves the same accuracy as that of the standard finite element method under certain smoothness assumptions of the nonlinear functions. Several numerical tests are presented to validate the proposed method and verify the theoretical results.

Thi-Thao-Phuong Hoang, Lili Ju, Wei Leng et al.

In this paper we present and analyze a general framework for constructing high order explicit local time stepping (LTS) methods for hyperbolic conservation laws. In particular, we consider the model problem discretized by Runge-Kutta discontinuous Galerkin (RKDG) methods and design LTS algorithms based on strong stability preserving Runge-Kutta (SSP-RK) schemes, that allow spatially variable time step sizes to be used for time integrations in different regions. The proposed algorithms are of predictor-corrector type, in which the interface information along the time direction is first predicted based on the SSP-RK approximations and Taylor expansions, and then the fluxes over the region of interface are corrected to conserve mass exactly at each time step. Following the proposed framework, we detail the corresponding LTS schemes with accuracy up to the fourth order, and prove their conservation property and nonlinear stability for the scalar conservation laws. Numerical experiments are also presented to demonstrate excellent performance of the proposed LTS algorithms.

Kristofer Schlachter, Benjamin Ahlbrand, Zhu Wang et al.

When creating 3D content, highly specialized skills are generally needed to design and generate models of objects and other assets by hand. We address this problem through high-quality 3D asset retrieval from multi-modal inputs, including 2D sketches, images and text. We use CLIP as it provides a bridge to higher-level latent features. We use these features to perform a multi-modality fusion to address the lack of artistic control that affects common data-driven approaches. Our approach allows for multi-modal conditional feature-driven retrieval through a 3D asset database, by utilizing a combination of input latent embeddings. We explore the effects of different combinations of feature embeddings across different input types and weighting methods.

Zhu Wang

Ontology matching (OM) entails the identification of semantic relationships between concepts within two or more knowledge graphs (KGs) and serves as a critical step in integrating KGs from various sources. Recent advancements in deep OM models have harnessed the power of transformer-based language models and the advantages of knowledge graph embedding. Nevertheless, these OM models still face persistent challenges, such as a lack of reference alignments, runtime latency, and unexplored different graph structures within an end-to-end framework. In this study, we introduce a novel self-supervised learning OM framework with input ontologies, called LaKERMap. This framework capitalizes on the contextual and structural information of concepts by integrating implicit knowledge into transformers. Specifically, we aim to capture multiple structural contexts, encompassing both local and global interactions, by employing distinct training objectives. To assess our methods, we utilize the Bio-ML datasets and tasks. The findings from our innovative approach reveal that LaKERMap surpasses state-of-the-art systems in terms of alignment quality and inference time. Our models and codes are available here: https://github.com/ellenzhuwang/lakermap.

Song Wang, Zhu Wang, Can Li et al.

In comparison to conventional RGB cameras, the superior temporal resolution of event cameras allows them to capture rich information between frames, making them prime candidates for object tracking. Yet in practice, despite their theoretical advantages, the body of work on event-based multi-object tracking (MOT) remains in its infancy, especially in real-world settings where events from complex background and camera motion can easily obscure the true target motion. In this work, an event-based multi-object tracker, called SpikeMOT, is presented to address these challenges. SpikeMOT leverages spiking neural networks to extract sparse spatiotemporal features from event streams associated with objects. The resulting spike train representations are used to track the object movement at high frequency, while a simultaneous object detector provides updated spatial information of these objects at an equivalent frame rate. To evaluate the effectiveness of SpikeMOT, we introduce DSEC-MOT, the first large-scale event-based MOT benchmark incorporating fine-grained annotations for objects experiencing severe occlusions, frequent trajectory intersections, and long-term re-identification in real-world contexts. Extensive experiments employing DSEC-MOT and another event-based dataset, named FE240hz, demonstrate SpikeMOT's capability to achieve high tracking accuracy amidst challenging real-world scenarios, advancing the state-of-the-art in event-based multi-object tracking.

Yan Luo, Zhu Wang

A first-order, Monte Carlo ensemble method has been recently introduced for solving parabolic equations with random coefficients in [26], which is a natural synthesis of the ensemble-based, Monte Carlo sampling algorithm and the ensemble-based, first-order time stepping scheme. With the introduction of an ensemble average of the diffusion function, this algorithm leads to a single discrete system with multiple right-hand sides for a group of realizations, which could be solved more efficiently than a sequence of linear systems. In this paper, we pursue in the same direction and develop a new multilevel Monte Carlo ensemble method for solving random parabolic partial differential equations. Comparing with the approach in [26], this method possesses a high-order accuracy in time and further reduces the computational cost by using the multilevel Monte Carlo method. Rigorous numerical analysis shows the method achieves the optimal rate of convergence. Several numerical experiments are presented to illustrate the theoretical results.

Jun Liu, Zhu Wang

Optimization with time-dependent partial differential equations (PDEs) as constraints {appears} in many science and engineering applications. The associated first-order necessary optimality system consists of one forward and one backward time-dependent PDE coupled with optimality conditions. An optimization process by using the one-shot method determines the optimal control, state and adjoint state at once, with the cost of solving a large scale, fully discrete optimality system. Hence, such {a} one-shot method could easily become computationally prohibitive when the time span is long or time step is small. To overcome this difficulty, we propose several time domain decomposition algorithms for improving the {computational efficiency of the one-shot method}. In these algorithms, the optimality system is split into many small subsystems over a much smaller time interval, which are coupled by appropriate continuity matching conditions. Both one-level and two-level multiplicative and additive Schwarz algorithms are developed for iteratively solving the decomposed subsystems in parallel. In particular, the convergence of the one-level, non-overlapping algorithms is proved. The effectiveness of our proposed algorithms is demonstrated by both 1D and 2D numerical experiments, where the developed two-level algorithms {show convergence rates that are scalable} with respect to the number of subdomains.

Zhu Wang, Praveen Raj Veluswami, Harsh Mishra et al.

Many neural networks deployed in the real world scenarios are trained using cross entropy based loss functions. From the optimization perspective, it is known that the behavior of first order methods such as gradient descent crucially depend on the separability of datasets. In fact, even in the most simplest case of binary classification, the rate of convergence depends on two factors: (1) condition number of data matrix, and (2) separability of the dataset. With no further pre-processing techniques such as over-parametrization, data augmentation etc., separability is an intrinsic quantity of the data distribution under consideration. We focus on the landscape design of the logistic function and derive a novel sequence of {\em strictly} convex functions that are at least as strict as logistic loss. The minimizers of these functions coincide with those of the minimum norm solution wherever possible. The strict convexity of the derived function can be extended to finetune state-of-the-art models and applications. In empirical experimental analysis, we apply our proposed rooted logistic objective to multiple deep models, e.g., fully-connected neural networks and transformers, on various of classification benchmarks. Our results illustrate that training with rooted loss function is converged faster and gains performance improvements. Furthermore, we illustrate applications of our novel rooted loss function in generative modeling based downstream applications, such as finetuning StyleGAN model with the rooted loss. The code implementing our losses and models can be found here for open source software development purposes: https://anonymous.4open.science/r/rooted_loss.

Xiangru Li, Zhu Wang, Si Zeng et al.

The accuracy of the estimated stellar atmospheric parameter decreases evidently with the decreasing of spectral signal-to-noise ratio (SNR) and there are a huge amount of this kind observations, especially in case of SNR$<$30. Therefore, it is helpful to improve the parameter estimation performance for these spectra and this work studied the ($T_\texttt{eff}, \log~g$, [Fe/H]) estimation problem for LAMOST DR8 low-resolution spectra with 20$\leq$SNR$<$30. We proposed a data-driven method based on machine learning techniques. Firstly, this scheme detected stellar atmospheric parameter-sensitive features from spectra by the Least Absolute Shrinkage and Selection Operator (LASSO), rejected ineffective data components and irrelevant data. Secondly, a Multi-layer Perceptron (MLP) method was used to estimate stellar atmospheric parameters from the LASSO features. Finally, the performance of the LASSO-MLP was evaluated by computing and analyzing the consistency between its estimation and the reference from the APOGEE (Apache Point Observatory Galactic Evolution Experiment) high-resolution spectra. Experiments show that the Mean Absolute Errors (MAE) of $T_\texttt{eff}, \log~g$, [Fe/H] are reduced from the LASP (137.6 K, 0.195 dex, 0.091 dex) to LASSO-MLP (84.32 K, 0.137 dex, 0.063 dex), which indicate evident improvements on stellar atmospheric parameter estimation. In addition, this work estimated the stellar atmospheric parameters for 1,162,760 low-resolution spectra with 20$\leq$SNR$<$30 from LAMOST DR8 using LASSO-MLP, and released the estimation catalog, learned model, experimental code, trained model, training data and test data for scientific exploration and algorithm study.

Zhu Wang, Sourav Medya, Sathya N. Ravi

Often, deep network models are purely inductive during training and while performing inference on unseen data. Thus, when such models are used for predictions, it is well known that they often fail to capture the semantic information and implicit dependencies that exist among objects (or concepts) on a population level. Moreover, it is still unclear how domain or prior modal knowledge can be specified in a backpropagation friendly manner, especially in large-scale and noisy settings. In this work, we propose an end-to-end vision and language model incorporating explicit knowledge graphs. We also introduce an interactive out-of-distribution (OOD) layer using implicit network operator. The layer is used to filter noise that is brought by external knowledge base. In practice, we apply our model on several vision and language downstream tasks including visual question answering, visual reasoning, and image-text retrieval on different datasets. Our experiments show that it is possible to design models that perform similarly to state-of-art results but with significantly fewer samples and training time.

Zhu Wang, Junnan Dong, Shuang Zhou et al.

Graph anomaly detection (GAD) is widely applied in many areas, such as financial fraud detection and social spammer detection. Anomalous nodes in the graph not only impact their own communities but also create a ripple effect on neighbors throughout the graph structure. Detecting anomalous nodes in complex graphs has been a challenging task. While existing GAD methods assume all labels are correct, real-world scenarios often involve inaccurate annotations. These noisy labels can severely degrade GAD performance because, with anomalies representing a minority class, even a small number of mislabeled instances can disproportionately interfere with detection models. Cutting edges to mitigate the negative effects of noisy labels is a good option; however, it has both positive and negative influences and also presents an issue of weak supervision. To perform effective GAD with noisy labels, we propose REinforced Graph Anomaly Detector (REGAD) by pruning the edges of candidate nodes potentially with mistaken labels. Moreover, we design the performance feedback based on strategically crafted confident labels to guide the cutting process, ensuring optimal results. Specifically, REGAD contains two novel components. (i) A tailored policy network, which involves two-step actions to remove negative effect propagation step by step. (ii) A policy-in-the-loop mechanism to identify suitable edge removal strategies that control the propagation of noise on the graph and estimate the updated structure to obtain reliable pseudo labels iteratively. Experiments on three real-world datasets demonstrate that REGAD outperforms all baselines under different noisy ratios.

Jie Chen, Zhu Wang, Chuanbin Liu et al.

Features of the same sample generated by different pretrained models often exhibit inherently distinct feature distributions because of discrepancies in the model pretraining objectives or architectures. Learning invariant representations from large-scale unlabeled visual data with various pretrained models in a fully unsupervised transfer manner remains a significant challenge. In this paper, we propose a multiview self-representation learning (MSRL) method in which invariant representations are learned by exploiting the self-representation property of features across heterogeneous views. The features are derived from large-scale unlabeled visual data through transfer learning with various pretrained models and are referred to as heterogeneous multiview data. An individual linear model is stacked on top of its corresponding frozen pretrained backbone. We introduce an information-passing mechanism that relies on self-representation learning to support feature aggregation over the outputs of the linear model. Moreover, an assignment probability distribution consistency scheme is presented to guide multiview self-representation learning by exploiting complementary information across different views. Consequently, representation invariance across different linear models is enforced through this scheme. In addition, we provide a theoretical analysis of the information-passing mechanism, the assignment probability distribution consistency and the incremental views. Extensive experiments with multiple benchmark visual datasets demonstrate that the proposed MSRL method consistently outperforms several state-of-the-art approaches.

Lijie Ji, Sabrina Rashid, Yanlai Chen et al.

Traditional projection-based reduced-order modeling approximates the full-order model by projecting it onto a linear subspace. With a fast-decaying Kolmogorov $n$-width of the solution manifold, the resulting reduced-order model (ROM) can be an efficient and accurate emulator. However, for parametric partial differential equations with slowly decaying Kolmogorov $n$-width, the dimension of the linear subspace required for a reasonable accuracy becomes very large, which undermines computational efficiency. To address this limitation, quadratic manifold methods have recently been proposed. These data-driven methods first identify a quadratic mapping by minimizing the linear projection error over a large set of snapshots, often with the aid of regularization techniques to solve the associated minimization problem, and then use this mapping to construct ROMs. In this paper, we propose and test a novel enhancement to this quadratic manifold approach by introducing a first-of-its-kind double-greedy algorithm on the regularization parameters coupled with a standard greedy algorithm on the physical parameter. Our approach balances the trade-off between the accuracy of the quadratic mapping and the stability of the resulting nonlinear ROM, leading to a highly efficient and data-sparse algorithm. Numerical experiments conducted on equations such as linear transport, acoustic wave, advection-diffusion, and Burgers' demonstrate the accuracy, efficiency, and stability of the proposed algorithm.

Jie Chen, Yuanbiao Gou, Chuanbin Liu et al.

The high-dimensional features extracted from large-scale unlabeled data via various pretrained models with diverse architectures are referred to as heterogeneous multiview data. Most existing unsupervised transfer learning methods fail to faithfully recover intrinsic subspace structures when exploiting complementary information across multiple views. Therefore, a fundamental challenge involves constructing sparse similarity graphs that preserve these underlying subspace structures for achieving semantic alignment across heterogeneous views. In this paper, we propose a sparse attention graph learning (SAGL) method that learns subspace-preserving sparse attention graphs from heterogeneous multiview data. Specifically, we introduce a bilinear attention factorization scheme to capture asymmetric similarities among the high-dimensional features, which breaks the symmetry bottleneck that is inherent in the traditional representation learning techniques. A dynamic sparsity gating mechanism then predicts a feature-specific compression factor for adaptively controlling the topological contributions of neighbors. Furthermore, we employ a structured sparse projection via $α$-entmax to generate subspace-preserving sparse attention graphs for individual views. SAGL leverages these view-specific graphs to conduct sparse information aggregation, yielding discriminative representations for multiview learning tasks. In addition, we provide a rigorous theoretical analysis that bridges differentiable sparse attention and probability simplex constraints. Extensive experiments conducted on multiple benchmark datasets demonstrate that SAGL consistently outperforms the state-of-the-art unsupervised transfer learning approaches.

Homaira Huda Shomee, Zhu Wang, Sathya N. Ravi et al.

Recent advances in Pretrained Language Models (PLMs) and Large Language Models (LLMs) have demonstrated transformative capabilities across diverse domains. The field of patent analysis and innovation is not an exception, where natural language processing (NLP) techniques presents opportunities to streamline and enhance important tasks -- such as patent classification and patent retrieval -- in the patent cycle. This not only accelerates the efficiency of patent researchers and applicants, but also opens new avenues for technological innovation and discovery. Our survey provides a comprehensive summary of recent NLP-based methods -- including multimodal ones -- in patent analysis. We also introduce a novel taxonomy for categorization based on tasks in the patent life cycle, as well as the specifics of the methods. This interdisciplinary survey aims to serve as a comprehensive resource for researchers and practitioners who work at the intersection of NLP, Multimodal AI, and patent analysis, as well as patent offices to build efficient patent systems.

Zijin Hong, Hao Wu, Su Dong et al.

Recent studies have raised significant concerns regarding the reliability of current mathematics benchmarks, highlighting issues such as simplistic design and potential data contamination. Consequently, developing a reliable benchmark that effectively evaluates large language models' (LLMs) genuine capabilities in mathematical reasoning remains a critical challenge. To address these concerns, we propose RV-Bench, a novel evaluation methodology for Benchmarking LLMs with Random Variables in mathematical reasoning. Specifically, we build question-generating functions to produce random variable questions (RVQs), whose background content mirrors original benchmark problems, but with randomized variable combinations, rendering them "unseen" to LLMs. Models must completely understand the inherent question pattern to correctly answer RVQs with diverse variable combinations. Thus, an LLM's genuine reasoning capability is reflected through its accuracy and robustness on RV-Bench. We conducted extensive experiments on over 30 representative LLMs across more than 1,000 RVQs. Our findings propose that LLMs exhibit a proficiency imbalance between encountered and ``unseen'' data distributions. Furthermore, RV-Bench reveals that proficiency generalization across similar mathematical reasoning tasks is limited, but we verified it can still be effectively elicited through test-time scaling.

Wenxian Wang, Xiaohu Luo, Junfeng Hao et al.

Sarcasm is a rhetorical device that expresses criticism or emphasizes characteristics of certain individuals or situations through exaggeration, irony, or comparison. Existing methods for Chinese sarcasm detection are constrained by limited datasets and high construction costs, and they mainly focus on textual features, overlooking user-specific linguistic patterns that shape how opinions and emotions are expressed. This paper proposes a Generative Adversarial Network (GAN) and Large Language Model (LLM)-driven data augmentation framework to dynamically model users' linguistic patterns for enhanced Chinese sarcasm detection. First, we collect raw data from various topics on Sina Weibo. Then, we train a GAN on these data and apply a GPT-3.5 based data augmentation technique to synthesize an extended sarcastic comment dataset, named SinaSarc. This dataset contains target comments, contextual information, and user historical behavior. Finally, we extend the BERT architecture to incorporate multi-dimensional information, particularly user historical behavior, enabling the model to capture dynamic linguistic patterns and uncover implicit sarcastic cues in comments. Experimental results demonstrate the effectiveness of our proposed method. Specifically, our model achieves the highest F1-scores on both the non-sarcastic and sarcastic categories, with values of 0.9138 and 0.9151 respectively, which outperforms all existing state-of-the-art (SOTA) approaches. This study presents a novel framework for dynamically modeling users' long-term linguistic patterns in Chinese sarcasm detection, contributing to both dataset construction and methodological advancement in this field.

Zhongbo Wang, Zhiyu Lin, Zhu Wang et al.

Large Language Model-driven (LLM-driven) social bots pose a growing threat to online discourse by generating human-like content that evades conventional detection. Existing methods suffer from limited detection accuracy due to overreliance on single-modality signals, insufficient sensitivity to the specific generative patterns of Artificial Intelligence-Generated Content (AIGC), and a failure to adequately model the interplay between linguistic patterns and behavioral dynamics. To address these limitations, we propose TRACE-Bot, a unified dual-channel framework that jointly models implicit semantic representations and AIGC-enhanced behavioral patterns. TRACE-Bot constructs fine-grained representations from heterogeneous sources, including personal information data, interaction behavior data and tweet data. A dual-channel architecture captures linguistic representations via a pretrained language model and behavioral irregularities via multidimensional activity features augmented with signals from state-of-the-art (SOTA) AIGC detectors. The fused representations are then classified through a lightweight prediction head. Experiments on two public LLM-driven social bot datasets demonstrate SOTA performance, achieving accuracies of 98.46% and 97.50%, respectively. The results further indicate strong robustness against advanced bot strategies, highlighting the effectiveness of jointly leveraging implicit semantic representations and AIGC-enhanced behavioral patterns for emerging LLM-driven social bot detection.

Zhu Wang, Homaira Huda Shomee, Sathya N. Ravi et al.

In the field of design patent analysis, traditional tasks such as patent classification and patent image retrieval heavily depend on the image data. However, patent images -- typically consisting of sketches with abstract and structural elements of an invention -- often fall short in conveying comprehensive visual context and semantic information. This inadequacy can lead to ambiguities in evaluation during prior art searches. Recent advancements in vision-language models, such as CLIP, offer promising opportunities for more reliable and accurate AI-driven patent analysis. In this work, we leverage CLIP models to develop a unified framework DesignCLIP for design patent applications with a large-scale dataset of U.S. design patents. To address the unique characteristics of patent data, DesignCLIP incorporates class-aware classification and contrastive learning, utilizing generated detailed captions for patent images and multi-views image learning. We validate the effectiveness of DesignCLIP across various downstream tasks, including patent classification and patent retrieval. Additionally, we explore multimodal patent retrieval, which provides the potential to enhance creativity and innovation in design by offering more diverse sources of inspiration. Our experiments show that DesignCLIP consistently outperforms baseline and SOTA models in the patent domain on all tasks. Our findings underscore the promise of multimodal approaches in advancing patent analysis. The codebase is available here: https://anonymous.4open.science/r/PATENTCLIP-4661/README.md.

George R. Nahass, Zhu Wang, Homa Rashidisabet et al.

Machine unlearning aims to remove the influence of specific training samples from a trained model without full retraining. While prior work has largely focused on privacy-motivated settings, we recast unlearning as a general-purpose tool for post-deployment model revision. Specifically, we focus on utilizing unlearning in clinical contexts where data shifts, device deprecation, and policy changes are common. To this end, we propose a bilevel optimization formulation of boundary-based unlearning that can be solved using iterative algorithms. We provide convergence guarantees when first-order algorithms are used to unlearn. Our method introduces tunable loss design for controlling the forgetting-retention tradeoff and supports novel model composition strategies that merge the strengths of distinct unlearning runs. Across benchmark and real-world clinical imaging datasets, our approach outperforms baselines on both forgetting and retention metrics, including scenarios involving imaging devices and anatomical outliers. This work establishes machine unlearning as a modular, practical alternative to retraining for real-world model maintenance in clinical applications.

Jie Chen, Hua Mao, Chuanbin Liu et al.

Leveraging the diversity and quantity of data provided by various graph-structured data augmentations while preserving intrinsic semantic information is challenging. Additionally, successive layers in graph neural network (GNN) tend to produce more similar node embeddings, while graph contrastive learning aims to increase the dissimilarity between negative pairs of node embeddings. This inevitably results in a conflict between the message-passing mechanism (MPM) of GNNs and the contrastive learning (CL) of negative pairs via intraviews. In this paper, we propose a conditional distribution learning (CDL) method that learns graph representations from graph-structured data for semisupervised graph classification. Specifically, we present an end-to-end graph representation learning model to align the conditional distributions of weakly and strongly augmented features over the original features. This alignment enables the CDL model to effectively preserve intrinsic semantic information when both weak and strong augmentations are applied to graph-structured data. To avoid the conflict between the MPM and the CL of negative pairs, positive pairs of node representations are retained for measuring the similarity between the original features and the corresponding weakly augmented features. Extensive experiments with several benchmark graph datasets demonstrate the effectiveness of the proposed CDL method.

Zhu Wang, Honglong Chen, Zhe Li et al.

Sparsity of user-to-item rating data becomes one of challenging issues in the recommender systems, which severely deteriorates the recommendation performance. Fortunately, context-aware recommender systems can alleviate the sparsity problem by making use of some auxiliary information, such as the information of both the users and items. In particular, the visual information of items, such as the movie poster, can be considered as the supplement for item description documents, which helps to obtain more item features. In this paper, we focus on movie recommender system and propose a probabilistic matrix factorization based recommendation scheme called visual recurrent convolutional matrix factorization (VRConvMF), which utilizes the textual and multi-level visual features extracted from the descriptive texts and posters respectively. We implement the proposed VRConvMF and conduct extensive experiments on three commonly used real world datasets to validate its effectiveness. The experimental results illustrate that the proposed VRConvMF outperforms the existing schemes.

Honglong Chen, Zhe Li, Zhu Wang et al.

The rapid growth of edge data generated by mobile devices and applications deployed at the edge of the network has exacerbated the problem of information overload. As an effective way to alleviate information overload, recommender system can improve the quality of various services by adding application data generated by users on edge devices, such as visual and textual information, on the basis of sparse rating data. The visual information in the movie trailer is a significant part of the movie recommender system. However, due to the complexity of visual information extraction, data sparsity cannot be remarkably alleviated by merely using the rough visual features to improve the rating prediction accuracy. Fortunately, the convolutional neural network can be used to extract the visual features precisely. Therefore, the end-to-end neural image caption (NIC) model can be utilized to obtain the textual information describing the visual features of movie trailers. This paper proposes a trailer inception probabilistic matrix factorization model called Ti-PMF, which combines NIC, recurrent convolutional neural network, and probabilistic matrix factorization models as the rating prediction model. We implement the proposed Ti-PMF model with extensive experiments on three real-world datasets to validate its effectiveness. The experimental results illustrate that the proposed Ti-PMF outperforms the existing ones.

Yuankai Teng, Zhu Wang, Lili Ju et al.

Due to the curse of dimensionality and the limitation on training data, approximating high-dimensional functions is a very challenging task even for powerful deep neural networks. Inspired by the Nonlinear Level set Learning (NLL) method that uses the reversible residual network (RevNet), in this paper we propose a new method of Dimension Reduction via Learning Level Sets (DRiLLS) for function approximation. Our method contains two major components: one is the pseudo-reversible neural network (PRNN) module that effectively transforms high-dimensional input variables to low-dimensional active variables, and the other is the synthesized regression module for approximating function values based on the transformed data in the low-dimensional space. The PRNN not only relaxes the invertibility constraint of the nonlinear transformation present in the NLL method due to the use of RevNet, but also adaptively weights the influence of each sample and controls the sensitivity of the function to the learned active variables. The synthesized regression uses Euclidean distance in the input space to select neighboring samples, whose projections on the space of active variables are used to perform local least-squares polynomial fitting. This helps to resolve numerical oscillation issues present in traditional local and global regressions. Extensive experimental results demonstrate that our DRiLLS method outperforms both the NLL and Active Subspace methods, especially when the target function possesses critical points in the interior of its input domain.

Anthony Gruber, Max Gunzburger, Lili Ju et al.

The popularity of deep convolutional autoencoders (CAEs) has engendered new and effective reduced-order models (ROMs) for the simulation of large-scale dynamical systems. Despite this, it is still unknown whether deep CAEs provide superior performance over established linear techniques or other network-based methods in all modeling scenarios. To elucidate this, the effect of autoencoder architecture on its associated ROM is studied through the comparison of deep CAEs against two alternatives: a simple fully connected autoencoder, and a novel graph convolutional autoencoder. Through benchmark experiments, it is shown that the superior autoencoder architecture for a given ROM application is highly dependent on the size of the latent space and the structure of the snapshot data, with the proposed architecture demonstrating benefits on data with irregular connectivity when the latent space is sufficiently large.

Yuankai Teng, Xiaoping Zhang, Zhu Wang et al.

Partial differential equations are often used to model various physical phenomena, such as heat diffusion, wave propagation, fluid dynamics, elasticity, electrodynamics and image processing, and many analytic approaches or traditional numerical methods have been developed and widely used for their solutions. Inspired by rapidly growing impact of deep learning on scientific and engineering research, in this paper we propose a novel neural network, GF-Net, for learning the Green's functions of linear reaction-diffusion equations in an unsupervised fashion. The proposed method overcomes the challenges for finding the Green's functions of the equations on arbitrary domains by utilizing physics-informed approach and the symmetry of the Green's function. As a consequence, it particularly leads to an efficient way for solving the target equations under different boundary conditions and sources. We also demonstrate the effectiveness of the proposed approach by experiments in square, annular and L-shape domains.

Anthony Gruber, Max Gunzburger, Lili Ju et al.

A dimension reduction method based on the "Nonlinear Level set Learning" (NLL) approach is presented for the pointwise prediction of functions which have been sparsely sampled. Leveraging geometric information provided by the Implicit Function Theorem, the proposed algorithm effectively reduces the input dimension to the theoretical lower bound with minor accuracy loss, providing a one-dimensional representation of the function which can be used for regression and sensitivity analysis. Experiments and applications are presented which compare this modified NLL with the original NLL and the Active Subspaces (AS) method. While accommodating sparse input data, the proposed algorithm is shown to train quickly and provide a much more accurate and informative reduction than either AS or the original NLL on two example functions with high-dimensional domains, as well as two state-dependent quantities depending on the solutions to parametric differential equations.

Zhu Wang, Anat Lubetzky, Charles Hendee et al.

We developed a novel assessment platform with untethered virtual reality, 3-dimensional sounds, and pressure sensing floor mat to help assess the walking balance and negotiation of obstacles given diverse sensory load and/or cognitive load. The platform provides an immersive 3D city-like scene with anticipated/unanticipated virtual obstacles. Participants negotiate the obstacles with perturbations of: auditory load by spatial audio, cognitive load by a memory task, and visual flow by generated by avatars movements at various amounts and speeds. A VR headset displays the scenes while providing real-time position and orientation of the participant's head. A pressure-sensing walkway senses foot pressure and visualizes it in a heatmap. The system helps to assess walking balance via pressure dynamics per foot, success rate of crossing obstacles, available response time as well as head kinematics in response to obstacles and multitasking. Based on the assessment, specific balance training and fall prevention program can be prescribed.

Zhu Wang

Penalized estimation can conduct variable selection and parameter estimation simultaneously. The general framework is to minimize a loss function subject to a penalty designed to generate sparse variable selection. The majorization-minimization (MM) algorithm is a computational scheme for stability and simplicity, and the MM algorithm has been widely applied in penalized estimation. Much of the previous work have focused on convex loss functions such as generalized linear models. When data are contaminated with outliers, robust loss functions can generate more reliable estimates. Recent literature has witnessed a growing impact of nonconvex loss-based methods, which can generate robust estimation for data contaminated with outliers. This article investigates MM algorithm for penalized estimation, provide innovative optimality conditions and establish convergence theory with both convex and nonconvex loss functions. With respect to applications, we focus on several nonconvex loss functions, which were formerly studied in machine learning for regression and classification problems. Performance of the proposed algorithms are evaluated on simulated and real data including healthcare costs and cancer clinical status. Efficient implementations of the algorithms are available in the R package mpath in CRAN.

Zhu Wang, Anat Lubetzky, Marta Gospodarek et al.

We developed a novel virtual reality [VR] platform with 3-dimensional sounds to help improve sensory integration and visuomotor processing for postural control and fall prevention in individuals with balance problems related to sensory deficits, such as vestibular dysfunction (disease of the inner ear). The system has scenes that simulate scenario-based environments. We can adjust the intensity of the visual and audio stimuli in the virtual scenes by controlling the user interface (UI) settings. A VR headset (HTC Vive or Oculus Rift) delivers stereo display while providing real-time position and orientation of the participants' head. The 3D game-like scenes make participants feel immersed and gradually exposes them to situations that may induce dizziness, anxiety or imbalance in their daily-living.

Zhu Wang, Bin Guo, Zhiwen Yu et al.

Human behavior recognition has been considered as a core technology that can facilitate variety of applications. However, accurate detection and recognition of human behavior is still a big challenge that attracts a lot of research efforts. Recent advances in the wireless technology (e.g., Wi-Fi Channel State Information, i.e., CSI) enable a new behavior recognition paradigm, which is able to recognize behaviors in a device-free and non-intrusive manner. In this article, we first provide an overview of the basics of Wi-Fi CSI based behavior recognition. Afterwards, we classify related applications into three-granularity: signals, actions and activities, and then provide some insights for designing new schemes. Finally, we conclude by discussing the challenges, possible solutions to these challenges and some open issues involved in CSI based behavior recognition.

Max Gunzburger, Nan Jiang, Zhu Wang

We consider settings for which one needs to perform multiple flow simulations based on the Navier-Stokes equations, each having different values for the physical parameters and/or different initial condition data, boundary conditions data, and/or forcing functions. For such settings, we propose a second-order time accurate ensemble-based method that to simulate the whole set of solutions, requires, at each time step, the solution of only a single linear system with multiple right-hand-side vectors. Rigorous analyses are given proving the conditional stability and error estimates for the proposed algorithm. Numerical experiments are provided that illustrate the analyses.

Max Gunzburger, Nan Jiang, Zhu Wang

Many applications of computational fluid dynamics require multiple simulations of a flow under different input conditions. In this paper, a numerical algorithm is developed to efficiently determine a set of such simulations in which the individually independent members of the set are subject to different viscosity coefficients, initial conditions, and/or body forces. The proposed scheme applied to the flow ensemble leads to need to solve a single linear system with multiple right-hand sides, and thus is computationally more efficient than solving for all the simulations separately. We show that the scheme is nonlinearly and long-term stable under certain conditions on the time-step size and a parameter deviation ratio. Rigorous numerical error estimate shows the scheme is of first-order accuracy in time and optimally accurate in space. Several numerical experiments are presented to illustrate the theoretical results.

Tong Xin, Bin Guo, Zhu Wang et al.

Human identification plays an important role in human-computer interaction. There have been numerous methods proposed for human identification (e.g., face recognition, gait recognition, fingerprint identification, etc.). While these methods could be very useful under different conditions, they also suffer from certain shortcomings (e.g., user privacy, sensing coverage range). In this paper, we propose a novel approach for human identification, which leverages WIFI signals to enable non-intrusive human identification in domestic environments. It is based on the observation that each person has specific influence patterns to the surrounding WIFI signal while moving indoors, regarding their body shape characteristics and motion patterns. The influence can be captured by the Channel State Information (CSI) time series of WIFI. Specifically, a combination of Principal Component Analysis (PCA), Discrete Wavelet Transform (DWT) and Dynamic Time Warping (DTW) techniques is used for CSI waveform-based human identification. We implemented the system in a 6m*5m smart home environment and recruited 9 users for data collection and evaluation. Experimental results indicate that the identification accuracy is about 88.9% to 94.5% when the candidate user set changes from 6 to 2, showing that the proposed human identification method is effective in domestic environments.

Yuezheng Gong, Qi Wang, Zhu Wang

The proper orthogonal decomposition reduced-order models (POD-ROMs) have been widely used as a computationally efficient surrogate models in large-scale numerical simulations of complex systems. However, when it is applied to a Hamiltonian system, a naive application of the POD method can destroy its Hamiltonian structure in the reduced-order model. In this paper, we develop a new reduce-order modeling approach for the Hamiltonian system, which uses the traditional framework of Galerkin projection-based model reduction but modifies the ROM so that the appropriate Hamiltonian structure is preserved. Since the POD truncation can degrade the approximation of the Hamiltonian function, we propose to use the POD basis from shifted snapshots to improve the Hamiltonian function approximation. We further derive a rigorous a priori error estimate of the structure-preserving ROM and demonstrate its effectiveness in several numerical examples. This approach can be readily extended to dissipative Hamiltonian systems, port-Hamiltonian systems etc.