arXiv subjects

Junping Wang

Publications and source records attributed to Junping Wang.

At least 19 recordsLinked to original sources

arXiv2026

Structured interactions improve distributed coordination beyond model scaling in a real-world multi-robot system

Scaling individual robot capabilities is common but costly. Here we investigate a system-level design question in real-world multi-robot coordination: given matched hardware budgets, does restructuring communication among robots yield larger gains than increasing onboard model size? Using a representative transport-and-mapping task with 10 physical robots (5 runs per condition, 60 runs total), we find that switching from fully connected to modular hierarchical interactions improves normalised performance by 47 points (0--100), whereas doubling neural network hidden size yields at most 9 points. Nested mixed-effects model comparisons show a substantially larger improvement in model fit for topology than for scale. The pattern is confirmed in independent SMAC replications; heterogeneous benchmark reanalyses provide secondary supporting consistency checks rather than primary evidence. Performance saturation beyond 1024 hidden units is observed in simulation-calibrated extrapolation, not directly on hardware. These results indicate that interaction structure can play a dominant role within the tested system and task setting, while broader quantitative generalisation remains to be established.

cs.RO↗

arXiv2026

Beyond Taylor: Divergence-Based Functional Expansions and Their Application to Numerical Integration

This paper introduces a new functional expansion framework that extends classical ideas beyond the Taylor series. Unlike traditional Taylor expansions based on local polynomial approximations, the proposed approach arises from exact differential identities that link a function and its derivatives through polynomial weight factors. This formulation expresses smooth functions via divergence-based relations connecting derivatives of all orders with systematically scaled polynomial coefficients. This framework provides a natural foundation for constructing high-order numerical quadrature formulas, particularly for multi-dimensional domains. By exploiting the divergence structure, volume integrals are systematically transformed into boundary integrals using the Divergence Theorem, recursively reducing the integration domain from an $n$-dimensional body to its $(n-1)$-dimensional facets, and ultimately to its vertices. The article further enhances the framework's accuracy by introducing a complex-shift technique. It is demonstrated that by positioning the expansion center at specific roots of unity in the complex plane, lower-order error terms are annihilated, yielding high-order real-valued quadrature rules with minimal function evaluations. Additionally, a rigorous geometric analysis of the affine transformations required for surface integration is provided, deriving explicit formulas for the transformation of normal vectors and surface measures. The proposed method offers a robust, systematic, and computationally efficient alternative to tessellation-based quadrature for arbitrary flat-faced polytopes.

math.NA↗

arXiv2026

A Generalized Weak Galerkin Method for Linear Elasticity with Nonpolynomial Approximations

This paper presents a generalized weak Galerkin (gWG) finite element method for linear elasticity problems on general polygonal and polyhedral meshes. The proposed framework is flexible and efficient, allowing for the use of nonpolynomial approximating functions. The generalized weak differential operators are defined as an element-level correction of the classical differential operators accounting for boundary discontinuities. This construction reduces computational cost and provides greater flexibility than standard weak Galerkin formulations. The gWG framework naturally accommodates arbitrary finite-dimensional approximation spaces, including nonpolynomial activation-based spaces with randomly selected parameters. Error equations and error estimates are established for the proposed method. Numerical experiments demonstrate that the method is locking-free, robust with respect to mesh geometry, and effective on general polygonal and polyhedral partitions. In particular, activation-based interior approximation spaces exhibit convergence behavior comparable to that of classical polynomial spaces.

math.NA↗

arXiv2025

Physics-Informed High-order Graph Dynamics Identification Learning for Predicting Complex Networks Long-term Dynamics

Learning complex network dynamics is fundamental to understanding, modelling and controlling real-world complex systems. There are two main problems in the task of predicting the dynamic evolution of complex networks: on the one hand, existing methods usually use simple graphs to describe the relationships in complex networks; however, this approach can only capture pairwise relationships, while there may be rich non-pairwise structured relationships in the network. First-order GNNs have difficulty in capturing dynamic non-pairwise relationships. On the other hand, theoretical prediction models lack accuracy and data-driven prediction models lack interpretability. To address the above problems, this paper proposes a higher-order network dynamics identification method for long-term dynamic prediction of complex networks. Firstly, to address the problem that traditional graph machine learning can only deal with pairwise relations, dynamic hypergraph learning is introduced to capture the higher-order non-pairwise relations among complex networks and improve the accuracy of complex network modelling. Then, a dual-driven dynamic prediction module for physical data is proposed. The Koopman operator theory is introduced to transform the nonlinear dynamical differential equations for the dynamic evolution of complex networks into linear systems for solving. Meanwhile, the physical information neural differential equation method is utilised to ensure that the dynamic evolution conforms to the physical laws. The dual-drive dynamic prediction module ensures both accuracy and interpretability of the prediction. Validated on public datasets and self-built industrial chain network datasets, the experimental results show that the method in this paper has good prediction accuracy and long-term prediction performance.

cs.AI↗

arXiv2025

Physics-Inspired Spatial Temporal Graph Neural Networks for Predicting Industrial Chain Resilience

Industrial chain plays an increasingly important role in the sustainable development of national economy. However, as a typical complex network, data-driven deep learning is still in its infancy in describing and analyzing the resilience of complex networks, and its core is the lack of a theoretical framework to describe the system dynamics. In this paper, we propose a physically informative neural symbolic approach to describe the evolutionary dynamics of complex networks for resilient prediction. The core idea is to learn the dynamics of the activity state of physical entities and integrate it into the multi-layer spatiotemporal co-evolution network, and use the physical information method to realize the joint learning of physical symbol dynamics and spatiotemporal co-evolution topology, so as to predict the industrial chain resilience. The experimental results show that the model can obtain better results and predict the elasticity of the industry chain more accurately and effectively, which has certain practical significance for the development of the industry.

cs.LG↗

arXiv2025

Industrial brain: a human-like autonomous neuro-symbolic cognitive decision-making system

Resilience non-equilibrium measurement, the ability to maintain fundamental functionality amidst failures and errors, is crucial for scientific management and engineering applications of industrial chain. The problem is particularly challenging when the number or types of multiple co-evolution of resilience (for example, randomly placed) are extremely chaos. Existing end-to-end deep learning ordinarily do not generalize well to unseen full-feld reconstruction of spatiotemporal co-evolution structure, and predict resilience of network topology, especially in multiple chaos data regimes typically seen in real-world applications. To address this challenge, here we propose industrial brain, a human-like autonomous cognitive decision-making and planning framework integrating higher-order activity-driven neuro network and CT-OODA symbolic reasoning to autonomous plan resilience directly from observational data of global variable. The industrial brain not only understands and model structure of node activity dynamics and network co-evolution topology without simplifying assumptions, and reveal the underlying laws hidden behind complex networks, but also enabling accurate resilience prediction, inference, and planning. Experimental results show that industrial brain significantly outperforms resilience prediction and planning methods, with an accurate improvement of up to 10.8\% over GoT and OlaGPT framework and 11.03\% over spectral dimension reduction. It also generalizes to unseen topologies and dynamics and maintains robust performance despite observational disturbances. Our findings suggest that industrial brain addresses an important gap in resilience prediction and planning for industrial chain.

cs.AI↗

arXiv2024

Mutual Information Guided Optimal Transport for Unsupervised Visible-Infrared Person Re-identification

Unsupervised visible infrared person re-identification (USVI-ReID) is a challenging retrieval task that aims to retrieve cross-modality pedestrian images without using any label information. In this task, the large cross-modality variance makes it difficult to generate reliable cross-modality labels, and the lack of annotations also provides additional difficulties for learning modality-invariant features. In this paper, we first deduce an optimization objective for unsupervised VI-ReID based on the mutual information between the model's cross-modality input and output. With equivalent derivation, three learning principles, i.e., "Sharpness" (entropy minimization), "Fairness" (uniform label distribution), and "Fitness" (reliable cross-modality matching) are obtained. Under their guidance, we design a loop iterative training strategy alternating between model training and cross-modality matching. In the matching stage, a uniform prior guided optimal transport assignment ("Fitness", "Fairness") is proposed to select matched visible and infrared prototypes. In the training stage, we utilize this matching information to introduce prototype-based contrastive learning for minimizing the intra- and cross-modality entropy ("Sharpness"). Extensive experimental results on benchmarks demonstrate the effectiveness of our method, e.g., 60.6% and 90.3% of Rank-1 accuracy on SYSU-MM01 and RegDB without any annotations.

cs.CV↗

arXiv2024

A Parallel iterative Algorithm for primal-dual weak Galerkin Schemes

This paper presents and analyzes a parallelizable iterative procedure based on domain decomposition for primal-dual weak Galerkin (PDWG) finite element methods applied to the Poisson equation. The existence and uniqueness of the PDWG solution are established. Optimal order of error estimates are derived in both a discrete norm and the $L^2$ norm. The convergence analysis is conducted for domain decompositions into individual elements associated with the PDWG methods, which can be extended to larger subdomains without any difficulty.

math.NA↗

arXiv2024

EMIE-MAP: Large-Scale Road Surface Reconstruction Based on Explicit Mesh and Implicit Encoding

Road surface reconstruction plays a vital role in autonomous driving systems, enabling road lane perception and high-precision mapping. Recently, neural implicit encoding has achieved remarkable results in scene representation, particularly in the realistic rendering of scene textures. However, it faces challenges in directly representing geometric information for large-scale scenes. To address this, we propose EMIE-MAP, a novel method for large-scale road surface reconstruction based on explicit mesh and implicit encoding. The road geometry is represented using explicit mesh, where each vertex stores implicit encoding representing the color and semantic information. To overcome the difficulty in optimizing road elevation, we introduce a trajectory-based elevation initialization and an elevation residual learning method based on Multi-Layer Perceptron (MLP). Additionally, by employing implicit encoding and multi-camera color MLPs decoding, we achieve separate modeling of scene physical properties and camera characteristics, allowing surround-view reconstruction compatible with different camera models. Our method achieves remarkable road surface reconstruction performance in a variety of real-world challenging scenarios.

cs.CV↗

arXiv2023

Weak Galerkin Finite Element Methods for Optimal Control Problems Governed by Second Order Elliptic Partial Differential Equations

This paper is concerned with the development of weak Galerkin (WG) finite element method for optimal control problems governed by second order elliptic partial differential equations (PDEs). It is advantageous to use discontinuous finite elements over the traditional $C^1$ finite elements here. Optimal order error estimates are established and confirmed by some numerical tests.

math.NA↗

arXiv2023

High Order Morley Elements for Biharmonic Equations on Polytopal Partitions

This paper introduces an extension of the Morley element for approximating solutions to biharmonic equations. Traditionally limited to piecewise quadratic polynomials on triangular elements, the extension leverages weak Galerkin finite element methods to accommodate higher degrees of polynomials and the flexibility of general polytopal elements. By utilizing the Schur complement of the weak Galerkin method, the extension allows for fewest local degrees of freedom while maintaining sufficient accuracy and stability for the numerical solutions. The numerical scheme incorporates locally constructed weak tangential derivatives and weak second order partial derivatives, resulting in an accurate approximation of the biharmonic equation. Optimal order error estimates in both a discrete $H^2$ norm and the usual $L^2$ norm are established to assess the accuracy of the numerical approximation. Additionally, numerical results are presented to validate the developed theory and demonstrate the effectiveness of the proposed extension.

math.NA↗

arXiv2023

Generalized weak Galerkin finite element methods for second order elliptic problems

This article proposes and analyzes the generalized weak Galerkin ({\rm g}WG) finite element method for the second order elliptic problem. A generalized discrete weak gradient operator is introduced in the weak Galerkin framework so that the {\rm g}WG methods would not only allow arbitrary combinations of piecewise polynomials defined in the interior and on the boundary of each local finite element, but also work on general polytopal partitions. Error estimates are established for the corresponding numerical functions in the energy norm and the usual $L^2$ norm. A series of numerical experiments are presented to demonstrate the performance of the newly proposed {\rm g}WG method.

math.NA↗

arXiv2023

Generalized Weak Galerkin Finite Element Methods for Biharmonic Equations

The generalized weak Galerkin (gWG) finite element method is proposed and analyzed for the biharmonic equation. A new generalized discrete weak second order partial derivative is introduced in the gWG scheme to allow arbitrary combinations of piecewise polynomial functions defined in the interior and on the boundary of general polygonal or polyhedral elements. The error estimates are established for the numerical approximation in a discrete H^2 norm and a L^2 norm. The numerical results are reported to demonstrate the accuracy and flexibility of our proposed gWG method for the biharmonic equation.

math.NA↗

arXiv2022

An $L^p$-primal-dual finite element method for first-order transport problems

A new $L^p$-primal-dual weak Galerkin method ($L^p$-PDWG) with $p>1$ is proposed for the first-order transport problems. The existence and uniqueness of the $L^p$-PDWG numerical solutions is established. In addition, the $L^p$-PDWG method offers a numerical solution which retains mass conservation locally on each element. An optimal order error estimate is established for the primal variable. A series of numerical results are presented to verify the efficiency and accuracy of the proposed $L^p$-PDWG scheme.

math.NA↗

arXiv2022

An Extension of the Morley Element on General Polytopal Partitions Using Weak Galerkin Methods

This paper introduces an extension of the well-known Morley element for the biharmonic equation, extending its application from triangular elements to general polytopal elements using the weak Galerkin finite element methods. By leveraging the Schur complement of the weak Galerkin method, this extension not only preserves the same degrees of freedom as the Morley element on triangular elements but also expands its applicability to general polytopal elements. The numerical scheme is devised by locally constructing weak tangential derivatives and weak second-order partial derivatives. Error estimates for the numerical approximation are established in both the energy norm and the $L^2$ norm. A series of numerical experiments are conducted to validate the theoretical developments.

math.NA↗

arXiv2022

Curved Elements in Weak Galerkin Finite Element Methods

A mathematical analysis is established for the weak Galerkin finite element methods for the Poisson equation with Dirichlet boundary value when the curved elements are involved on the interior edges of the finite element partition or/and on the boundary of the whole domain in two dimensions. The optimal orders of error estimates for the weak Galerkin approximations in both the $H^1$-norm and the $L^2$-norm are established. Numerical results are reported to demonstrate the performance of the weak Galerkin methods on general curved polygonal partitions.

math.NA↗

arXiv2022

Weak Galerkin Finite Element Methods for Quad-Curl Problems

This article introduces a weak Galerkin (WG) finite element method for quad-curl problems in three dimensions. It is proved that the proposed WG method is stable and accurate in an optimal order of error estimates for the exact solution in discrete norms. In addition, an $L^2$ error estimate in an optimal order except the lowest orders $k=1, 2$ is derived for the WG solution. Some numerical experiments are conducted to verify the efficiency and accuracy of our WG method and furthermore a superconvergence has been observed from the numerical results.

math.NA↗

arXiv2022

Constrained Maximum Cross-Domain Likelihood for Domain Generalization

As a recent noticeable topic, domain generalization aims to learn a generalizable model on multiple source domains, which is expected to perform well on unseen test domains. Great efforts have been made to learn domain-invariant features by aligning distributions across domains. However, existing works are often designed based on some relaxed conditions which are generally hard to satisfy and fail to realize the desired joint distribution alignment. In this paper, we propose a novel domain generalization method, which originates from an intuitive idea that a domain-invariant classifier can be learned by minimizing the KL-divergence between posterior distributions from different domains. To enhance the generalizability of the learned classifier, we formalize the optimization objective as an expectation computed on the ground-truth marginal distribution. Nevertheless, it also presents two obvious deficiencies, one of which is the side-effect of entropy increase in KL-divergence and the other is the unavailability of ground-truth marginal distributions. For the former, we introduce a term named maximum in-domain likelihood to maintain the discrimination of the learned domain-invariant representation space. For the latter, we approximate the ground-truth marginal distribution with source domains under a reasonable convex hull assumption. Finally, a Constrained Maximum Cross-domain Likelihood (CMCL) optimization problem is deduced, by solving which the joint distributions are naturally aligned. An alternating optimization strategy is carefully designed to approximately solve this optimization problem. Extensive experiments on four standard benchmark datasets, i.e., Digits-DG, PACS, Office-Home and miniDomainNet, highlight the superior performance of our method.

cs.CV↗