arXiv subjects

Chun Liu

Publications and source records attributed to Chun Liu.

At least 37 records · Page 2Linked to original sources

arXiv2025

Unified Learning of the Profile Function in Discrete Keller-Segel Models

We propose a unified learning framework for identifying the profile function in discrete Keller-Segel equations, which are widely used mathematical models for understanding chemotaxis. Training data are obtained via either a rigorously developed particle method designed for stable simulation of high-dimensional Keller-Segel systems, or stochastic differential equations approximating the continuous Keller-Segel PDE. Our approach addresses key challenges, including data instability in dimensions higher than two and the accurate capture of singular behavior in the profile function. Additionally, we introduce an adaptive learning strategy to enhance performance. Extensive numerical experiments are presented to validate the effectiveness of our method.

math.NA↗

arXiv2025

Generating Transferrable Adversarial Examples via Local Mixing and Logits Optimization for Remote Sensing Object Recognition

Deep Neural Networks (DNNs) are vulnerable to adversarial attacks, posing significant security threats to their deployment in remote sensing applications. Research on adversarial attacks not only reveals model vulnerabilities but also provides critical insights for enhancing robustness. Although current mixing-based strategies have been proposed to increase the transferability of adversarial examples, they either perform global blending or directly exchange a region in the images, which may destroy global semantic features and mislead the optimization of adversarial examples. Furthermore, their reliance on cross-entropy loss for perturbation optimization leads to gradient diminishing during iterative updates, compromising adversarial example quality. To address these limitations, we focus on non-targeted attacks and propose a novel framework via local mixing and logits optimization. First, we present a local mixing strategy to generate diverse yet semantically consistent inputs. Different from MixUp, which globally blends two images, and MixCut, which stitches images together, our method merely blends local regions to preserve global semantic information. Second, we adapt the logit loss from targeted attacks to non-targeted scenarios, mitigating the gradient vanishing problem of cross-entropy loss. Third, a perturbation smoothing loss is applied to suppress high-frequency noise and enhance transferability. Extensive experiments on FGSCR-42 and MTARSI datasets demonstrate superior performance over 12 state-of-the-art methods across 6 surrogate models. Notably, with ResNet as the surrogate on MTARSI, our method achieves a 17.28% average improvement in black-box attack success rate.

cs.CV↗

arXiv2025

Adversarial Patch Attack for Ship Detection via Localized Augmentation

Current ship detection techniques based on remote sensing imagery primarily rely on the object detection capabilities of deep neural networks (DNNs). However, DNNs are vulnerable to adversarial patch attacks, which can lead to misclassification by the detection model or complete evasion of the targets. Numerous studies have demonstrated that data transformation-based methods can improve the transferability of adversarial examples. However, excessive augmentation of image backgrounds or irrelevant regions may introduce unnecessary interference, resulting in false detections of the object detection model. These errors are not caused by the adversarial patches themselves but rather by the over-augmentation of background and non-target areas. This paper proposes a localized augmentation method that applies augmentation only to the target regions, avoiding any influence on non-target areas. By reducing background interference, this approach enables the loss function to focus more directly on the impact of the adversarial patch on the detection model, thereby improving the attack success rate. Experiments conducted on the HRSC2016 dataset demonstrate that the proposed method effectively increases the success rate of adversarial patch attacks and enhances their transferability.

cs.CV↗

arXiv2025

Few-shot Unknown Class Discovery of Hyperspectral Images with Prototype Learning and Clustering

Open-set few-shot hyperspectral image (HSI) classification aims to classify image pixels by using few labeled pixels per class, where the pixels to be classified may be not all from the classes that have been seen. To address the open-set HSI classification challenge, current methods focus mainly on distinguishing the unknown class samples from the known class samples and rejecting them to increase the accuracy of identifying known class samples. They fails to further identify or discovery the unknow classes among the samples. This paper proposes a prototype learning and clustering method for discoverying unknown classes in HSIs under the few-shot environment. Using few labeled samples, it strives to develop the ability of infering the prototypes of unknown classes while distinguishing unknown classes from known classes. Once the unknown class samples are rejected by the learned known class classifier, the proposed method can further cluster the unknown class samples into different classes according to their distance to the inferred unknown class prototypes. Compared to existing state-of-the-art methods, extensive experiments on four benchmark HSI datasets demonstrate that our proposed method exhibits competitive performance in open-set few-shot HSI classification tasks. All the codes are available at \href{https://github.com/KOBEN-ff/OpenFUCD-main} {https://github.com/KOBEN-ff/OpenFUCD-main}

cs.CV↗

arXiv2025

Boosting Adversarial Transferability for Hyperspectral Image Classification Using 3D Structure-invariant Transformation and Weighted Intermediate Feature Divergence

Deep Neural Networks (DNNs) are vulnerable to adversarial attacks, which pose security challenges to hyperspectral image (HSI) classification based on DNNs. Numerous adversarial attack methods have been designed in the domain of natural images. However, different from natural images, HSIs contains high-dimensional rich spectral information, which presents new challenges for generating adversarial examples. Based on the specific characteristics of HSIs, this paper proposes a novel method to enhance the transferability of the adversarial examples for HSI classification using 3D structure-invariant transformation and weighted intermediate feature divergence. While keeping the HSIs structure invariant, the proposed method divides the image into blocks in both spatial and spectral dimensions. Then, various transformations are applied on each block to increase input diversity and mitigate the overfitting to substitute models. Moreover, a weighted intermediate feature divergence loss is also designed by leveraging the differences between the intermediate features of original and adversarial examples. It constrains the perturbation direction by enlarging the feature maps of the original examples, and assigns different weights to different feature channels to destroy the features that have a greater impact on HSI classification. Extensive experiments demonstrate that the adversarial examples generated by the proposed method achieve more effective adversarial transferability on three public HSI datasets. Furthermore, the method maintains robust attack performance even under defense strategies.

cs.CV↗

arXiv2025

On a Continuum Model for Random Genetic Drift: A Dynamic Boundary Condition Approach

We propose a new continuum model for random genetic drift by employing a dynamic boundary condition approach. The model can be viewed as a regularized version of the Kimura equation and admits a continuous solution. We establish the existence and uniqueness of a strong solution to the regularized system. Numerical experiments illustrate that, for sufficiently small regularization parameters, the model can capture key phenomena of the original Kimura equation, such as gene fixation and conservation of the first moment.

math.AP↗

arXiv2025

Non-isothermal diffuse interface model for phase transition and interface evolution

In this paper, we derive a thermodynamically consistent non-isothermal diffuse interface model for phase transition and interface evolution involving heat transfer. This model is constructed by integrating concepts from classical irreversible thermodynamics with the energetic variational approach. By making specific assumptions about the kinematics of the temperature, we derive a non-isothermal Allen-Cahn equation. Through both asymptotic analysis and numerical simulations, we demonstrate that in the sharp interface limit, the non-isothermal Allen-Cahn equation converges to a two-phase nonlinear Stefan type problem, under a certain scale of the melting/freezing energy. In this regime, the motion of the liquid-solid interface and the temperature interface coincide and are governed by the mean curvature, at least for a short time. The result provides a justification for the classical Stefan problem within a certain physical regime.

math.AP↗

arXiv2025

A deterministic-particle-based scheme for micro-macro viscoelastic flows

In this article, we introduce a new method for discretizing micro-macro models of dilute polymeric fluids by integrating a finite element discretization for the macroscopic fluid dynamic equation with a deterministic variational particle scheme for the microscopic Fokker-Planck equation. To address challenges arising from micro-macro coupling, we employ a discrete energetic variational approach to derive a coarse-grained micro-macro model with a particle approximation first and then develop a particle-FEM discretization for the coarse-grained model. The accuracy of the proposed method is evaluated for a Hookean dumbbell model in a Couette flow by comparing the computed velocity field with existing analytical solutions. We also use our method to study nonlinear FENE dumbbell models in different scenarios, such as extension flow, pure shear flow, and lid-driven cavity flow. Numerical examples demonstrate that the proposed deterministic particle approach can accurately capture the various key rheological phenomena in the original FENE model, including hysteresis and δ-function-like spike behavior in extension flows, velocity overshoot phenomenon in pure shear flow, symmetries breaking, vortex center shifting and vortices weakening in the lid-driven cavity flow, with a small number of particles.

math.NA↗

arXiv2025

Active Learning for Manifold Gaussian Process Regression

This paper introduces an active learning framework for manifold Gaussian Process (GP) regression, combining manifold learning with strategic data selection to improve accuracy in high-dimensional spaces. Our method jointly optimizes a neural network for dimensionality reduction and a Gaussian process regressor in the latent space, supervised by an active learning criterion that minimizes global prediction error. Experiments on synthetic data demonstrate superior performance over randomly sequential learning. The framework efficiently handles complex, discontinuous functions while preserving computational tractability, offering practical value for scientific and engineering applications. Future work will focus on scalability and uncertainty-aware manifold learning.

stat.ML↗

arXiv2025

Factorization method for near-field inverse scattering problems in elastodynamics

Consider a time-harmonic elastic point source incident on a bounded obstacle which is embedded in an open space filled with a homogeneous and isotropic elastic medium. This paper is concerned with the inverse problem of recovering the location and shape of the obstacle from near-field data generated by infinitely many incident point source waves at a fixed energy. The incident point sources and the receivers for recording scattered signals are both located on a spherical closed surface, on which an outgoing-to-incoming operator is defined for facilitating the factorization of the near-field operator. Numerical examples in 2D are presented to show the validity and accuracy of the inversion algorithm.

math.AP↗

arXiv2025

On a Modified Random Genetic Drift Model: Derivation and a Structure-Preserving Operator-Splitting Discretization

One of the fundamental mathematical models for studying random genetic drift is the Kimura equation, derived as the large-population limit of the discrete Wright-Fisher model. However, due to the degeneracy of the diffusion coefficient, it is impossible to impose a suitable boundary condition that ensures the Kimura equation admits a classical solution while preserving biological significance. In this work, we propose a modified model for random genetic drift that admits classical solutions by modifying the domain of the Kimura equation from $(0, 1)$ to $(δ, 1 - δ)$ with $δ$ being a small parameter, which allows us to impose a Robin-type boundary condition. By introducing two additional variables for the probabilities in the boundary region, we effectively capture the conservation of mass and the fixation dynamics in the original model. To numerically investigate the modified model, we develop a hybrid Eulerian-Lagrangian operator splitting scheme. The scheme first solves the flow map equation in the bulk region using a Lagrangian approach with a no-flux boundary condition, followed by handling the boundary dynamics in Eulerian coordinates. This hybrid scheme ensures mass conservation, maintains positivity, and preserves the first moment. Various numerical tests demonstrate the efficiency, accuracy, and structure-preserving properties of the proposed scheme. Numerical results demonstrate the key qualitative features of the original Kimura equation, including the fixation behavior and the correct stationary distribution in the small-$δ$ limit.

math.NA↗

arXiv2025

On pattern formation in the thermodynamically-consistent variational Gray-Scott model

In this paper, we explore pattern formation in a four-species variational Gary-Scott model, which includes all reverse reactions and introduces a virtual species to describe the birth-death process in the classical Gray-Scott model. This modification transforms the classical Gray-Scott model into a thermodynamically consistent closed system. The classical two-species Gray-Scott model can be viewed as a subsystem of the variational model in the limiting case when the small parameter $ε$, related to the reaction rate of the reverse reactions, approaches zero. We numerically explore pattern formation in this physically more complete Gray-Scott model in one spatial dimension, using non-uniform steady states of the classical model as initial conditions. By decreasing $ε$, we observed that the stationary pattern in the classical Gray-Scott model can be stabilized as the transient state in the variational model for a significantly small $ε$. Additionally, the variational model admits oscillating and traveling-wave-like patterns for small $ε$. The persistent time of these patterns is on the order of $O(ε^{-1})$. We also analyze the energy stability of two uniform steady states in the variational Gary-Scott model for fixed $ε$. Although both states are stable in a certain sense, the gradient flow type dynamics of the variational model exhibit a selection effect based on the initial conditions, with pattern formation occurring only if the initial condition does not converge to the boundary steady state, which corresponds to the trivial uniform steady state in the classical Gray-Scott model.

math.NA↗

arXiv2025

Data-Driven Modeling of Amyloid-beta Targeted Antibodies for Alzheimer's Disease

Alzheimer's disease (AD) is driven by the accumulation of amyloid-beta (Abeta) proteins in the brain, leading to memory loss and cognitive decline. While monoclonal antibodies targeting Abetahave been approved, optimizing their use to maximize benefits while minimizing side effects remains a challenge. This study develops a mathematical model to describe Abeta aggregation, capturing its progression from monomers to toxic oligomers, protofibrils, and fibrils using mass-action kinetics and coarse-grained modeling. The model is calibrated with experimental data, incorporating parameter estimation and sensitivity analysis to ensure accuracy. An optimal control framework is introduced to determine the best drug dosing strategy that reduces toxic Abeta aggregates while minimizing adverse effects, such as amyloid-related imaging abnormalities (ARIA). Results indicate that Donanemab achieves the greatest reduction in fibrils. This work provides a quantitative framework for optimizing AD treatment strategies, offering insights into balancing therapeutic efficacy and safety.

q-bio.QM↗

arXiv2025

Long-time asymptotic behavior of nonlinear Fokker-Planck type equations with periodic boundary conditions

In this paper, we study the asymptotic behavior of a class of nonlinear Fokker-Planck type equations in a bounded domain with periodic boundary conditions. The system is motivated by our study of grain boundary dynamics, especially under the non-isothermal environments. To obtain the long time behavior of the solutions, in particular, the exponential decay, the kinematic structures of the systems are investigated using novel reinterpretation of the classical entropy method.

math.AP↗

arXiv2025

BLI: A High-performance Bucket-based Learned Index with Concurrency Support

Learned indexes are promising to replace traditional tree-based indexes. They typically employ machine learning models to efficiently predict target positions in strictly sorted linear arrays. However, the strict sorted order 1) significantly increases insertion overhead, 2) makes it challenging to support lock-free concurrency, and 3) harms in-node lookup/insertion efficiency due to model inaccuracy.\ In this paper, we introduce a \textit{Bucket-based Learned Index (BLI)}, which is an updatable in-memory learned index that adopts a "globally sorted, locally unsorted" approach by replacing linear sorted arrays with \textit{Buckets}. BLI optimizes the insertion throughput by only sorting Buckets, not the key-value pairs within a Bucket. BLI strategically balances three critical performance metrics: tree fanouts, lookup/insert latency for inner nodes, lookup/insert latency for leaf nodes, and memory consumption. To minimize maintenance costs, BLI performs lightweight bulk loading, insert, node scaling, node split, model retraining, and node merging adaptively. BLI supports lock-free concurrency thanks to the unsorted design with Buckets. Our results show that BLI achieves up to 2.21x better throughput than state-of-the-art learned indexes, with up to 3.91x gains under multi-threaded conditions.

cs.DB↗

arXiv2024

LLMEmbed: Rethinking Lightweight LLM's Genuine Function in Text Classification

With the booming of Large Language Models (LLMs), prompt-learning has become a promising method mainly researched in various research areas. Recently, many attempts based on prompt-learning have been made to improve the performance of text classification. However, most of these methods are based on heuristic Chain-of-Thought (CoT), and tend to be more complex but less efficient. In this paper, we rethink the LLM-based text classification methodology, propose a simple and effective transfer learning strategy, namely LLMEmbed, to address this classical but challenging task. To illustrate, we first study how to properly extract and fuse the text embeddings via various lightweight LLMs at different network depths to improve their robustness and discrimination, then adapt such embeddings to train the classifier. We perform extensive experiments on publicly available datasets, and the results show that LLMEmbed achieves strong performance while enjoys low training overhead using lightweight LLM backbones compared to recent methods based on larger LLMs, i.e. GPT-3, and sophisticated prompt-based strategies. Our LLMEmbed achieves adequate accuracy on publicly available benchmarks without any fine-tuning while merely use 4% model parameters, 1.8% electricity consumption and 1.5% runtime compared to its counterparts. Code is available at: https://github.com/ChunLiu-cs/LLMEmbed-ACL2024.

cs.CL↗

arXiv2024

Fast Estimation of Relative Transformation Based on Fusion of Odometry and UWB Ranging Data

In this paper, we investigate the problem of estimating the 4-DOF (three-dimensional position and orientation) robot-robot relative frame transformation using odometers and distance measurements between robots. Firstly, we apply a two-step estimation method based on maximum likelihood estimation. Specifically, a good initial value is obtained through unconstrained least squares and projection, followed by a more accurate estimate achieved through one-step Gauss-Newton iteration. Additionally, the optimal installation positions of Ultra-Wideband (UWB) are provided, and the minimum operating time under different quantities of UWB devices is determined. Simulation demonstrates that the two-step approach offers faster computation with guaranteed accuracy while effectively addressing the relative transformation estimation problem within limited space constraints. Furthermore, this method can be applied to real-time relative transformation estimation when a specific number of UWB devices are installed.

cs.RO↗

arXiv2024

Energetic Variational Neural Network Discretizations of Gradient Flows

We present a structure-preserving Eulerian algorithm for solving $L^2$-gradient flows and a structure-preserving Lagrangian algorithm for solving generalized diffusions. Both algorithms employ neural networks as tools for spatial discretization. Unlike most existing methods that construct numerical discretizations based on the strong or weak form of the underlying PDE, the proposed schemes are constructed based on the energy-dissipation law directly. This guarantees the monotonic decay of the system's free energy, which avoids unphysical states of solutions and is crucial for the long-term stability of numerical computations. To address challenges arising from nonlinear neural network discretization, we perform temporal discretizations on these variational systems before spatial discretizations. This approach is computationally memory-efficient when implementing neural network-based algorithms. The proposed neural network-based schemes are mesh-free, allowing us to solve gradient flows in high dimensions. Various numerical experiments are presented to demonstrate the accuracy and energy stability of the proposed numerical schemes.

math.NA↗