arXiv subjects

Yuanfei Huang

Publications and source records attributed to Yuanfei Huang.

At least 19 recordsLinked to original sources

arXiv2026

Geometric Methods for Stochastic Dynamical Systems

Geometric methods are indispensable for analyzing, predicting, and mitigating the complex behaviors inherent in nonlinear systems. In this regime, the most probable transition path minimizes the Onsager-Machlup action functional, marking the likeliest route across an energy barrier. Lifting the analysis from individual sample paths to the infinite-dimensional space of probability densities, the book recasts these transitions as Schrödinger bridges - optimal paths between boundary distributions defined by minimizing relative entropy - and shows that the Onsager-Machlup path emerges as a special case when metastable states are idealized as Dirac masses. Generalizing further through α-divergences, which connect to entropies and the thermodynamic cost of nonequilibrium transitions, it introduces information geodesics as the resulting optimal density paths, offering a unified geometric account of how complex systems move between metastable regimes under uncertainty.

math.DS↗

arXiv2026

A study of path measures based on second-order Hamilton--Jacobi equations and their applications in stochastic thermodynamics

This paper provides a systematic investigation of the mathematical structure of path measures and their profound connections to stochastic differential equations (SDEs) through the framework of second-order Hamilton--Jacobi (HJ) equations. This approach establishes a unified methodology for analyzing large deviation principles (LDPs), entropy minimization, and entropy production in stochastic systems. Second-order HJ equations are shown to play a central role in bridging stochastic dynamics and measure theory while forming the foundation of stochastic geometric mechanics and their applications in stochastic thermodynamics. The large deviation rate function is rigorously derived from the probabilistic structure of path measures and proved to be equivalent to the Onsager--Machlup functional of stochastic gradient systems coupled with second-order HJ equations. We revisit entropy minimization problems, including finite time horizon problems and Schrödinger's problem, demonstrating the connections with stochastic geometric mechanics. Furthermore, we present a novel decomposition of entropy production for stochastic systems, revealing that thermodynamic irreversibility can be interpreted as the difference of the corresponding forward and backward second-order HJ equations. Together, this work establishes a comprehensive mathematical study of the relations between path measures and stochastic dynamical systems, and their diverse applications in stochastic thermodynamics and beyond.

math-ph↗

arXiv2026

Breaking Spatial Uniformity: Prior-Guided Mamba with Radial Serialization for Lens Flare Removal

Lens flares, caused by complex optical aberrations, severely degrade image quality especially in nighttime photography. Although recent restoration methods have made remarkable progress, most still rely on spatially uniform processing. They are failing to handle the region-dependent restoration demands of flare scenes, where saturated light sources should be preserved, flare artifacts removed, and background details recovered. To address this challenge, we propose DeflareMambav2, a prior-guided Mamba framework for lens flare removal. Specifically, we introduce a Flare Prior Network (FPN) to estimate flare priors and guide adaptive restoration. Besides, a novel radial serialization strategy breaks spatially homogeneous processing by performing flare-aware targeted sampling, and better supports long-range modeling in State Space Models (SSMs). Based on these priors, the backbone adopts a dual-level adaptive scheme. It explicitly preserves light-source regions to avoid over-processing, and applies curriculum-based restoration to the remaining contaminated areas while calibrating restoration intensity at the pixel level. Extensive experiments demonstrate that DeflareMambav2 achieves state-of-the-art performance with reduced parameter burden. Code is available at https://github.com/BNU-ERC-ITEA/DeflareMambav2.

cs.CV↗

arXiv2026

Transition Path Theory For Lévy-Type Processes: SDE Representation and Statistics

This paper establishes a Transition Path Theory (TPT) for Lévy-type processes, addressing a critical gap in the study of the transition mechanism between meta-stabile states in non-Gaussian stochastic systems. A key contribution is the rigorous derivation of the stochastic differential equation (SDE) representation for transition path processes, which share the same distributional properties as transition trajectories, along with a proof of its well-posedness. This result provides a solid theoretical foundation for sampling transition trajectories. The paper also investigates the statistical properties of transition trajectories, including their probability distribution, probability current, and rate of occurrence.

math.PR↗

arXiv2025

Physics-Informed Video Flare Synthesis and Removal Leveraging Motion Independence between Flare and Scene

Lens flare is a degradation phenomenon caused by strong light sources. Existing researches on flare removal have mainly focused on images, while the spatiotemporal characteristics of video flare remain largely unexplored. Video flare synthesis and removal pose significantly greater challenges than in image, owing to the complex and mutually independent motion of flare, light sources, and scene content. This motion independence further affects restoration performance, often resulting in flicker and artifacts. To address this issue, we propose a physics-informed dynamic flare synthesis pipeline, which simulates light source motion using optical flow and models the temporal behaviors of both scattering and reflective flares. Meanwhile, we design a video flare removal network that employs an attention module to spatially suppress flare regions and incorporates a Mamba-based temporal modeling component to capture long range spatio-temporal dependencies. This motion-independent spatiotemporal representation effectively eliminates the need for multi-frame alignment, alleviating temporal aliasing between flares and scene content and thereby improving video flare removal performance. Building upon this, we construct the first video flare dataset to comprehensively evaluate our method, which includes a large set of synthetic paired videos and additional real-world videos collected from the Internet to assess generalization capability. Extensive experiments demonstrate that our method consistently outperforms existing video-based restoration and image-based flare removal methods on both real and synthetic videos, effectively removing dynamic flares while preserving light source integrity and maintaining spatiotemporal consistency of scene.

cs.CV↗

arXiv2025

Lévy Score Function and Score-Based Particle Algorithm for Nonlinear Lévy--Fokker--Planck Equations

The score function for the diffusion process, also known as the gradient of the log-density, is a basic concept to characterize the probability flow with important applications in the score-based diffusion generative modelling and the simulation of Itô stochastic differential equations. However, neither the probability flow nor the corresponding score function for the diffusion-jump process are known. This paper delivers mathematical derivation, numerical algorithm, and error analysis focusing on the corresponding score function in non-Gaussian systems with jumps and discontinuities represented by the nonlinear Lévy--Fokker--Planck equations. We propose the Lévy score function for such stochastic equations, which features a nonlocal double-integral term, and we develop its training algorithm by minimizing the proposed loss function from samples. Based on the equivalence of the probability flow with deterministic dynamics, we develop a self-consistent score-based transport particle algorithm to sample the interactive Lévy stochastic process at discrete time grid points. We provide error bound for the Kullback--Leibler divergence between the numerical and true probability density functions by overcoming the nonlocal challenges in the Lévy score. The full error analysis with the Monte Carlo error and the time discretization error is furthermore established. To show the usefulness and efficiency of our approach, numerical examples from applications in biology and finance are tested.

math.NA↗

arXiv2025

Entropy Production in Non-Gaussian Active Matter: A Unified Fluctuation Theorem and Deep Learning Framework

We present a general framework for deriving entropy production rates (EPRs) in active matter systems driven by non-Gaussian active fluctuations. Employing the probability-flow equivalence technique, we rigorously obtain an entropy production (EP) decomposition formula. We demonstrate that the EP, $Δs_\mathrm{tot}$, satisfies a detailed fluctuation theorem, $ρ_{\mathcal{R}}(Σ)/ρ_{\mathcal{R}}(-Σ)=e^Σ$, which holds for the distribution $ρ_{\mathcal{R}}(Σ)$ defined as the probability of observing a value $Σ$ of the quantity $\mathcal{R}\equiv Δs_\mathrm{tot}-B_\mathrm{act}$, where $B_\mathrm{act}$ is a path-dependent random variable associated with active fluctuations. Moreover, an integral fluctuation theorem, $\langle e^{- \mathcal{R} } \rangle = 1$, and the generalized second law of thermodynamics, $\langle Δs_\mathrm{tot} \rangle \ge \langle B_\mathrm{act} \rangle$, follow directly. Our results hold under steady-state conditions and can be straightforwardly extended to arbitrary initial states. In the limiting case where active fluctuations vanish, these theorems reduce to the established results of stochastic thermodynamics. Building on this theoretical foundation, we introduce a deep-learning-based methodology for efficiently computing the EP, utilizing the Lévy score we propose. To illustrate the validity of our approach, we apply it to two representative systems: a Brownian particle in a periodic active bath and an active polymer composed of an active Brownian cross-linker interacting with passive Brownian beads. Our work provides a unified framework for analyzing EP in active matter and offers practical computational tools for investigating complex nonequilibrium behavior.

cond-mat.stat-mech↗

arXiv2025

Tackling Ill-posedness of Reversible Image Conversion with Well-posed Invertible Network

Reversible image conversion (RIC) suffers from ill-posedness issues due to its forward conversion process being considered an underdetermined system. Despite employing invertible neural networks (INN), existing RIC methods intrinsically remain ill-posed as inevitably introducing uncertainty by incorporating randomly sampled variables. To tackle the ill-posedness dilemma, we focus on developing a reliable approximate left inverse for the underdetermined system by constructing an overdetermined system with a non-zero Gram determinant, thus ensuring a well-posed solution. Based on this principle, we propose a well-posed invertible $1\times1$ convolution (WIC), which eliminates the reliance on random variable sampling and enables the development of well-posed invertible networks. Furthermore, we design two innovative networks, WIN-Naïve and WIN, with the latter incorporating advanced skip-connections to enhance long-term memory. Our methods are evaluated across diverse RIC tasks, including reversible image hiding, image rescaling, and image decolorization, consistently achieving state-of-the-art performance. Extensive experiments validate the effectiveness of our approach, demonstrating its ability to overcome the bottlenecks of existing RIC solutions and setting a new benchmark in the field. Codes are available in https://github.com/BNU-ERC-ITEA/WIN.

eess.IV↗

arXiv2025

DeflareMamba: Hierarchical Vision Mamba for Contextually Consistent Lens Flare Removal

Lens flare removal remains an information confusion challenge in the underlying image background and the optical flares, due to the complex optical interactions between light sources and camera lens. While recent solutions have shown promise in decoupling the flare corruption from image, they often fail to maintain contextual consistency, leading to incomplete and inconsistent flare removal. To eliminate this limitation, we propose DeflareMamba, which leverages the efficient sequence modeling capabilities of state space models while maintains the ability to capture local-global dependencies. Particularly, we design a hierarchical framework that establishes long-range pixel correlations through varied stride sampling patterns, and utilize local-enhanced state space models that simultaneously preserves local details. To the best of our knowledge, this is the first work that introduces state space models to the flare removal task. Extensive experiments demonstrate that our method effectively removes various types of flare artifacts, including scattering and reflective flares, while maintaining the natural appearance of non-flare regions. Further downstream applications demonstrate the capacity of our method to improve visual object recognition and cross-modal semantic understanding. Code is available at https://github.com/BNU-ERC-ITEA/DeflareMamba.

cs.CV↗

arXiv2025

Beyond Image Prior: Embedding Noise Prior into Conditional Denoising Transformer

Existing learning-based denoising methods typically train models to generalize the image prior from large-scale datasets, suffering from the variability in noise distributions encountered in real-world scenarios. In this work, we propose a new perspective on the denoising challenge by highlighting the distinct separation between noise and image priors. This insight forms the basis for our development of conditional optimization framework, designed to overcome the constraints of traditional denoising framework. To this end, we introduce a Locally Noise Prior Estimation (LoNPE) algorithm, which accurately estimates the noise prior directly from a single raw noisy image. This estimation acts as an explicit prior representation of the camera sensor's imaging environment, distinct from the image prior of scenes. Additionally, we design an auxiliary learnable LoNPE network tailored for practical application to sRGB noisy images. Leveraging the estimated noise prior, we present a novel Conditional Denoising Transformer (Condformer), by incorporating the noise prior into a conditional self-attention mechanism. This integration allows the Condformer to segment the optimization process into multiple explicit subspaces, significantly enhancing the model's generalization and flexibility. Extensive experimental evaluations on both synthetic and real-world datasets, demonstrate that the proposed method achieves superior performance over current state-of-the-art methods. The source code is available at https://github.com/YuanfeiHuang/Condformer.

eess.IV↗

arXiv2025

Weak Generative Sampler to Efficiently Sample Invariant Distribution of Stochastic Differential Equation

Sampling invariant distributions from an Itô diffusion process presents a significant challenge in stochastic simulation. Traditional numerical solvers for stochastic differential equations require both a fine step size and a lengthy simulation period, resulting in biased and correlated samples. The current deep learning-based method solves the stationary Fokker--Planck equation to determine the invariant probability density function in the form of deep neural networks, but they generally do not directly address the problem of sampling from the computed density function. In this work, we introduce a framework that employs a weak generative sampler (WGS) to directly generate independent and identically distributed (iid) samples induced by a transformation map derived from the stationary Fokker--Planck equation. Our proposed loss function is based on the weak form of the Fokker--Planck equation, integrating normalizing flows to characterize the invariant distribution and facilitate sample generation from a base distribution. Our randomized test function circumvents the need for min-max optimization in the traditional weak formulation. Our method necessitates neither the computationally intensive calculation of the Jacobian determinant nor the invertibility of the transformation map. A crucial component of our framework is the adaptively chosen family of test functions in the form of Gaussian kernel functions with centers related to the generated data samples. Experimental results on several benchmark examples demonstrate the effectiveness and scalability of our method, which offers both low computational costs and excellent capability in exploring multiple metastable states.

cs.LG↗

arXiv2024

Probability Flow Approach to the Onsager--Machlup Functional for Jump-Diffusion Processes

The Onsager--Machlup action functional is an important concept in statistical mechanics and thermodynamics to describe the probability of fluctuations in nonequilibrium systems. It provides a powerful tool for analyzing and predicting the behavior of complex stochastic systems. For diffusion process, the path integral method and the Girsanov transformation are two main approaches to construct the Onsager--Machlup functional. However, it is a long-standing challenge to apply these two methods to the jump-diffusion process, because the complexity of jump noise presents intrinsic technical barriers to derive the Onsager--Machlup functional. In this work, we propose a new strategy to solve this problem by utilizing the equivalent probabilistic flow between the pure diffusion process and the jump-diffusion process. For the first time, we rigorously establish the closed-form expression of the Onsager--Machlup functional for jump-diffusion processes with finite jump activity, which include an important term of the Lévy intensity at the origin. The same probability flow approach is further applied to the Lévy process with infinite jump activity, and yields a time-discrete version of the Onsager--Machlup functional.

math.PR↗

arXiv2024

The SIR epidemic on a dynamic Erdős-Rényi random graph

We investigate the SIR epidemic on a dynamic inhomogeneous Erdős-Rényi random graph, in which vertices are of one of $k$ types and in which edges appear and disappear independently of each other. We establish a functional law of large numbers for the susceptible, infected, and recovered ratio curves after a random time shift, and demonstrate that, under a variety of possible scaling limits of the model parameters, the epidemic curves are solutions to a system of ordinary differential equations. In most scaling regimes, these equations coincide with the classical SIR epidemic equations. In the regime where the average degree of the network remains constant and the edge-flipping dynamics remain on the same time scale as the infectious contact process, however, a novel set of differential equations emerges. This system contains additional quantities related to the infectious edges, but somewhat surprisingly, contains no quantities related to higher-order local network configurations. To the best of our knowledge, this study represents the first thorough and rigorous analysis of large population epidemic processes on dynamic random graphs, although our findings are contingent upon conditioning on a (possibly strict) subset of the event of an epidemic outbreak.

math.PR↗

arXiv2023

The Most Probable Transition Paths of Stochastic Dynamical Systems: A Sufficient and Necessary Characterization

The most probable transition paths of a stochastic dynamical system are the global minimizers of the Onsager-Machlup action functional and can be described by a necessary but not sufficient condition, the Euler-Lagrange equation (a second-order differential equation with initial-terminal conditions) from a variational principle. This work is devoted to showing a sufficient and necessary characterization for the most probable transition paths of stochastic dynamical systems with Brownian noise. We prove that, under appropriate conditions, the most probable transition paths are completely determined by a first-order ordinary differential equation. The equivalence is established by showing that the Onsager-Machlup action functional of the original system can be derived from the corresponding Markovian bridge process. For linear stochastic systems and the nonlinear Hongler's model, the first-order differential equations determining the most probable transition paths are shown analytically to imply the Euler-Lagrange equations of the Onsager-Machlup functional. For general nonlinear systems, the determining first-order differential equations can be approximated, in a short time or for the small noise case. Some numerical experiments are presented to illustrate our results.

math-ph↗

arXiv2022

NTIRE 2022 Challenge on Efficient Super-Resolution: Methods and Results

This paper reviews the NTIRE 2022 challenge on efficient single image super-resolution with focus on the proposed solutions and results. The task of the challenge was to super-resolve an input image with a magnification factor of $\times$4 based on pairs of low and corresponding high resolution images. The aim was to design a network for single image super-resolution that achieved improvement of efficiency measured according to several metrics including runtime, parameters, FLOPs, activations, and memory consumption while at least maintaining the PSNR of 29.00dB on DIV2K validation set. IMDN is set as the baseline for efficiency measurement. The challenge had 3 tracks including the main track (runtime), sub-track one (model complexity), and sub-track two (overall performance). In the main track, the practical runtime performance of the submissions was evaluated. The rank of the teams were determined directly by the absolute value of the average runtime on the validation set and test set. In sub-track one, the number of parameters and FLOPs were considered. And the individual rankings of the two metrics were summed up to determine a final ranking in this track. In sub-track two, all of the five metrics mentioned in the description of the challenge including runtime, parameter count, FLOPs, activations, and memory consumption were considered. Similar to sub-track one, the rankings of five metrics were summed up to determine a final ranking. The challenge had 303 registered participants, and 43 teams made valid submissions. They gauge the state-of-the-art in efficient single image super-resolution.

cs.CV↗

arXiv2021

Transitional Learning: Exploring the Transition States of Degradation for Blind Super-resolution

Being extremely dependent on iterative estimation of the degradation prior or optimization of the model from scratch, the existing blind super-resolution (SR) methods are generally time-consuming and less effective, as the estimation of degradation proceeds from a blind initialization and lacks interpretable degradation priors. To address it, this paper proposes a transitional learning method for blind SR using an end-to-end network without any additional iterations in inference, and explores an effective representation for unknown degradation. To begin with, we analyze and demonstrate the transitionality of degradations as interpretable prior information to indirectly infer the unknown degradation model, including the widely used additive and convolutive degradations. We then propose a novel Transitional Learning method for blind Super-Resolution (TLSR), by adaptively inferring a transitional transformation function to solve the unknown degradations without any iterative operations in inference. Specifically, the end-to-end TLSR network consists of a degree of transitionality (DoT) estimation network, a homogeneous feature extraction network, and a transitional learning module. Quantitative and qualitative evaluations on blind SR tasks demonstrate that the proposed TLSR achieves superior performances and costs fewer complexities against the state-of-the-art blind SR methods. The code is available at github.com/YuanfeiHuang/TLSR.

cs.CV↗

arXiv2021

Image-specific Convolutional Kernel Modulation for Single Image Super-resolution

Recently, deep-learning-based super-resolution methods have achieved excellent performances, but mainly focus on training a single generalized deep network by feeding numerous samples. Yet intuitively, each image has its representation, and is expected to acquire an adaptive model. For this issue, we propose a novel image-specific convolutional kernel modulation (IKM) by exploiting the global contextual information of image or feature to generate an attention weight for adaptively modulating the convolutional kernels, which outperforms the vanilla convolution and several existing attention mechanisms while embedding into the state-of-the-art architectures without any additional parameters. Particularly, to optimize our IKM in mini-batch training, we introduce an image-specific optimization (IsO) algorithm, which is more effective than the conventional mini-batch SGD optimization. Furthermore, we investigate the effect of IKM on the state-of-the-art architectures and exploit a new backbone with U-style residual learning and hourglass dense block learning, terms U-Hourglass Dense Network (U-HDN), which is an appropriate architecture to utmost improve the effectiveness of IKM theoretically and experimentally. Extensive experiments on single image super-resolution show that the proposed methods achieve superior performances over state-of-the-art methods. Code is available at github.com/YuanfeiHuang/IKM.

eess.IV↗

arXiv2020

Interpretable Detail-Fidelity Attention Network for Single Image Super-Resolution

Benefiting from the strong capabilities of deep CNNs for feature representation and nonlinear mapping, deep-learning-based methods have achieved excellent performance in single image super-resolution. However, most existing SR methods depend on the high capacity of networks which is initially designed for visual recognition, and rarely consider the initial intention of super-resolution for detail fidelity. Aiming at pursuing this intention, there are two challenging issues to be solved: (1) learning appropriate operators which is adaptive to the diverse characteristics of smoothes and details; (2) improving the ability of model to preserve the low-frequency smoothes and reconstruct the high-frequency details. To solve them, we propose a purposeful and interpretable detail-fidelity attention network to progressively process these smoothes and details in divide-and-conquer manner, which is a novel and specific prospect of image super-resolution for the purpose on improving the detail fidelity, instead of blindly designing or employing the deep CNNs architectures for merely feature representation in local receptive fields. Particularly, we propose a Hessian filtering for interpretable feature representation which is high-profile for detail inference, a dilated encoder-decoder and a distribution alignment cell to improve the inferred Hessian features in morphological manner and statistical manner respectively. Extensive experiments demonstrate that the proposed methods achieve superior performances over the state-of-the-art methods quantitatively and qualitatively. Code is available at https://github.com/YuanfeiHuang/DeFiAN.

cs.CV↗