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Yanqing Wang

Publications and source records attributed to Yanqing Wang.

At least 19 recordsLinked to original sources
arXiv2026

Numerical Analysis on Backward Stochastic Differential Equations by Finite Transposition Method

In this paper, we propose a finite transposition method to solve backward stochastic differential equations (BSDEs, for short). Based on the transposition solution theory for BSDEs, our method offers a promising way of efficiently computing solutions, which can be regarded as an analogous method for BSDEs as the classical finite element method for partial differential equations. Our method has the advantage of easily computable conditional expectations.

math.PR↗
arXiv2026

Equivalence between time and norm optimal control problems of stochastic differential equations

In this paper, we establish the equivalence between minimal time and minimal norm control problems for controllable stochastic differential equations (SDEs). The core of this equivalence lies in proving the continuity of the minimal norm function. Unlike the deterministic setting, where the time translation technique is effective, this approach is not applicable due to the adapted nature of the admissible controls in SDEs. To address this challenge, we construct the minimal norm control explicitly, thereby achieving the desired continuity. This constructive approach not only proves theoretical equivalence but also facilitates the design of efficient numerical schemes for minimal norm and time controls.

math.OC↗
arXiv2025

Knowledge Graph-Guided Multi-Agent Distillation for Reliable Industrial Question Answering with Datasets

Industrial question-answering (QA) systems require higher safety and reliability than general-purpose dialogue models, as errors in high-risk scenarios such as equipment fault diagnosis can have severe consequences. Although multi-agent large language models enhance reasoning depth, they suffer from uncontrolled iterations and unverifiable outputs, and conventional distillation methods struggle to transfer collaborative reasoning capabilities to lightweight, deployable student models. To address these challenges, we propose Knowledge Graph-guided Multi-Agent System Distillation (KG-MASD). Our approach formulates distillation as a Markov Decision Process and incorporates a knowledge graph as a verifiable structured prior to enrich state representation and ensure convergence. By integrating collaborative reasoning with knowledge grounding, KG-MASD generates high-confidence instruction-tuning data and jointly distills reasoning depth and verifiability into compact student models suitable for edge deployment. Experiments on an industrial QA dataset show that KG-MASD improves accuracy by 2.4 per cent to 20.1 per cent over baselines and significantly enhances reliability, enabling trustworthy AI deployment in safety-critical industrial scenarios. Code and data are available at https://github.com/erwinmsmith/KG-MAD/.

cs.CL↗
arXiv2025

On anisotropic energy conservation criteria of incompressible fluids

In this paper, by means of divergence-free condition, we establish an anisotropic energy conservation class enabling one component of velocity in the largest space $L^{3} (0,T; B^{1/3}_{3,\infty})$ for the 3D inviscid incompressible fluids, which extends the celebrated result obtained by Cheskidov, Constantin, Friedlander and Shvydkoy in [15, Nonlinearity 21 (2008)]. For viscous flows, we generalize famous Lions's energy conservation criteria to allow the horizontal components and vertical part of velocity to have different integrability.

math.AP↗
arXiv2025

ECCoT: A Framework for Enhancing Effective Cognition via Chain of Thought in Large Language Model

In the era of large-scale artificial intelligence, Large Language Models (LLMs) have made significant strides in natural language processing. However, they often lack transparency and generate unreliable outputs, raising concerns about their interpretability. To address this, the Chain of Thought (CoT) prompting method structures reasoning into step-by-step deductions. Yet, not all reasoning chains are valid, and errors can lead to unreliable conclusions. We propose ECCoT, an End-to-End Cognitive Chain of Thought Validation Framework, to evaluate and refine reasoning chains in LLMs. ECCoT integrates the Markov Random Field-Embedded Topic Model (MRF-ETM) for topic-aware CoT generation and Causal Sentence-BERT (CSBert) for causal reasoning alignment. By filtering ineffective chains using structured ordering statistics, ECCoT improves interpretability, reduces biases, and enhances the trustworthiness of LLM-based decision-making. Key contributions include the introduction of ECCoT, MRF-ETM for topic-driven CoT generation, and CSBert for causal reasoning enhancement. Code is released at: https://github.com/erwinmsmith/ECCoT.git.

cs.CL↗
arXiv2024

Numerical Methods for Optimal Control Problems with SPDEs

This paper investigates numerical methods for solving stochastic linear quadratic (SLQ) optimal control problems governed by stochastic partial differential equations (SPDEs). Two distinct approaches, the open-loop and closed-loop ones, are developed to ensure convergence rates in the fully discrete setting. The open-loop approach, utilizing the finite element method for spatial discretization and the Euler method for temporal discretization, addresses the complexities of coupled forward-backward SPDEs and employs a gradient descent framework suited for high-dimensional spaces. Separately, the closed-loop approach applies a feedback strategy, focusing on Riccati equation for spatio-temporal discretization. Both approaches are rigorously designed to handle the challenges of fully discrete SLQ problems, providing rigorous convergence rates and computational frameworks.

math.OC↗
arXiv2024

Four-fifths laws in incompressible and magnetized fluids: Helicity, Energy and Cross-helicity

In this paper, we are concerned with the Kolmogorov's scaling laws of conserved quantities. By means of Eyink's longitudinal structure functions and the analysis of interaction of different physical quantities, we extend celebrated four-fifths laws from energy to helicity in incompressible fluid and, energy and cross-helicity in magnetohydrodynamic flow. In contrast to pervious 4/5 laws of energy and cross-helicity in magnetized fluids obtained by Politano and Pouquet, they are in terms of the mixed three-order structure functions rather than the structure coupling correlation functions.

math.AP↗
arXiv2023

On the energy and helicity conservation of the incompressible Euler equations

In this paper, we are concerned with the minimal regularity of weak solutions implying the law of balance for both energy and helicity in the incompressible Euler equations. In the spirit of recent works due to Berselli [5] and Berselli-Georgiadis [6], it is shown that the energy of weak solutions is invariant if $v\in L^{p}(0,T;B^{\frac1p}_{\frac{2p}{p-1},c(\mathbb{N})} )$ with $1<p\leq3$ and the helicity is conserved if $v\in L^{p}(0,T;B^{\frac2p}_{\frac{2p}{p-1},c(\mathbb{N})} )$ with $2<p\leq3 $ for both the periodic domain and the whole space, which generalizes the classical work of Cheskidov-Constantin-Friedlander-Shvydkoy in [10]. This indicates the role of the time integrability, spatial integrability and differential regularity of the velocity in the conserved quantities of weak solutions of the ideal fluid.

math.AP↗
arXiv2023

Coordinated Transformer with Position \& Sample-aware Central Loss for Anatomical Landmark Detection

Heatmap-based anatomical landmark detection is still facing two unresolved challenges: 1) inability to accurately evaluate the distribution of heatmap; 2) inability to effectively exploit global spatial structure information. To address the computational inability challenge, we propose a novel position-aware and sample-aware central loss. Specifically, our central loss can absorb position information, enabling accurate evaluation of the heatmap distribution. More advanced is that our central loss is sample-aware, which can adaptively distinguish easy and hard samples and make the model more focused on hard samples while solving the challenge of extreme imbalance between landmarks and non-landmarks. To address the challenge of ignoring structure information, a Coordinated Transformer, called CoorTransformer, is proposed, which establishes long-range dependencies under the guidance of landmark coordination information, making the attention more focused on the sparse landmarks while taking advantage of global spatial structure. Furthermore, CoorTransformer can speed up convergence, effectively avoiding the defect that Transformers have difficulty converging in sparse representation learning. Using the advanced CoorTransformer and central loss, we propose a generalized detection model that can handle various scenarios, inherently exploiting the underlying relationship between landmarks and incorporating rich structural knowledge around the target landmarks. We analyzed and evaluated CoorTransformer and central loss on three challenging landmark detection tasks. The experimental results show that our CoorTransformer outperforms state-of-the-art methods, and the central loss significantly improves the performance of the model with p-values< 0.05.

cs.CV↗
arXiv2023

On two conserved quantities in the inviscid electron and Hall magnetohydrodynamic equations

In this paper, we are concerned with the energy and magnetic helicity conservation of weak solutions for both the electron and Hall magnetohydrodynamic equations. Various sufficient criteria to ensure the energy and magnetic helicity conservation in Onsager's critical spaces $\underline{B}^α_{p,VMO}$ and $B^α_{p,c(\mathbb{N})}$ in these systems are established. Moreover, for the E-MHD equations, we observe that the conservation criteria of energy and magnetic helicity to the E-MHD equations correspond to the helicity and energy to the ideal incompressible Euler equations, respectively.

math.AP↗
arXiv2023

Four-thirds law of energy and magnetic helicity in electron and Hall magnetohydrodynamic fluids

In this paper, by exploiting the feature of the Hall term, we establish some local version four-thirds laws for the dissipation rates of energy and magnetic helicity in both electron and Hall magnetohydrodynamic equations in the sense of Duchon-Robert type. New 4/3 laws for the dissipation rates of magnetic helicity in these systems are first observed and four-thirds law involving the dissipation rates of energy for the Hall magnetohydrodynamic equations generalizes the work of Galtier.

physics.plasm-ph↗
arXiv2023

Yaglom's law and conserved quantity dissipation in turbulence

In this paper, we are concerned with the local exact relationship for third-order structure functions in the temperature equation, the inviscid MHD equations and the Euler equations in the sense of Duchon-Robert type and Eyink type. It is shown that the local version of Yaglom's $4/3$ law is valid for the dissipation rates of conserved quantities such as the energy, cross-helicity and helicity in these systems. In the spirit of Duchon-Robert's classical work, we derive the dissipation term resulted from the lack of smoothness of the solutions in corresponding conservation relation. It seems that these results suggest that the Yaglom's law of the hydrodynamic equations holds if an analogue of dissipation term as Duchon-Robert's is obtained. Base on this, the first Yaglom's relation for the Oldroyd-B model and, inspired by the very recent work due to Boutros-Titi, six new 4/3 laws for subgrid scale $α$-models of turbulence are also presented.

math.AP↗
arXiv2023

Convergence rates of a discrete feedback control arising in mean-field linear quadratic optimal control problems

In this work, we propose a feedback control based temporal discretization for linear quadratic optimal control problems (LQ problems) governed by controlled mean-field stochastic differential equations. We firstly decompose the original problem into two problems: a stochastic LQ problem and a deterministic one. Secondly, we discretize both LQ problems one after another relying on Riccati equations and control's feedback representations. Then, we prove the convergence rates for the proposed discretization and present an effective algorithm. Finally, a numerical example is provided to support the theoretical finding.

math.OC↗
arXiv2022

Energy and helicity conservation for the generalized quasi-geostrophic equation

In this paper, we consider the 2-D generalized surface quasi-geostrophic equation with the velocity $v$ determined by $v=\mathcal{R}^{\perp}Λ^{γ-1}θ$. It is shown that the $L^p$ type energy norm of weak solutions is conserved provided $θ\in L^{p+1}(0,T; {B}^{\fracγ{3}}_{p+1, c(\mathbb{N})})$ for $0<γ<\frac32$ or $θ\in L^{p+1}(0,T; {B}^α_{p+1,\infty})~\text{for any}~γ-1<α<1 \text{ with} ~\frac{3}{2}\leq γ<2$. Moreover, we also prove that the helicity of weak solutions satisfying $\nablaθ\in L^{3}(0,T;\dot{B}_{3,c(\mathbb{N})}^{\fracγ{3}})$ for $0<γ<\frac32$ or $\nablaθ\in L^{3}(0,T; \dot{B}^α_{3,\infty})~\text{for any}~γ-1<α<1 \text{ with} ~\frac{3}{2}\leq γ<2$ is invariant. Therefore, the accurate relationships between the critical regularity for the energy (helicity) conservation of the weak solutions and the regularity of velocity in 2-D generalized quasi-geostrophic equation are presented.

math.AP↗
arXiv2022

Fractal dimension of potential singular points set in the Navier-Stokes equations under supercritical regularity

The main objective of this paper is to answer the questions posed by Robinson and Sadowski [21, p. 505, Comm. Math. Phys., 2010]{[RS3]} for the Navier-Stokes equations. Firstly, we prove that the upper box dimension of the potential singular points set $\mathcal{S}$ of suitable weak solution $u$ belonging in $ L^{q}(0,T;L^{p}(\mathbb{R}^{3}))$ for $1\leq\frac{2}{q}+\frac{ 3}{p}\leq\frac32$ with $2\leq q<\infty$ and $2<p<\infty$ is at most $\max\{p,q\}(\frac{2}{q}+\frac{ 3}{p}-1)$ in this system. Secondly, it is shown that $1-2 s$ dimension Hausdorff measure of potential singular points set of suitable weak solutions satisfying $ u\in L^{2}(0,T;\dot{H}^{s+1}(\mathbb{R}^{3}))$ for $0\leq s\leq\frac12$ is zero, whose proof relies on Caffarelli-Silvestre's extension. Inspired by Baker-Wang's recent work [1], this further allows us to discuss the Hausdorff dimension of potential singular points set of suitable weak solutions if the gradient of the velocity under some supercritical regularity.

math.AP↗
arXiv2022

Energy conservation of weak solutions for the incompressible Euler equations via vorticity

Motivated by the works of Cheskidov, Lopes Filho, Nussenzveig Lopes and Shvydkoy in [8, Commun. Math. Phys. 348: 129-143, 2016] and Chen and Yu in [5, J. Math. Pures Appl. 131: 1-16, 2019], we address how the $L^p$ control of vorticity could influence the energy conservation for the incompressible homogeneous and nonhomogeneous Euler equations in this paper. For the homogeneous flow in the periodic domain or whole space, we provide a self-contained proof for the criterion $ω=\text{curl}u\in L^{3}(0,T;L^{\frac{3n}{n+2}}(Ω))\,(n=2,3)$, which generalizes the corresponding result in [8] and can be viewed as in Onsager critical spatio-temporal spaces. Regarding the nonhomogeneous flow, it is shown that the energy is conserved as long as the vorticity lies in the same space as before and $\nabla\sqrtρ$ belongs to $L^{\infty}(0,T;L^{n}(\mathbb{T}^{n}))\,(n=2,3)$, which gives an affirmative answer to a problem proposed by Chen and Yu in [5].

math.AP↗
arXiv2022

Analytical validation of the helicity conservation for the compressible Euler equations

In [25], Moffatt introduced the concept of helicity in an inviscid fluid and examined the helicity preservation of smooth solution to barotropic compressible flow. In this paper, it is shown that the weak solutions of the above system in Onsager type spaces $\dot{B}^{1/3}_{p,c(\mathbb{N})}$ guarantee the conservation of the helicity. The parallel results of homogeneous incompressible Euler equations and the surface quasi-geostrophic equation are also obtained.

math.AP↗