arXiv subjects

Yajuan Sun

Publications and source records attributed to Yajuan Sun.

At least 19 recordsLinked to original sources

arXiv2026

Algebraic Invariant Quadratization Schemes for Cahn--Hilliard Equations

In this paper, we propose the Algebraic Invariant Quadratization (AIQ) framework for rational-like energy functions by introducing auxiliary variables, which are interpreted as Casimir functions of the extended system. Combining AIQ with symplectic Runge--Kutta (SRK) methods in time and Fourier pseudo-spectral discretization in space, we obtain fully discrete schemes. The resulting schemes are applied to Cahn--Hilliard equations in both the isotropic and anisotropic cases. We analyze the discrete dispersion relation, spinodal instability, coarsening behavior, and missing-orientation phenomena. Numerical comparisons demonstrate the improved performance superiority of the proposed method over the stabilized invariant energy quadratization (S-IEQ) and scalar auxiliary variable (SAV) methods in preserving the original energy evolution and capturing the underlying physical phenomena.

math.NA↗

arXiv2026

Energy stable auxiliary variable method for Cahn--Hilliard equations

In this paper, we propose a quadratic reformulation theory for rational-like functions. Based on this theory, we develop the Quadratic Conservation Elevation (QCE) method, which combines the Scalar Auxiliary Variable (SAV) method with the implicit midpoint rule. We apply this approach to the Cahn-Hilliard (CH) equation with rational-like free-energy terms, obtaining numerical discretizations that preserve the original energy dissipation law. We further derive the discrete dispersion relation and coarsening dynamics, confirming the efficiency and consistency of the method with the continuous counterpart. In addition, we use the proposed method to capture missing orientations for different anisotropic functions. Numerical simulations with various initial conditions illustrate phase separation and anisotropic evolution.

math.NA↗

arXiv2026

Multi-agent Reinforcement Learning for Low-Carbon P2P Energy Trading among Self-Interested Microgrids

Uncertainties in renewable generation and demand dynamics challenge day-ahead scheduling. To enhance renewable penetration and maintain intra-day balance, we develop a multi-agent reinforcement learning framework for self-interested microgrids participating in peer-to-peer (P2P) electricity trading. Each microgrid independently bids both price and quantity while optimizing its own profit via storage arbitrage under time-varying main-grid prices. A market-clearing mechanism coordinating trades and promoting incentive compatibility is proposed. Simulation results show that the learned bidding policy improves renewable utilization and reduces reliance on high-carbon electricity, while increasing community-level economic welfare, delivering a win-win situation in emission reduction and local prosperity.

cs.MA↗

arXiv2026

Multi-agent Reinforcement Learning-based Joint Design of Low-Carbon P2P Market and Bidding Strategy in Microgrids

The challenges of the uncertainties in renewable energy generation and the instability of the real-time market limit the effective utilization of clean energy in microgrid communities. Existing peer-to-peer (P2P) and microgrid coordination approaches typically rely on certain centralized optimization or restrictive coordination rules which are difficult to be implemented in real-life applications. To address the challenge, we propose an intraday P2P trading framework that allows self-interested microgrids to pursue their economic benefits, while allowing the market operator to maximize the social welfare, namely the low carbon emission objective, of the entire community. Specifically, the decision-making processes of the microgrids are formulated as a Decentralized Partially Observable Markov Decision Process (DEC-POMDP) and solved using a Multi-Agent Reinforcement Learning (MARL) framework. Such an approach grants each microgrid a high degree of decision-making autonomy, while a novel market clearing mechanism is introduced to provide macro-regulation, incentivizing microgrids to prioritize local renewable energy consumption and hence reduce carbon emissions. Simulation results demonstrate that the combination of the self-interested bidding strategy and the P2P market design helps significantly improve renewable energy utilization and reduce reliance on external electricity with high carbon-emissions. The framework achieves a balanced integration of local autonomy, self-interest pursuit, and improved community-level economic and environmental benefits.

cs.MA↗

arXiv2024

Variational Discretizations for Hamiltonian Systems

In this paper, we study the Lagrangian functions for a class of second-order differential systems arising from physics. For such systems, we present necessary and sufficient conditions for the existence of Lagrangian functions. Based on the variational principle and the splitting technique, we construct variational integrators and prove their equivalence to the composition of explicit symplectic methods. We apply the newly derived variational integrators to the Kepler problem and demonstrate their effectiveness in numerical simulations. Moreover, using the modified Lagrangian, we analyze the dynamical behavior of the numerical solutions in preserving the Laplace--Runge--Lenz (LRL) vector.

math.NA↗

arXiv2024

A Unified Framework to Classify Business Activities into International Standard Industrial Classification through Large Language Models for Circular Economy

Effective information gathering and knowledge codification are pivotal for developing recommendation systems that promote circular economy practices. One promising approach involves the creation of a centralized knowledge repository cataloguing historical waste-to-resource transactions, which subsequently enables the generation of recommendations based on past successes. However, a significant barrier to constructing such a knowledge repository lies in the absence of a universally standardized framework for representing business activities across disparate geographical regions. To address this challenge, this paper leverages Large Language Models (LLMs) to classify textual data describing economic activities into the International Standard Industrial Classification (ISIC), a globally recognized economic activity classification framework. This approach enables any economic activity descriptions provided by businesses worldwide to be categorized into the unified ISIC standard, facilitating the creation of a centralized knowledge repository. Our approach achieves a 95% accuracy rate on a 182-label test dataset with fine-tuned GPT-2 model. This research contributes to the global endeavour of fostering sustainable circular economy practices by providing a standardized foundation for knowledge codification and recommendation systems deployable across regions.

cs.CL↗

arXiv2024

Top K Enhanced Reinforcement Learning Attacks on Heterogeneous Graph Node Classification

Graph Neural Networks (GNNs) have attracted substantial interest due to their exceptional performance on graph-based data. However, their robustness, especially on heterogeneous graphs, remains underexplored, particularly against adversarial attacks. This paper proposes HeteroKRLAttack, a targeted evasion black-box attack method for heterogeneous graphs. By integrating reinforcement learning with a Top-K algorithm to reduce the action space, our method efficiently identifies effective attack strategies to disrupt node classification tasks. We validate the effectiveness of HeteroKRLAttack through experiments on multiple heterogeneous graph datasets, showing significant reductions in classification accuracy compared to baseline methods. An ablation study underscores the critical role of the Top-K algorithm in enhancing attack performance. Our findings highlight potential vulnerabilities in current models and provide guidance for future defense strategies against adversarial attacks on heterogeneous graphs.

cs.LG↗

arXiv2023

Asymptotically stable Particle-in-Cell methods for the magnetized Vlasov--Poisson equations in orthogonal curvilinear coordinates

In high-temperature plasma physics, a strong magnetic field is usually used to confine charged particles. Therefore, for studying the classical mathematical models of the physical problems it needs to consider the effect of external magnetic fields. One of the important model equations in plasma is the Vlasov-Poisson equation with an external magnetic field. This equation usually has multi-scale characteristics and rich physical properties, thus it is very important and meaningful to construct numerical methods that can maintain the physical properties inherited by the original systems over long time. This paper extends the corresponding theory in Cartesian coordinates to general orthogonal curvilinear coordinates, and proves that a Poisson-bracket structure can still be obtained after applying the corresponding finite element discretization. However, the Hamiltonian systems in the new coordinate systems generally cannot be decomposed into sub-systems that can be solved accurately, so it is impossible to use the splitting methods to construct the corresponding geometric integrators. Therefore, this paper proposes a semi-implicit method for strong magnetic fields and analyzes the asymptotic stability of this method.

math.NA↗

arXiv2023

Convergence of Hamiltonian Particle methods for Vlasov--Poisson equations with a nonhomogeneous magnetic field

math.NA↗

arXiv2022

Hamiltonian Particle-in-Cell methods for Vlasov-Poisson equations

In this paper, Particle-in-Cell algorithms for the Vlasov-Poisson system are presented based on its Poisson bracket structure. The Poisson equation is solved by finite element methods, in which the appropriate finite element spaces are taken to guarantee that the semi-discretized system possesses a well defined discrete Poisson bracket structure. Then, splitting methods are applied to the semi-discretized system by decomposing the Hamiltonian function. The resulting discretizations are proved to be Poisson bracket preserving. Moreover, the conservative quantities of the system are also well preserved. In numerical experiments, we use the presented numerical methods to simulate various physical phenomena. Due to the huge computational effort of the practical computations, we employ the strategy of parallel computing. The numerical results verify the efficiency of the new derived numerical discretizations.

math.NA↗

arXiv2018

The transport phenomenon of inertia Brownian particles in a periodic potential with non-Gaussian noise

The transport phenomenon (movement and diffusion) of inertia Brownian particles in a periodic potential with non-Gaussian noise is investigated. It is found that proper noise intensity Q will promote particles directional movement(or diffusion), but large Q will inhibit this phenomenon. For large value of Q, the average velocity V (or the diffusion coefficient D) has a maximum with increasing correlation time tau. But for small value of Q, V (or D) decreases with increasing tau. In some cases, for the same value of Q and the same value of tau, non-Gaussian noise can induce particles directional movement(or diffusion), but Gaussian colored noise can not.

cond-mat.stat-mech↗

arXiv2016

High order volume-preserving algorithms for relativistic charged particles in general electromagnetic fields

We construct high order symmetric volume-preserving methods for the relativistic dynamics of a charged particle by the splitting technique with processing. Via expanding the phase space to include time $t$, we give a more general construction of volume-preserving methods that can be applied to systems with time-dependent electromagnetic fields. The newly derived methods provide numerical solutions with good accuracy and conservative properties over long time of simulation. Furthermore, because of the use of processing technique the high order methods are explicit, and cost less than the methods derived from standard compositions, thus are more efficient. The results are verified by the numerical experiments. Linear stability analysis of the methods show that the high order processed method allows larger time step size during integration.

physics.comp-ph↗

arXiv2016

Hamiltonian particle-in-cell methods for Vlasov-Maxwell equations

In this paper, we develop Hamiltonian particle-in-cell methods for Vlasov-Maxwell equations by applying conforming finite element methods in space and splitting methods in time. For the spatial discretisation, the criteria for choosing finite element spaces are presented such that the semi-discrete system possesses a discrete non-canonical Poisson structure. We apply a Hamiltonian splitting method to the semi-discrete system in time, then the resulting algorithm is Poisson preserving and explicit. The conservative properties of the algorithm guarantee the efficient and accurate numerical simulation of the Vlasov-Maxwell equations over long-time.

physics.comp-ph↗

arXiv2016

Explicit high-order non-canonical symplectic particle-in-cell algorithms for Vlasov-Maxwell systems

Explicit high-order non-canonical symplectic particle-in-cell algorithms for classical particle-field systems governed by the Vlasov-Maxwell equations are developed. The algorithm conserves a discrete non-canonical symplectic structure derived from the Lagrangian of the particle-field system, which is naturally discrete in particles. The electromagnetic field is spatially-discretized using the method of discrete exterior calculus with high-order interpolating differential forms for a cubic grid. The resulting time-domain Lagrangian assumes a non-canonical symplectic structure. It is also gauge invariant and conserves charge. The system is then solved using a splitting method discovered by He et al., which produces five exactly-soluable sub-systems, and high-order structure- preserving algorithms follow by combinations. The explicit, high-order, and conservative nature of the algorithms is especially suitable for long-term simulations of particle-field systems with extremely large number of degrees of freedom on massively parallel supercomputers. The algorithms have been tested and verified by the two physics problems, i.e., the nonlinear Landau damping and the electron Bernstein wave.

physics.plasm-ph↗

arXiv2015

High order symplectic integrators based on continuous-stage Runge-Kutta Nystrom methods

On the basis of the previous work by Tang \& Zhang (Appl. Math. Comput. 323, 2018, p. 204--219), in this paper we present a more effective way to construct high-order symplectic integrators for solving second order Hamiltonian equations. Instead of analyzing order conditions step by step as shown in the previous work, the new technique of this paper is using Legendre expansions to deal with the simplifying assumptions for order conditions. With the new technique, high-order symplectic integrators can be conveniently devised by truncating an orthogonal series.

math.NA↗

arXiv2015

Explicit non-canonical symplectic algorithms for charged particle dynamics

We study the non-canonical symplectic structure, or K-symplectic structure inherited by the charged particle dynamics. Based on the splitting technique, we construct non-canonical symplectic methods which is explicit and stable for the long-term simulation. The key point of splitting is to decompose the Hamiltonian as four parts, so that the resulting four subsystems have the same structure and can be solved exactly. This guarantees the K-symplectic preservation of the numerical methods constructed by composing the exact solutions of the subsystems. The error convergency of numerical solutions is analyzed by means of the Darboux transformation. The numerical experiment display the long-term stability and efficiency for these methods.

physics.comp-ph↗

arXiv2015

Canonical symplectic particle-in-cell method for long-term large-scale simulations of the Vlasov-Maxwell system

Particle-in-Cell (PIC) simulation is the most important numerical tool in plasma physics. However, its long-term accuracy has not been established. To overcome this difficulty, we developed a canonical symplectic PIC method for the Vlasov-Maxwell system by discretizing its canonical Poisson bracket. A fast local algorithm to solve the symplectic implicit time advance is discovered without root searching or global matrix inversion, enabling applications of the proposed method to very large-scale plasma simulations with many, e.g., $10^{9}$, degrees of freedom. The long-term accuracy and fidelity of the algorithm enables us to numerically confirm Mouhot and Villani's theory and conjecture on nonlinear Landau damping over several orders of magnitude using the PIC method, and to calculate the nonlinear evolution of the reflectivity during the mode conversion process from extraordinary waves to Bernstein waves.

physics.plasm-ph↗

arXiv2015

Hamiltonian integration methods for Vlasov-Maxwell equations

Hamiltonian integration methods for the Vlasov-Maxwell equations are developed by a Hamiltonian splitting technique. The Hamiltonian functional is split into five parts, i.e., the electrical energy, the magnetic energy, and the kinetic energy in three Cartesian components. Each of the subsystems is a Hamiltonian system with respect to the Morrison-Marsden-Weinstein Poisson bracket and can be solved exactly. Compositions of the exact solutions yield Poisson structure preserving, or Hamiltonian, integration methods for the Vlasov-Maxwell equations, which have superior long-term fidelity and accuracy.

physics.comp-ph↗