AI 中文总结
GradAgent是一个知识引导的多智能体系统，通过协调分析、设计和验证智能体并利用知识图谱，为复杂耦合梯度流系统自动构建并验证保结构数值格式，成功应用于多组分囊泡动力学。
AI 中文摘要
高阶微分算子和非线性耦合使得为耦合梯度流系统构造守恒且能量稳定的格式具有挑战性。我们提出了GradAgent，一个知识引导的多智能体系统，它协调三个智能体，涵盖模型分析、算法设计与证明、数值实现与验证。独立的审计通过发现数学错误和证明漏洞、指导修订以及在各阶段保持一致性来增强可靠性。在重建模式下，GradAgent重建了20项已发表的研究，并在一个可扩展的知识图谱（KG）GradAgent-KG中组织经过审计的知识，该图谱连接模型结构、离散化策略与证明、实现以及数值证据。在设计模式下，智能体评估检索到的知识的适用性，并根据相关的离散化策略开发新格式。应用于完全耦合的多组分囊泡相场-流体模型时，GradAgent在三个算法家族中产生了三个一阶和三个二阶格式，其中包括四个线性、解耦格式。在所陈述的假设下，所有六个格式都守恒膜组分质量和囊泡体积，并无条件耗散各自的时间离散能量。与有无GradAgent-KG的对比表明，它促进了该目标模型保结构格式设计的多样性。数值测试确认了二阶空间精度、预期的时间阶数、守恒性以及时间离散能量耗散，而三维剪切流模拟与实验定性一致。这些结果证明了GradAgent结合可重用知识、协调推理和独立审计来开发和验证复杂耦合系统保结构算法的能力。
英文摘要
High-order differential operators and nonlinear coupling make it challenging to construct conservative and energy-stable schemes for coupled gradient-flow systems. We present GradAgent, a knowledge-guided multi-agent system that coordinates three agents across model analysis, algorithm design and proofs, and numerical implementation and validation. Independent audits strengthen reliability by uncovering mathematical errors and proof gaps, guiding revisions, and maintaining consistency across stages. In Reconstruction Mode, GradAgent reconstructs 20 published studies and organizes audited knowledge in an extensible knowledge graph (KG), GradAgent-KG, linking model structures, discretization strategies and proofs, implementations, and numerical evidence. In Design Mode, the agents assess the applicability of retrieved knowledge and develop new schemes informed by relevant discretization strategies. Applied to the fully coupled multicomponent vesicle phase-field-fluid model, GradAgent yields three first-order and three second-order schemes across three algorithmic families, including four linear, decoupled schemes. Under stated assumptions, all six schemes conserve membrane component mass and vesicle volume and dissipate their respective temporally discrete energies unconditionally. Comparisons with and without GradAgent-KG show that it promotes diversity in structure-preserving scheme design for this target model. Numerical tests confirm second-order spatial accuracy, the expected temporal orders, conservation, and temporally discrete energy dissipation, while three-dimensional shear-flow simulations agree qualitatively with experiments. These results demonstrate GradAgent's ability to combine reusable knowledge, coordinated reasoning, and independent auditing to develop and validate structure-preserving algorithms for complex coupled systems.
CommentsThe authors have identified errors in the manuscript that affect some of the results and require substantial revision. We therefore withdraw the manuscript while these issues are being corrected
