Chaolong Jiang

Chaolong Jiang, Wenjun Cai, Yushun Wang et al.

In this paper, a novel sixth order energy-conserved method is proposed for solving the three-dimensional time-domain Maxwell's equations. The new scheme preserves five discrete energy conservation laws, three momentum conservation laws, symplectic conservation law as well as two divergence-free properties and is proved to be unconditionally stable, non-dissipative. An optimal error estimate is established based on the energy method, which shows that the proposed method is of sixth order accuracy in time and spectral accuracy in space in discrete $L^{2}$-norm. The constant in the error estimate is proved to be only $O(T)$. Furthermore, the numerical dispersion relation is analyzed in detail and a fast solver is presented to solve the resulting discrete linear equations efficiently. Numerical results are addressed to verify our theoretical analysis.

Zhenghan Tai, Hanwei Wu, Qingchen Hu et al.

Retrieval-Augmented Generation (RAG) is becoming increasingly essential for Question Answering (QA) in the financial sector, where accurate and contextually grounded insights from complex public disclosures are crucial. However, existing financial RAG systems face two significant challenges: (1) they struggle to process heterogeneous data formats, such as text, tables, and figures; and (2) they encounter difficulties in balancing general-domain applicability with company-specific adaptation. To overcome these challenges, we present VeritasFi, an innovative hybrid RAG framework that incorporates a multi-modal preprocessing pipeline alongside a cutting-edge two-stage training strategy for its re-ranking component. VeritasFi enhances financial QA through three key innovations: (1) A multi-modal preprocessing pipeline that seamlessly transforms heterogeneous data into a coherent, machine-readable format. (2) A tripartite hybrid retrieval engine that operates in parallel, combining deep multi-path retrieval over a semantically indexed document corpus, real-time data acquisition through tool utilization, and an expert-curated memory bank for high-frequency questions, ensuring comprehensive scope, accuracy, and efficiency. (3) A two-stage training strategy for the document re-ranker, which initially constructs a general, domain-specific model using anonymized data, followed by rapid fine-tuning on company-specific data for targeted applications. By integrating our proposed designs, VeritasFi presents a groundbreaking framework that greatly enhances the adaptability and robustness of financial RAG systems, providing a scalable solution for both general-domain and company-specific QA tasks. Code accompanying this work is available at https://github.com/simplew4y/VeritasFi.git.

Wenjun Cai, Chaolong Jiang, Yushun Wang

This paper presents two kinds of strategies to construct structure-preserving algorithms with homogeneous Neumann boundary conditions for the sine-Gordon equation, while most existing structure-preserving algorithms are only valid for zero or periodic boundary conditions. The first strategy is based on the conventional second-order central difference quotient but with a cell-centered grid, while the other is established on the regular grid but incorporated with summation by parts (SBP) operators. Both the methodologies can provide conservative semi-discretizations with different forms of Hamiltonian structures and the discrete energy. However, utilizing the existing SBP formulas, schemes obtained by the second strategy can directly achieve higher-order accuracy while it is not obvious for schemes based on the cell-centered grid to make accuracy improved easily. Further combining the symplectic Runge-Kutta method and the scalar auxiliary variable (SAV) approach, we construct symplectic integrators and linearly implicit energy-preserving schemes for the two-dimensional sine-Gordon equation, respectively. Extensive numerical experiments demonstrate their effectiveness with the homogeneous Neumann boundary conditions.