arXiv subjects

Liwei Tan

Publications and source records attributed to Liwei Tan.

8 recordsLinked to original sources

arXiv2024

Traditional Chinese Medicine Case Analysis System for High-Level Semantic Abstraction: Optimized with Prompt and RAG

This paper details a technical plan for building a clinical case database for Traditional Chinese Medicine (TCM) using web scraping. Leveraging multiple platforms, including 360doc, we gathered over 5,000 TCM clinical cases, performed data cleaning, and structured the dataset with crucial fields such as patient details, pathogenesis, syndromes, and annotations. Using the $Baidu\_ERNIE\_Speed\_128K$ API, we removed redundant information and generated the final answers through the $DeepSeekv2$ API, outputting results in standard JSON format. We optimized data recall with RAG and rerank techniques during retrieval and developed a hybrid matching scheme. By combining two-stage retrieval method with keyword matching via Jieba, we significantly enhanced the accuracy of model outputs.

cs.CL↗

arXiv2024

A Non-staggered Projection Algorithm for Two-Phase Fluid-Structure Interaction Simulation Using the Phase-Field/Immersed-Boundary Method

We present a Pressure-Oscillation-Free projection algorithm for large-density-ratio multiphase fluid-structure interaction simulations, implemented on a non-staggered Cartesian grid. The incompressible Navier-Stokes is decoupled with an improved five-step incremental pressure correction algorithm. Fluid-fluid interface is captured using the Cahn-Hilliard equation, and the surface tension model is coupled with a momentum-weighted interpolation scheme to suppress unphysical pressure oscillations, ensuring accurate evolution of multiphase interfaces. Interaction at the fluid-structure interface is obtained by implicitly solving for the feedback acceleration in the Eulerian-Lagrangian system. For validation of the present method, the comparison studies for Pressure-Oscillation-Free effect are systematically conducted using lid driving cavity and droplet deformation cases. Moreover, several challenging multiphase simulations are implemented and discussed. As a demonstrating example of fluid-structure interaction, a rising bubble bypassing an obstacle is tested.

physics.flu-dyn↗

arXiv2024

A GPU-accelerated Cartesian grid method is proposed for solving the heat, wave, and Schrodinger equations on irregular domains

This paper introduces a second-order method for solving general elliptic partial differential equations (PDEs) on irregular domains using GPU acceleration, based on Ying's kernel-free boundary integral (KFBI) method. The method addresses limitations imposed by CFL conditions in explicit schemes and accuracy issues in fully implicit schemes for the Laplacian operator. To overcome these challenges, the paper employs a series of second-order time discrete schemes and splits the Laplacian operator into explicit and implicit components. Specifically, the Crank-Nicolson method discretizes the heat equation in the temporal dimension, while the implicit scheme is used for the wave equation. The Schrodinger equation is treated using the Strang splitting method. By discretizing the temporal dimension implicitly, the heat, wave, and Schrodinger equations are transformed into a sequence of elliptic equations. The Laplacian operator on the right-hand side of the elliptic equation is obtained from the numerical scheme rather than being discretized and corrected by the five-point difference method. A Cartesian grid-based KFBI method is employed to solve the resulting elliptic equations. GPU acceleration, achieved through a parallel Cartesian grid solver, enhances the computational efficiency by exploiting high degrees of parallelism. Numerical results demonstrate that the proposed method achieves second-order accuracy for the heat, wave, and Schrodinger equations. Furthermore, the GPU-accelerated solvers for the three types of time-dependent equations exhibit a speedup of 30 times compared to CPU-based solvers.

math.NA↗

arXiv2024

A Hybrid Kernel-Free Boundary Integral Method with Operator Learning for Solving Parametric Partial Differential Equations In Complex Domains

The Kernel-Free Boundary Integral (KFBI) method presents an iterative solution to boundary integral equations arising from elliptic partial differential equations (PDEs). This method effectively addresses elliptic PDEs on irregular domains, including the modified Helmholtz, Stokes, and elasticity equations. The rapid evolution of neural networks and deep learning has invigorated the exploration of numerical PDEs. An increasing interest is observed in deep learning approaches that seamlessly integrate mathematical principles for investigating numerical PDEs. We propose a hybrid KFBI method, integrating the foundational principles of the KFBI method with the capabilities of deep learning. This approach, within the framework of the boundary integral method, designs a network to approximate the solution operator for the corresponding integral equations by mapping the parameters, inhomogeneous terms and boundary information of PDEs to the boundary density functions, which can be regarded as the solution of the integral equations. The models are trained using data generated by the Cartesian grid-based KFBI algorithm, exhibiting robust generalization capabilities. It accurately predicts density functions across diverse boundary conditions and parameters within the same class of equations. Experimental results demonstrate that the trained model can directly infer the boundary density function with satisfactory precision, obviating the need for iterative steps in solving boundary integral equations. Furthermore, applying the inference results of the model as initial values for iterations is also reasonable; this approach can retain the inherent second-order accuracy of the KFBI method while accelerating the traditional KFBI approach by reducing about 50% iterations.

cs.LG↗

arXiv2024

A GPU-accelerated Cartesian grid method for PDEs on irregular domain

The kernel-free boundary integral (KFBI) method has successfully solved partial differential equations (PDEs) on irregular domains. Diverging from traditional boundary integral methods, the computation of boundary integrals in KFBI is executed through the resolution of equivalent simple interface problems on Cartesian grids, utilizing fast algorithms. While existing implementations of KFBI methods predominantly utilize CPU platforms, GPU architecture's superior computational capabilities and extensive memory bandwidth offer an efficient resolution to computational bottlenecks. This paper delineates the algorithms adapted for both single-GPU and multiple-GPU applications. On a single GPU, assigning individual threads can control correction, interpolation, and jump calculations. The algorithm is expanded to multiple GPUs to enhance the processing of larger-scale problems. The arrowhead decomposition method is employed in multiple-GPU settings, ensuring optimal computational efficiency and load balancing. Numerical examples show that the proposed algorithm is second-order accurate and efficient. Single-GPU solver speeds 50-200 times than traditional CPU while the eight GPUs distributed solver yields up to 60% parallel efficiency.

math.NA↗

arXiv2024

PM2D: A parallel GPU-based code for the kinetic simulation of laser plasma instabilities in large scale plasmas

Laser plasma instabilities (LPIs) have significant influences on the laser energy deposition efficiency, hot electron generation, and uniformity of irradiation in inertial confined fusion (ICF). In contrast to theoretical analysis of linear development of LPIs, numerical simulations play a more and more important role in revealing the complex physics of LPIs. Since LPIs are typically a three-wave coupling process, the precise kinetic simulation of LPIs requires to resolve the laser period (around one femtosecond) and laser wavelength (less than one micron). In this paper, a full wave fluid model of LPIs is constructed and numerically solved by the particle-mesh method, where the plasma is described by macro particles that can move across the mesh grids freely. Based upon this model, a two-dimensional (2D) GPU code named PM2D is developed. It can simulate the kinetic effects of LPIs self-consistently as normal particle-in-cell (PIC) codes. Moreover, as the physical model adopted in the PM2D code is specifically constructed for LPIs, the required macro particles per grid in the simulations can be largely reduced and thus overall simulation cost is considerably reduced comparing with typical PIC codes. Moreover, the numerical noise in our PM2D code is much lower, which makes it more robust than PIC codes in the simulation of LPIs for the long-time scale above 10 picoseconds. After the distributed computing is realized, our PM2D code is able to run on GPU clusters with a total mesh grids up to several billions, which meets the typical requirements for the simulations of LPIs at ICF experimental scale with reasonable cost.

physics.plasm-ph↗

arXiv2024

High-accurate and efficient numerical algorithms for the self-consistent field theory of liquid-crystalline polymers

Self-consistent field theory (SCFT) is one of the most widely-used framework in studying the equilibrium phase behaviors of inhomogenous polymers. For liquid crystalline polymeric systems, the main numerical challenges of solving SCFT encompass efficiently solving plenty of six dimensional partial differential equations (PDEs), precisely determining the subtle energy difference among self-assembled structures, and developing effective iterative methods for nonlinear SCF iteration. To address these challenges, this work introduces a suite of high-order and efficient numerical methods tailored for SCFT of liquid-crystalline polymers. These methods include various advaced PDE solvers, an improved Anderson iteration algorithm to accelerate SCFT calculations, and an optimization technique of adjusting the computational domain during the SCF iterations. Extensive numerical tests demonstrate the efficiency of the proposed methods. Based on these algorithms, we further explore the self-assembly behavior of liquid crystalline polymers through simulations in four, five, and six dimensions, uncovering intricate three-dimensional spatial structures.

math.NA↗

arXiv2023

Auto-ICell: An Accessible and Cost-Effective Integrative Droplet Microfluidic System for Real-Time Single-Cell Morphological and Apoptotic Analysis

The Auto-ICell system, a novel, and cost-effective integrated droplet microfluidic system, is introduced for real-time analysis of single-cell morphology and apoptosis. This system integrates a 3D-printed microfluidic chip with image analysis algorithms, enabling the generation of uniform droplet reactors and immediate image analysis. The system employs a color-based image analysis algorithm in the bright field for droplet content analysis. Meanwhile, in the fluorescence field, cell apoptosis is quantitatively measured through a combination of deep-learning-enabled multiple fluorescent channel analysis and a live/dead cell stain kit. Breast cancer cells are encapsulated within uniform droplets, with diameters ranging from 70 {\mu}m to 240 {\mu}m, generated at a high throughput of 1,500 droplets per minute. Real-time image analysis results are displayed within 2 seconds on a custom graphical user interface (GUI). The system provides an automatic calculation of the distribution and ratio of encapsulated dyes in the bright field, and in the fluorescent field, cell blebbing and cell circularity are observed and quantified respectively. The Auto-ICell system is non-invasive and provides online detection, offering a robust, time-efficient, user-friendly, and cost-effective solution for single-cell analysis. It significantly enhances the detection throughput of droplet single-cell analysis by reducing setup costs and improving operational performance. This study highlights the potential of the Auto-ICell system in advancing biological research and personalized disease treatment, with promising applications in cell culture, biochemical microreactors, drug carriers, cell-based assays, synthetic biology, and point-of-care diagnostics.

eess.IV↗