arXiv subjects

Weizong Wang

Publications and source records attributed to Weizong Wang.

4 recordsLinked to original sources

arXiv2026

ChatCFD: An LLM-Driven Agent for End-to-End CFD Automation with Structured Knowledge and Reasoning

Computational Fluid Dynamics (CFD) is critical for scientific advancement but is hindered by operational complexity and high expertise barriers. This paper introduces ChatCFD, a Large Language Model (LLM)-driven multi-agent system designed for end-to-end CFD automation using OpenFOAM. Powered by DeepSeek-R1/V3, ChatCFD integrates structured domain knowledge bases, a precise error locator, and iterative reflection to dramatically outperform existing methods. On 315 benchmark cases, ChatCFD achieves 82.1% execution success (vs. 6.2% for MetaOpenFOAM and 42.3% for Foam-Agent) and 68.12% physical fidelity - a novel metric assessing scientific meaningfulness beyond mere runnability. A dedicated Physics Interpreter attains 97.4% summary fidelity, bridging the gap between narrative fluency and the enforcement of tight physical constraints. Resource analysis confirms efficiency, averaging 192.1k tokens and $0.208 per case, significantly lower than baseline costs. Ablation studies identify the Error Locator and Solver Template DB as critical, with the latter's removal collapsing accuracy to 48%. The system exhibits robust flexibility, achieving 95.23% success in autonomous solver selection and 100% in turbulence modeling, while successfully reproducing complex literature cases (e.g., NACA0012, supersonic nozzle) with 60-80% success rates where baselines failed. Featuring a modular, MCP-compatible design, ChatCFD facilitates scalable, collaborative AI-driven CFD. Code is available at: https://github.com/ConMoo/ChatCFD

cs.CL↗

arXiv2026

Numerical Error Analysis of the Poisson Equation under RHS Inaccuracies in Particle-in-Cell Simulations

Particle-in-Cell (PIC) simulations rely on accurate solutions of the electrostatic Poisson equation, yet accuracy often deteriorates near irregular Dirichlet boundaries on Cartesian meshes. While much research has addressed discretization errors on the left-hand side (LHS) of the Poisson equation, the impact of right-hand-side (RHS) inaccuracies - arising from charge density sampling near boundaries in PIC methods - remains largely unexplored. This study analyzes the numerical errors induced by underestimated RHS values at near-boundary nodes when solving the Poisson equation using embedded boundary finite difference schemes with linear and quadratic treatments. Analytical derivations in one dimension and truncation error analyses in two dimensions reveal that such RHS inaccuracies modify local truncation behavior differently: they reduce the dominant truncation error in the linear scheme but introduce a zeroth-order term in the quadratic scheme, leading to larger global errors. Numerical experiments in one-, two-, and three-dimensional domains confirm these findings. Contrary to expectations, the linear scheme yields superior overall accuracy under typical PIC-induced RHS inaccuracies. A simple RHS calibration strategy is further proposed to restore the accuracy of the quadratic scheme. These results offer new insight into the interplay between boundary-induced RHS errors and discretization accuracy in Poisson-type problems.

math.NA↗

arXiv2025

An output scaling layer boosts deep neural networks for multiscale ODE systems

Simulating complex diffusion-reaction systems is often prohibitively expensive due to the high dimensionality and stiffness of the underlying ODEs, where state variables may span tens of orders of magnitude. Deep learning has recently emerged as a powerful tool in scientific computing, achieving remarkable progress in modeling and sampling stiff systems. However, data scaling techniques remain largely underexplored, despite their crucial role in addressing the frequency bias of deep neural networks when handling multi-magnitude or high-frequency data. In this work, we propose the Generalized Box-Cox Transformation (GBCT), a novel nonlinear scaling method designed to mitigate multiscale challenges by rescaling inherent multi-magnitude components toward a more consistent order of magnitude. We integrate GBCT into our previous data-driven framework and evaluate its performance against the original baseline surrogate model across six representative scenarios: a 21-species chemical reaction kinetics, a 13-isotope nuclear reaction model, the well-known Robertson problem coupled with diffusion, and practically relevant simulations of two-dimensional turbulent reaction-diffusion systems as well as one- and two-dimensional nuclear reactive flows. Numerical experiments demonstrate that GBCT reduces prediction errors by up to two orders of magnitude compared with the baseline model - particularly in the long-term evolution of dynamical systems - and achieves comparable performance with only about one-sixth of the training epochs. Frequency analysis further reveals that GBCT rescales high-frequency components of the objective function toward lower frequencies to align with the neural network's natural low frequency bias, thereby boosting training and generalization. The source code to reproduce the results in this paper is available at https://github.com/Seauagain/GBCT.

math.DS↗

arXiv2025

Solving multiscale dynamical systems by deep learning

Multiscale dynamical systems, modeled by high-dimensional stiff ordinary differential equations (ODEs) with wide-ranging characteristic timescales, arise across diverse fields of science and engineering, but their numerical solvers often encounter severe efficiency bottlenecks. This paper introduces a novel DeePODE method, which consists of an Evolutionary Monte Carlo Sampling method (EMCS) and an efficient end-to-end deep neural network (DNN) to predict multiscale dynamical systems. We validate this finding across dynamical systems from ecological systems to reactive flows, including a predator-prey model, a power system oscillation, a battery electrolyte thermal runaway, and turbulent reaction-diffusion systems with complex chemical kinetics. The method demonstrates robust generalization capabilities, allowing pre-trained DNN models to accurately predict the behavior in previously unseen scenarios, largely due to the delicately constructed dataset. While theoretical guarantees remain to be established, empirical evidence shows that DeePODE achieves the accuracy of implicit numerical schemes while maintaining the computational efficiency of explicit schemes. This work underscores the crucial relationship between training data distribution and neural network generalization performance. This work demonstrates the potential of deep learning approaches in modeling complex dynamical systems across scientific and engineering domains.

math.NA↗