Zhichao Wang

2papers

2 Papers

3.8LGJan 29Code
LLM4Fluid: Large Language Models as Generalizable Neural Solvers for Fluid Dynamics

Qisong Xiao, Xinhai Chen, Qinglin Wang et al.

Deep learning has emerged as a promising paradigm for spatio-temporal modeling of fluid dynamics. However, existing approaches often suffer from limited generalization to unseen flow conditions and typically require retraining when applied to new scenarios. In this paper, we present LLM4Fluid, a spatio-temporal prediction framework that leverages Large Language Models (LLMs) as generalizable neural solvers for fluid dynamics. The framework first compresses high-dimensional flow fields into a compact latent space via reduced-order modeling enhanced with a physics-informed disentanglement mechanism, effectively mitigating spatial feature entanglement while preserving essential flow structures. A pretrained LLM then serves as a temporal processor, autoregressively predicting the dynamics of physical sequences with time series prompts. To bridge the modality gap between prompts and physical sequences, which can otherwise degrade prediction accuracy, we propose a dedicated modality alignment strategy that resolves representational mismatch and stabilizes long-term prediction. Extensive experiments across diverse flow scenarios demonstrate that LLM4Fluid functions as a robust and generalizable neural solver without retraining, achieving state-of-the-art accuracy while exhibiting powerful zero-shot and in-context learning capabilities. Code and datasets are publicly available at https://github.com/qisongxiao/LLM4Fluid.

4.9LGJan 29
PRISM: Distribution-free Adaptive Computation of Matrix Functions for Accelerating Neural Network Training

Shenghao Yang, Zhichao Wang, Oleg Balabanov et al.

Matrix functions such as square root, inverse roots, and orthogonalization play a central role in preconditioned gradient methods for neural network training. This has motivated the development of iterative algorithms that avoid explicit eigendecompositions and rely primarily on matrix multiplications, making them well suited for modern GPU accelerators. We present PRISM (Polynomial-fitting and Randomized Iterative Sketching for Matrix functions computation), a general framework for accelerating iterative algorithms for computing matrix functions. PRISM combines adaptive polynomial approximation with randomized sketching: at each iteration, it fits a polynomial surrogate to the current spectrum via a sketched least-squares problem, adapting to the instance at hand with minimal overhead. We apply PRISM to accelerate Newton-Schulz-like iterations for matrix square roots and orthogonalization, which are core primitives in machine learning. Unlike prior methods, PRISM requires no explicit spectral bounds or singular value estimates; and it adapts automatically to the evolving spectrum. Empirically, PRISM accelerates training when integrated into Shampoo and Muon optimizers.