Zezheng Song

Haixin Wang, Yadi Cao, Zijie Huang et al. · stanford

This paper explores the recent advancements in enhancing Computational Fluid Dynamics (CFD) tasks through Machine Learning (ML) techniques. We begin by introducing fundamental concepts, traditional methods, and benchmark datasets, then examine the various roles ML plays in improving CFD. The literature systematically reviews papers in recent five years and introduces a novel classification for forward modeling: Data-driven Surrogates, Physics-Informed Surrogates, and ML-assisted Numerical Solutions. Furthermore, we also review the latest ML methods in inverse design and control, offering a novel classification and providing an in-depth discussion. Then we highlight real-world applications of ML for CFD in critical scientific and engineering disciplines, including aerodynamics, combustion, atmosphere & ocean science, biology fluid, plasma, symbolic regression, and reduced order modeling. Besides, we identify key challenges and advocate for future research directions to address these challenges, such as multi-scale representation, physical knowledge encoding, scientific foundation model and automatic scientific discovery. This review serves as a guide for the rapidly expanding ML for CFD community, aiming to inspire insights for future advancements. We draw the conclusion that ML is poised to significantly transform CFD research by enhancing simulation accuracy, reducing computational time, and enabling more complex analyses of fluid dynamics. The paper resources can be viewed at https://github.com/WillDreamer/Awesome-AI4CFD.

Zezheng Song, Maria K. Cameron, Haizhao Yang

Transition path theory (TPT) is a mathematical framework for quantifying rare transition events between a pair of selected metastable states $A$ and $B$. Central to TPT is the committor function, which describes the probability to hit the metastable state $B$ prior to $A$ from any given starting point of the phase space. Once the committor is computed, the transition channels and the transition rate can be readily found. The committor is the solution to the backward Kolmogorov equation with appropriate boundary conditions. However, solving it is a challenging task in high dimensions due to the need to mesh a whole region of the ambient space. In this work, we explore the finite expression method (FEX, Liang and Yang (2022)) as a tool for computing the committor. FEX approximates the committor by an algebraic expression involving a fixed finite number of nonlinear functions and binary arithmetic operations. The optimal nonlinear functions, the binary operations, and the numerical coefficients in the expression template are found via reinforcement learning. The FEX-based committor solver is tested on several high-dimensional benchmark problems. It gives comparable or better results than neural network-based solvers. Most importantly, FEX is capable of correctly identifying the algebraic structure of the solution which allows one to reduce the committor problem to a low-dimensional one and find the committor with any desired accuracy.

Chengxin Hu, Hao Li, Yihe Yuan et al.

In the molecular domain, numerous studies have explored the use of multimodal large language models (LLMs) to construct a general-purpose, multi-task molecular model. However, these efforts are still far from achieving a truly universal molecular model. We identify three key challenges in this endeavor: (1) Existing molecular task datasets are typically small in scale and lack comprehensive domain coverage. (2) Tasks from different molecular subfields are difficult to effectively learn jointly through LLMs due to significant distributional shifts and competition among tasks, which introduces instability in the learning process. (3) Both inter-task and intra-task molecular representations demand different intrinsic dimensions in the language space, making it challenging to balance between redundancy and insufficiency in language model representations. To address these challenges, we innovatively categorize existing small-molecule tasks into four types: Mol2Mol, Mol2Text, Mol2Num, and Text2Mol. We then collect a dataset encompassing over 16 tasks with more than 1.4 million samples, making it the largest molecular instruction-tuning dataset to date. Leveraging the extensive pretraining of LLMs on existing chemical literature, we propose a novel multimodal LLM framework, named Omni-Mol, which unifies all small-molecule tasks and supports both molecular generation and understanding. The core of Omni-Mol is our proposed MoGE, which dynamically adapts to the intrinsic rank of different tasks. This mixture-of-experts architecture enhances the model's ability to handle diverse tasks and modalities effectively. Our model achieves unified instruction tuning across 16 tasks and attains state-of-the-art performance on 13 of them. Extensive experiments further demonstrate the scalability and versatility of Omni-Mol.