人工智能加速科学仿真、设计、控制和发现

doi:10.19596/j.cnki.1001-246x.9020

摘要/Abstract

摘要：

近年来, 随着AI for science(科学智能)的蓬勃发展, 人工智能与各门学科的交叉融合逐渐成为一个显著的科学研究趋势。但是, AI for science所涉及的范围很广、学科众多, 因此, 将其梳理成一个统一的体系能够更好地为初入领域的研究者导航。本文认为, 尽管每一门学科研究的对象、方法看似千差万别, 但人工智能可以为科学研究提供一套普适的范式和方法, 解决各科学领域内的重要问题。本文将从科学仿真、设计和控制、发现三个方面展开综述, 明确任务设置, 梳理当前的代表性工作, 并通过具体的例子, 阐释人工智能如何为科学研究助力, 以期使读者能够更好应用已有的方法, 或者研究新的方法。

关键词: 人工智能, 科学仿真, 设计, 控制, 科学发现

Abstract:

With the vigorous development of AI for Science in recent years, the integration of artificial intelligence and various scientific disciplines has become a major trend. However, AI for Science covers a wide range and involves many disciplines. Therefore, organizing it into a unified framework will enable better navigation for newcomers to the field. In this article, we posit that although the objects and methods of scientific research seem to be vastly different, AI can provide a universal paradigm and methods for scientific research in the following three aspects: scientific simulation, design and control, and discovery, solving problems in the field. This article will specifically elaborate on the task setting and current representative work. Through specific examples, we will explain how AI can concretely assist scientific research, facilitating researchers to better apply existing methods or develop novel methods.

Key words: artificial intelligence, scientific simulation, design, control, scientific discovery

吴泰霖. 人工智能加速科学仿真、设计、控制和发现[J]. 计算物理, 2025, 42(2): 127-145.

Tailin WU. AI for Accelerating Scientific Simulation, Design, Control, and Discovery[J]. Chinese Journal of Computational Physics, 2025, 42(2): 127-145.

图/表 24

图1 不同科学领域的大致空间尺度和时间尺度

Fig.1 The spatial and temporal scales for different scientific disciplines

图2 系统动力学的描述设置

Fig.2 Notation for the system's dynamics

图3 不同仿真方法在光谱上的分布(第一性原理的传统数值方法(最左端)、数据驱动(最右端)以及其优势(蓝色)和局限性(橙色)。)

Fig.3 Different simulation methods lying on a spectrum (On the leftmost are classical numerical methods based on first principles. On the rightmost are the pure data-driven methods. Also denoted are the pros and cons for different methods.)

图4 传统数值方法将偏微分方程在时间和空间上离散化以便于数值求解

Fig.4 Classical numerical method discretizes the PDE in time and space to facilitate numerically solving them

图5 AI仿真模型学习代理模型fθ，最小化预测误差

Fig.5 AI-based simulation method learns a surrogate model fθ and minimizes prediction error

表1 AI仿真模型常用神经网络架构及其优缺点

Table 1 Commonly used neural network architecture of AI simulation model and its advantages and disadvantages

	优点	缺点
GNN (图神经网络)	显示地对对象和它们之间关系建模；适用于描述相互作用复杂、非规则网格等；需要较少的样本	基础的GNN难以对长程影响建模，需要添加多尺度的边
Transformer (变换器架构)	比较适合建模长程关系	参数量较多，需要较多的训练数据
U-Net (U型神经网络)	能够建模规则网格中多尺度的动力学	只能用于规则网格
Neural operator (神经算子)	能够实现超分辨率	大部分只能适用于规则网格，需要较多训练数据

表2 AI仿真模型常用学习范式及其优缺点

Table 2 Common learning paradigms of AI simulation models and their advantages and disadvantages

	优点	缺点
回归	最常用场景	学习的代理模型对于分布外数据泛化性较差；预测效果不会超出所给目标
生成模型	适用于任何回归用的场景，更适合于高维系统，更适合整体、长程的优化	需要一定量的训练数据(但随维度增加，训练数据需要量增加没有回归快)
强化学习	预测效果需要超出所给的目标；在整个环境无法求导时仍可以优化	样本效率较低，需要与环境的大量交互
物理信息	知道系统的控制方程，可以减少样本的需要量	难以泛化到新的边界或者初始条件；系统控制方程不一定准确

图6 GNS将物理系统建模成粒子系统，模拟水流(左)、沙子(中)、胶泥(右)的含时演化[14] (a) GNS预测结果；(b) 经过渲染后的结果

Fig.6 GNS models a physical system as a particle-based system, simulating the temporal dynamics of water (left), sand (middle), and gel (right)[14] (a) prediction results of GNS; (b) after rending

图7 GNS[14]网络架构: 系统在t时刻的状态(各粒子的位置和速度)作为输入，经过(c)编码器, (d)消息传递, (e)解码器，预测t+1时刻的加速度，经过欧拉法预测t+1时刻的系统状态。

Fig.7 GNS[14] network architecture: The input to the GNS is the state of the system at time t, including every particle's position and velocity. Then through (c) encoder, (d) message passing, and (e) decoder, it predicts the acceleration at time step t+1. Euler's method is used to predict the state at time step t+1.

图8 (a) HGNS架构[15]; (b) HGNS对水流体积的预测结果(截面)与真实值比较(可见其在20个月内预测效果与真实值精确符合。)

Fig.8 (a) HGNS architecture[15]; (b) its prediction of water volume (cross-section) vs. ground-truth (We see that its prediction matches well with ground-truth.)

图9 GraphCast架构[16](其构建的多尺度图神经网络，可以同时汇聚局域和多尺度的信息。) (a)encoder; (b) processor; (c) decoder; (d) simultaneous multi-mesh message-passing

Fig.9 Architecture of GraphCast[16] (Its multiscale graph network can aggregate local and multiscale information.) (a)encoder; (b) processor; (c) decoder; (d) simultaneous multi-mesh message-passing

图10 神经算子可以将无限维的函数映射到另一个无限维函数

Fig.10 Neural operator can map an infinite-dimensional function to another infinite dimensional function

图11 傅立叶神经算子[26]的网络架构

Fig.11 Architecture for the Fourier neural operators[26]

图12 科学设计和控制的任务设置(根据目标J，优化初始条件u0、控制序列m[0, T]、参数a或者边界$\partial \mathbb{X} $。)

Fig.12 Task setting for scientific design and control (Based on the objective J, it optimizes the initial condition u0, control sequence m[0, T], parameter a or boundary $\partial \mathbb{X} $.)

图13 在文[28]对飞机翼型的设计，优化目标为减小阻力(提出的基于代理模型+反向传播的方法达到传统求解器(DAFoam)优化的性能，并且速度更快。)(a)initial design; (b) optimized design; (c) drag; (d)reward

Fig.13 The airfoil design task in Ref.[28], where the design objective is minimizing drag (The surrogate model+backpropagation proposed by the authors attains similar performance as the classical solver (DAFoam), while significantly faster.) (a)initial design; (b) optimized design; (c) drag; (d) reward

图14 文[30]的实验结果(对于逆问题，如果在原空间进行反向传播优化系统初始条件(第一行，without prior)，则会优化出具有高频噪声的对抗样本。而根据文章所提出的在隐空间进行设计，由于有了先验知识，则能优化出与真实值非常一致的初始条件。)

Fig.14 Experimental results Ref.[30] (For the inverse problem, if backpropagation is performed in the original space to optimize the initial conditions of the system (first row, without prior), it will obtain adversarial samples with high-frequency noise. On the other hand, if performing optimization in the latent space as introduced in the paper, due to the prior knowledge, it will attain the initial conditions that match well with the ground-truth.)

图15 强化学习设置

Fig.15 Task setup for reinforcement learning

图16 瑞士的TCV磁约束可控核聚变托卡马克装置

Fig.16 Tokamakà configuration variable (TCV) fusion device in Switzerland

图17 文[31]的深度强化学习与托卡马克装置交互示意图(a)deployment; (b)TCV; (c)vessel cross section

Fig.17 Illustration of the interaction between the deep reinforcement learning method[31] and the tokamak device in TCV (a)deployment; (b)TCV; (c)vessel cross section

图18 文[35]中训练和推理的方法架构(a)训练时；(b)推理时

Fig.18 Illustration of training and inference pipeline[35] (a)train; (b) compositional design

图19 同时生成的系统仿真轨迹和机翼形状[35] (a)气流水平速度场；(b)气流垂直速度场; (c)压强场(中间红色和蓝色表示机翼形状，并发现在训练中未见的“编队飞行”模式。)

Fig.19 The system's state trajectory and airfoil shape by simultaneously generated[35] (a) horizontal velocity field; (b) vertical velocity field; (c) pressure field. (It also discovers formation flying, which does not appear in training.)

图20 (a) AI费曼架构及(b)其重新发现的部分方程

Fig.20 Architecture of (a) AI Feynman and (b) some of its re-discovered equations

图21 KAN架构[54]

Fig.21 Architecture of KAN[54]

图22 AI笛卡尔架构[64]

Fig.22 Pipeline of AI-descartes[64]

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