标题： 基于深度神经网络的数据驱动代理建模方法对DSMC解的模拟 显示英文标题

标题： Data-Driven Surrogate Modeling of DSMC Solutions Using Deep Neural Networks

摘要： 本研究提出了一种深度神经网络（DNN）框架，该框架加速了稀薄气体流动的直接模拟蒙特卡洛（DSMC）计算，同时保持了高物理保真度。首先，一个全连接的深度神经网络在七种温度（200-650 K）的高质量DSMC数据上进行训练，以再现氩气的麦克斯韦-玻尔兹曼速度分布。将物理边界点注入训练集，可以确保正确的低速极限。它将均方误差降低到10^-5以下，从而将每次DSMC运行的推理时间从几十分钟减少到毫秒级。对于一维激波，配备可学习傅里叶特征的多输出网络学习密度、速度和温度的完整剖面。仅在马赫数1.4-1.9范围内进行训练，它对马赫数2和2.5的情况预测与DSMC有近乎完美的吻合，展示了强大的训练外泛化能力。在驱动腔中，通过“专家族”策略处理克努森数的广泛参数范围：在离散的克努森（Kn）值上分别训练专业模型，并通过对数空间插值融合它们的输出。这种混合代理模型在未见过的Kn下以小于2%的空间误差恢复完整的二维速度和温度场。关键创新包括（i）在数据预处理过程中显式注入物理约束，（ii）可学习的傅里叶特征映射以捕捉陡峭的激波梯度，以及（iii）模块化的专家-插值方案以覆盖广泛的克努森范围。它们共同建立了一个通用的可靠、快速代理模型方法，可以扩展到非平衡现象、气体混合物和设计优化流程。 显示英文摘要

摘要： This study presents a deep neural network (DNN) framework that accelerates Direct Simulation Monte Carlo (DSMC) computations for rarefied-gas flows, while maintaining high physical fidelity. First, a fully connected deep neural network is trained on high-quality DSMC data for seven temperatures (200-650 K) to reproduce the Maxwell-Boltzmann speed distribution of argon. Injecting the physical boundary point into the training set enforces the correct low-speed limit. It reduces the mean-squared error to below 10^-5, thereby decreasing inference time from tens of minutes per DSMC run to milliseconds. For one-dimensional shock waves, a multi-output network equipped with learnable Fourier features learns the complete profiles of density, velocity, and temperature. Trained only on Mach numbers 1.4-1.9, it predicts a Mach 2 and 2.5 case with near-perfect agreement to DSMC, demonstrating robust out-of-training generalization. In a lid-driven cavity, the large parametric spread in Knudsen number is handled by a "family-of-experts" strategy: separate specialist models are trained at discrete Knudsen (Kn) values, and log-space interpolation fuses their outputs. This hybrid surrogate recovers the full 2-D velocity and temperature fields at unseen Kn with less than 2% spatial error. Key innovations include (i) explicit injection of physical constraints during data preprocessing, (ii) learnable Fourier feature mapping to capture steep shock gradients, and (iii) a modular expert-interpolation scheme to cover wide Knudsen ranges. Together, they establish a general recipe for trustworthy, rapid surrogate models that can be extended to non-equilibrium phenomena, gas mixtures, and design optimization workflows