论文标题
耦合粘性汉堡方程的快速模拟的深度有限差模拟器
A Deep Finite Difference Emulator for the Fast Simulation of Coupled Viscous Burgers' Equation
论文作者
论文摘要
这项工作提出了一种基于学习的模拟器，用于有效地计算具有随机初始条件的耦合粘性汉堡方程。在与传统数据驱动的深度学习方法背道而驰的情况下，提出的模拟器不需要经典的数值求解器来收集培训数据。相反，它可以直接使用问题的物理学。具体而言，该模型模拟了二阶有限差求解器，即学习动力学中的曲柄 - 尼科尔森方案。进行了系统的案例研究，以检查模型的预测性能，泛化能力和计算效率。计算的结果是图形表示的，并将其与最新数值求解器的结果进行了比较。
This work proposes a deep learning-based emulator for the efficient computation of the coupled viscous Burgers' equation with random initial conditions. In a departure from traditional data-driven deep learning approaches, the proposed emulator does not require a classical numerical solver to collect training data. Instead, it makes direct use of the problem's physics. Specifically, the model emulates a second-order finite difference solver, i.e., the Crank-Nicolson scheme in learning dynamics. A systematic case study is conducted to examine the model's prediction performance, generalization ability, and computational efficiency. The computed results are graphically represented and compared to those of state-of-the-art numerical solvers.
