论文标题
对波动力方程的非平稳解决方案的深度学习近似
A Deep Learning Approximation of Non-Stationary Solutions to Wave Kinetic Equations
论文作者
论文摘要
我们提出了深度学习近似，基于随机优化的波动力学方程方法。为了建立对我们的方法的信心，我们将方法应用于Smoluchowski凝血方程，并具有具有分析溶液的乘法核。然后，我们的深度学习方法被用来将非平稳解决方案近似于与声波系统相对应的3波动力学方程。为了验证神经网络近似，我们将总能量的衰减速率与先前获得的理论结果进行了比较。提出了有限体积解决方案，并将其与当前方法进行比较。
We present a deep learning approximation, stochastic optimization based, method for wave kinetic equations. To build confidence in our approach, we apply the method to a Smoluchowski coagulation equation with multiplicative kernel for which an analytic solution exists. Our deep learning approach is then used to approximate the non-stationary solution to a 3-wave kinetic equation corresponding to acoustic wave systems. To validate the neural network approximation, we compare the decay rate of the total energy with previously obtained theoretical results. A finite volume solution is presented and compared with the present method.
