A deep learning approximation of non-stationary solutions to wave kinetic equations
A deep learning approximation of non-stationary solutions to wave kinetic equations
复制标题
波动动力学方程非平稳解的深度学习近似
DOI：
10.1016/j.apnum.2022.12.010
复制
发表时间：
2022
影响因子：
2.8
通讯作者：
Bensoussan, Alain
中科院分区：
文献类型：
--
作者：
Walton, Steven;Tran, Minh-Binh;Bensoussan, Alain
我们提出了一种基于随机优化的深度学习近似波动力学方程方法。为了建立对我们方法的信心，我们将该方法应用于具有乘法核的 Smoluchowski 凝固方程，该方程存在解析解。然后，我们的深度学习方法用于近似与声波系统相对应的三波动力学方程的非平稳解。为了验证神经网络近似，我们将总能量的衰减率与之前获得的理论结果进行比较。提出了有限体积解决方案并与现有方法进行了比较。
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.