物理通知神经网络代码二维瞬态问题(PINN-2DT)与谷歌Colab兼容

Paweł Maczuga, Maciej Skoczeń, Przemysław Rożnawski, Filip Tłuszcz, Marcin Szubert, Marcin Łoś, Witold Dzwinel, Keshav Pingali, Maciej Paszyński
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引用次数: 0

摘要

我们提出了一个开源的物理信息神经网络环境,用于模拟二维矩形域上的瞬态现象,具有以下特点:(1)它与Google Colab兼容,允许在云环境下自动执行;(2)支持二维时变偏微分方程;(3)为剩余损失、边界条件和初始损失及其权值的定义提供了简单的界面;(4)支持Neumann和Dirichlet边界条件;(5)允许自定义层数和每层神经元数,以及任意激活函数;(6)可作为参数的学习率和epoch个数;(7)根据时空变量自动区分PINN;(8)它提供了用于绘制收敛(具有运行平均值)的例程,学习的初始条件,模拟和电影中的2d和3D快照(9)它包括一个问题库:(a)非平稳传热;(b)波浪方程模拟海啸;(c)大气模拟,包括热反演;(d)肿瘤生长模拟。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Physics Informed Neural Network Code for 2D Transient Problems (PINN-2DT) Compatible with Google Colab
We present an open-source Physics Informed Neural Network environment for simulations of transient phenomena on two-dimensional rectangular domains, with the following features: (1) it is compatible with Google Colab which allows automatic execution on cloud environment; (2) it supports two dimensional time-dependent PDEs; (3) it provides simple interface for definition of the residual loss, boundary condition and initial loss, together with their weights; (4) it support Neumann and Dirichlet boundary conditions; (5) it allows for customizing the number of layers and neurons per layer, as well as for arbitrary activation function; (6) the learning rate and number of epochs are available as parameters; (7) it automatically differentiates PINN with respect to spatial and temporal variables; (8) it provides routines for plotting the convergence (with running average), initial conditions learnt, 2D and 3D snapshots from the simulation and movies (9) it includes a library of problems: (a) non-stationary heat transfer; (b) wave equation modeling a tsunami; (c) atmospheric simulations including thermal inversion; (d) tumor growth simulations.
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