Comments (2)
感谢作者分享的代码,在阅读过程中遇到一些疑问希望作者能够解答。
第一,在一维热传导方程的训练中,作者将解析解生成的数据带入损失函数,获得的模型,是否存在不妥,
第二,同时在边界条件获取的时候,边界条件为解析解求导得到的方程式,其实在很多时候我们是希望PINN能够解不存在解析解的模型
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@xuzhiwen155
感谢作者分享的代码,在阅读过程中遇到一些疑问希望作者能够解答。
第一,在一维热传导方程的训练中,作者将解析解生成的数据带入损失函数,获得的模型,是否存在不妥,
第二,同时在边界条件获取的时候,边界条件为解析解求导得到的方程式,其实在很多时候我们是希望PINN能够解不存在解析解的模型
感谢您的提问,文中示例的代码只是一个便于实现的demo,因此关于您提问的两个问题其实是做了简化。我用的是一个存在解析解的简单例子,因此所有的数据都用解析解直接生成,这样一是产生模型训练数据比较方便,二是方便将模型拟合效果与解析解直接比较。实际应用中,用来训练模型的数据通常是用数值模拟的方法生成,包括边界条件的数据。文中的简单例子肯定有很多与实际应用场景不符的地方,还望见谅。
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