论文标题
$ξ$ -torch：可区分的科学计算库
$ξ$-torch: differentiable scientific computing library
论文作者
论文摘要
物理知识的学习已显示出比没有物理先验的学习更好的概括。 但是，培训物理学的深神经网络需要以不同的方式编写物理模拟的某些方面。 不幸的是，某些在物理模拟中常用的操作和功能是分散的，难以集成，并且缺乏物理模拟中需要的更高阶数。 在这项工作中，我们提出了$ξ$ -torch，这是一个可与科学模拟的可区分功能的库。 示例功能是根发现器和初始值问题解决者。 $ξ$ -torch中功能的梯度是根据其分析表达式编写的，以提高数值稳定性并减少内存需求。 $ξ$ -torch还提供了在现有软件包中很少可用的功能的第二和更高阶导数。 我们显示了该库在优化物理模拟中的参数时的两个应用。 可以在https://github.com/xitorch/xitorch/以及https://xitorch.readthedocs.io的文档上找到库和所有测试用例。
Physics-informed learning has shown to have a better generalization than learning without physical priors. However, training physics-informed deep neural networks requires some aspect of physical simulations to be written in a differentiable manner. Unfortunately, some operations and functionals commonly used in physical simulations are scattered, hard to integrate, and lack higher order derivatives which are needed in physical simulations. In this work, we present $ξ$-torch, a library of differentiable functionals for scientific simulations. Example functionals are a root finder and an initial value problem solver, among others. The gradient of functionals in $ξ$-torch are written based on their analytical expression to improve numerical stability and reduce memory requirements. $ξ$-torch also provides second and higher order derivatives of the functionals which are rarely available in existing packages. We show two applications of this library in optimizing parameters in physics simulations. The library and all test cases in this work can be found at https://github.com/xitorch/xitorch/ and the documentation at https://xitorch.readthedocs.io.
