【源码】物理信息神经网络设计与仿真

我们介绍的物理信息神经网络-神经网络是通过训练来解决监督学习任务，同时遵守一般非线性偏微分方程描述的任何给定物理定律的神经网络。

We introduce physics informed neural networks – neural networks that are trained to solve supervised learning tasks while respecting any given law of physics described by general nonlinear partial differential equations.

我们介绍了在解决两类主要问题方面的进展：数据驱动解和数据驱动的偏微分方程的发现。

We present our developments in the context of solving two main classes of problems: data-driven solution and data-driven discovery of partial differential equations.

根据可用数据的性质和排列，我们设计了两类不同的算法，即连续时间模型和离散时间模型。

Depending on the nature and arrangement of the available data, we devise two distinct classes of algorithms, namely continuous time and discrete time models.

由此产生的神经网络形成了一类新的数据有效的通用函数逼近器，自然地将任何潜在的物理规律编码为先验信息。

The resulting neural networks form a new class of data-efficient universal function approximators that naturally encode any underlying physical laws as prior information.

在第一部分中，我们展示了如何利用这些网络来推断偏微分方程的解，并获得了物理意义上的代理模型，这些模型对于所有输入坐标和自由参数都是完全可微的。

In the first part, we demonstrate how these networks can be used to infer solutions to partial differential equations, and obtain physics-informed surrogate models that are fully differentiable with respect to all input coordinates and free parameters.

在第二部分中，我们重点讨论数据驱动的偏微分方程发现问题。

In the second part, we focus on the problem of data-driven discovery of partial differential equations.

For more information, please refer to the following: (https://maziarraissi.github.io/PINNs/)

参考文献：

Raissi, Maziar, Paris Perdikaris, and George E. Karniadakis. “Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations.” Journal of Computational Physics 378 (2019): 686-707.

Raissi, Maziar, Paris Perdikaris, and George Em Karniadakis. “Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations.” arXiv preprint arXiv:1711.10561 (2017).

Raissi, Maziar, Paris Perdikaris, and George Em Karniadakis. “Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations.” arXiv preprint arXiv:1711.10566 (2017).

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