论文标题
通过物理知情的神经网络，通过高度损坏的数据进行了强大的回归
Robust Regression with Highly Corrupted Data via Physics Informed Neural Networks
论文作者
论文摘要
已经提出了物理知识的神经网络（PINN）来解决两个主要问题类别：数据驱动的解决方案和数据驱动的部分微分方程的发现。由于可能的传感器机制失败，此类数据高度损坏时，此任务变得过于艰难。我们建议基于绝对偏差的PINN（LAD -PINN）重建解决方案并恢复PDE中的未知参数 - 即使伪数据或异常值损害了很大一部分观测值，也是如此。为了进一步提高恢复隐藏物理的准确性，提出了两阶段的基于绝对偏差的PINN（MAD-PINN），其中提出了LAD-PINN用作离群检测器，然后用MAD筛选出高度损坏的数据。然后，可以应用香草Pinn或其变体来利用其余的正常数据。通过几个示例，包括泊松方程，波动方程以及稳定或不稳定的Navier-Stokes方程，我们说明了从噪声和高度损坏的测量数据中恢复管理方程的提议算法的普遍性，准确性和效率。
Physics-informed neural networks (PINNs) have been proposed to solve two main classes of problems: data-driven solutions and data-driven discovery of partial differential equations. This task becomes prohibitive when such data is highly corrupted due to the possible sensor mechanism failing. We propose the Least Absolute Deviation based PINN (LAD-PINN) to reconstruct the solution and recover unknown parameters in PDEs - even if spurious data or outliers corrupt a large percentage of the observations. To further improve the accuracy of recovering hidden physics, the two-stage Median Absolute Deviation based PINN (MAD-PINN) is proposed, where LAD-PINN is employed as an outlier detector followed by MAD screening out the highly corrupted data. Then the vanilla PINN or its variants can be subsequently applied to exploit the remaining normal data. Through several examples, including Poisson's equation, wave equation, and steady or unsteady Navier-Stokes equations, we illustrate the generalizability, accuracy and efficiency of the proposed algorithms for recovering governing equations from noisy and highly corrupted measurement data.
