论文标题
具有未知测量噪声的物理信息神经网络
Physics-informed Neural Networks with Unknown Measurement Noise
论文作者
论文摘要
物理知识的神经网络（PINN）构成了一种灵活的方法，可以找到解决方案和识别偏微分方程的参数。大多数关于该主题的作品都假设无噪声数据或被弱高斯噪声污染的数据。我们表明，在非高斯噪声的情况下，标准的Pinn框架会崩溃。我们提供了解决这个基本问题的方法，并建议共同培训基于能量的模型（EBM）以学习正确的噪声分布。我们使用多个示例说明了方法的改进性能。
Physics-informed neural networks (PINNs) constitute a flexible approach to both finding solutions and identifying parameters of partial differential equations. Most works on the topic assume noiseless data, or data contaminated with weak Gaussian noise. We show that the standard PINN framework breaks down in case of non-Gaussian noise. We give a way of resolving this fundamental issue and we propose to jointly train an energy-based model (EBM) to learn the correct noise distribution. We illustrate the improved performance of our approach using multiple examples.
