论文标题
使用稀疏标签的随机传感器进行状态估计的能源网络
Energy networks for state estimation with random sensors using sparse labels
论文作者
论文摘要
每当我们处理高维动力系统时，就需要进行状态估计，因为完整的测量通常不可用。这是获得洞察力，执行控制或优化设计任务的关键。大多数基于深度学习的方法都需要高分辨率标签并与固定传感器位置一起工作，从而在其范围中受到限制。同样，在稀疏数据上进行适当的正交分解（POD）是不平凡的。为了解决这些问题，我们提出了一种具有隐式优化层和基于物理损耗功能的技术，该功能可以从稀疏标签中学习。它通过最大程度地减少神经网络预测的能量来起作用，使其能够在不同位置与不同数量的传感器一起使用。基于此技术，我们提出了两个用于空间中离散和连续预测的模型。我们使用两个高维流体问题的汉堡方程式和流动缸的流动性问题来证明性能，以进行离散模型，并使用Allen CAHN方程和对流扩散方程进行连续模型。我们显示模型对测量中的噪声也很强。
State estimation is required whenever we deal with high-dimensional dynamical systems, as the complete measurement is often unavailable. It is key to gaining insight, performing control or optimizing design tasks. Most deep learning-based approaches require high-resolution labels and work with fixed sensor locations, thus being restrictive in their scope. Also, doing Proper orthogonal decomposition (POD) on sparse data is nontrivial. To tackle these problems, we propose a technique with an implicit optimization layer and a physics-based loss function that can learn from sparse labels. It works by minimizing the energy of the neural network prediction, enabling it to work with a varying number of sensors at different locations. Based on this technique we present two models for discrete and continuous prediction in space. We demonstrate the performance using two high-dimensional fluid problems of Burgers' equation and Flow Past Cylinder for discrete model and using Allen Cahn equation and Convection-diffusion equations for continuous model. We show the models are also robust to noise in measurements.
