论文标题
稀疏限制的神经网络用于模型发现PDE
Sparsely constrained neural networks for model discovery of PDEs
论文作者
论文摘要
在候选特征库上的稀疏回归已作为发现时空数据集的基础的偏微分方程的主要方法。这些功能由高阶导数组成，将模型发现限制为噪声低的数据集。基于神经网络的方法通过构建数据的替代模型来规避此限制，但迄今为止，忽略了稀疏回归算法的进步。在本文中，我们提出了一个模块化框架，该框架动态地确定了使用任何稀疏回归技术的基于深度学习的替代物的稀疏模式。使用我们的新方法，我们介绍了对神经网络的新约束，并展示了不同的网络体系结构和稀疏估计器如何提高模型发现的准确性和在几个基准示例上的收敛性。我们的框架可在\ url {https://github.com/phimal/deepymod}上找到
Sparse regression on a library of candidate features has developed as the prime method to discover the partial differential equation underlying a spatio-temporal data-set. These features consist of higher order derivatives, limiting model discovery to densely sampled data-sets with low noise. Neural network-based approaches circumvent this limit by constructing a surrogate model of the data, but have to date ignored advances in sparse regression algorithms. In this paper we present a modular framework that dynamically determines the sparsity pattern of a deep-learning based surrogate using any sparse regression technique. Using our new approach, we introduce a new constraint on the neural network and show how a different network architecture and sparsity estimator improve model discovery accuracy and convergence on several benchmark examples. Our framework is available at \url{https://github.com/PhIMaL/DeePyMoD}
