论文标题
通过有限元网络从稀疏观察中学习物理系统的动态
Learning the Dynamics of Physical Systems from Sparse Observations with Finite Element Networks
论文作者
论文摘要
我们为任意分布点上的时空预测提出了一种新方法。假设观察到的系统遵循一个未知的偏微分方程，我们通过有限元方法得出了数据动力学的连续时间模型。所得的图神经网络估计了空间结构域网格中每个细胞的未知动力学的瞬时效应。我们的模型可以通过对未知PDE形式的假设纳入先验知识，这会引起结构性偏见，以学习特定的过程。通过这种机制，我们从对流方程中得出了模型的传输变体，并表明它将转移性能提高到对海面温度和气体流量对基线模型预测的高分辨率网格，这些模型代表了代表时空预测方法的选择。定性分析表明，我们的模型将数据动态分解为其组成部分，这使其具有独特的解释。
We propose a new method for spatio-temporal forecasting on arbitrarily distributed points. Assuming that the observed system follows an unknown partial differential equation, we derive a continuous-time model for the dynamics of the data via the finite element method. The resulting graph neural network estimates the instantaneous effects of the unknown dynamics on each cell in a meshing of the spatial domain. Our model can incorporate prior knowledge via assumptions on the form of the unknown PDE, which induce a structural bias towards learning specific processes. Through this mechanism, we derive a transport variant of our model from the convection equation and show that it improves the transfer performance to higher-resolution meshes on sea surface temperature and gas flow forecasting against baseline models representing a selection of spatio-temporal forecasting methods. A qualitative analysis shows that our model disentangles the data dynamics into their constituent parts, which makes it uniquely interpretable.
