Automated model discovery of partial differential equations (PDEs) usually considers a single experiment or dataset to infer the underlying governing equations. In practice, experiments have inherent natural variability in parameters, initial and boundary conditions that cannot be simply averaged out. We introduce a randomised adaptive group Lasso sparsity estimator to promote grouped sparsity and implement it in a deep learning based PDE discovery framework. It allows to create a learning bias that implies the a priori assumption that all experiments can be explained by the same underlying PDE terms with potentially different coefficients. Our experimental results show more generalizable PDEs can be found from multiple highly noisy datasets, by this grouped sparsity promotion rather than simply performing independent model discoveries.
翻译:部分差异方程式(PDEs)的自动模型发现通常会考虑单一的实验或数据集来推断基本参数方程式。 实际上,实验在参数、初始和边界条件上具有固有的自然变异性,这些参数、初始和边界条件无法简单地平均出来。 我们引入了随机调整的Lasso Esparsity估计数组群群, 以推广群聚宽度, 并在基于深层次学习的PDE发现框架内实施。 它允许产生一种学习偏差, 意味着先验的假设, 即所有实验都可以用具有潜在不同系数的相同的PDE基本条件来解释。 我们的实验结果显示, 通过这种群集宽度促进, 而不是简单地进行独立的模型发现, 可以从多个高度吵闹的数据集中找到可比较普遍的PDEs 。