We propose a paradigm for interpretable Manifold Learning for scientific data analysis, whereby we parametrize a manifold with $d$ smooth functions from a scientist-provided dictionary of meaningful, domain-related functions. When such a parametrization exists, we provide an algorithm for finding it based on sparse non-linear regression in the manifold tangent bundle, bypassing more standard manifold learning algorithms. We also discuss conditions for the existence of such parameterizations in function space and for successful recovery from finite samples. We demonstrate our method with experimental results from a real scientific domain.

翻译：我们提出一种用于科学数据分析的可解释流形学习范式，其中通过科学家提供的、与领域相关的有意义的字典函数集，用 $d$ 个光滑函数对流形进行参数化。当此类参数化存在时，我们提供一种基于流形切丛中稀疏非线性回归的算法来发现它，从而绕开更标准的流形学习算法。我们还讨论函数空间中此类参数化存在的条件以及从有限样本中成功恢复的条件。我们通过来自真实科学领域的实验结果展示了该方法。