We present an algorithm for learning operators between Banach spaces, based on the use of Leray-Schauder mappings to learn a finite-dimensional approximation of compact subspaces. We show that the resulting method is a universal approximator of (possibly nonlinear) operators. We demonstrate the efficiency of the approach on two benchmark datasets showing it achieves results comparable to state of the art models.

翻译：我们提出了一种基于Leray-Schauder映射来学习Banach空间之间算子的算法，该方法通过Leray-Schauder映射学习紧子空间的有限维近似。我们证明了所得到的算法是（可能非线性的）算子的通用逼近器。我们在两个基准数据集上验证了该方法的有效性，结果表明其性能达到了与当前最先进模型相当的水平。