arXiv:2410.01746cs.LGcs.NA2024-10被引 1
用勒雷-施耐德映射学习巴拿赫空间间算子，可逼近任意非线性算子。
Leray-Schauder Mappings for Operator Learning
- 基于勒雷-施耐德映射构建算子学习框架，实现有限维逼近
- 在两个基准数据集上达到当前最优模型的性能水平
- 适用于需要高精度算子逼近的科学计算与工程建模场景
我们提出一种在巴拿赫空间之间学习算子的算法，基于勒雷-施耐德映射来学习紧子空间的有限维近似。我们证明该方法是（可能非线性）算子的通用逼近器。在两个基准数据集上的实验表明，该方法效率高，性能可媲美当前最先进模型。
原文摘要 · Abstract (English)
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.
算子学习泛函分析通用逼近
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