Leray-Schauder Mappings for Operator Learning
<|reference_start|>Leray-Schauder Mappings for Operator Learning: 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.<|reference_end|>
@article{zappala2024leray-schauder,
    title={Leray-Schauder Mappings for Operator Learning},
    author={Emanuele Zappala},
    journal={arXiv preprint arXiv:2410.01746},
    year={2024},
    archivePrefix={arXiv},
    eprint={2410.01746},
    primaryClass={cs.LG cs.NA math.NA}
}