Spectral methods for Neural Integral Equations
Emanuele Zappala
神经积分方程是基于积分方程理论的深度学习模型,其中模型由积分运算符和相应的方程(第二类)组成,通过优化过程学习。 这种方法允许在机器学习中利用积分运算符的非本地属性,但它的计算成本很高。 在本文中,我们介绍了基于光谱方法的神经积分方程框架,使我们能够在光谱域中学习运算符,从而产生更便宜的计算成本,以及高插值精度。 我们研究方法的属性,并展示有关模型近似能力的各种理论保证,以及数值方法解决方案的收敛。 我们提供数值实验来证明结果模型的实际有效性。
Neural integral equations are deep learning models based on the theory of integral equations, where the model consists of an integral operator and the corresponding equation (of the second kind) which is learned through an optimization procedure. This approach allows to leverage the nonlocal properties of integral operators in machine learning, but it is computationally expensive. In this article, we introduce a framework for neural integral equations based on spectral methods that allows us to ...