论文标题
使用神经网络解决功能性特征问题
Solving the functional Eigen-Problem using Neural Networks
论文作者
论文摘要
在这项工作中，我们探讨了NN（神经网络）作为查找普通微分方程的特征对的工具的能力。我们要解决的问题是，鉴于一个自我伴侣操作员，我们是否可以了解什么是特征函数及其匹配的特征值。在图像处理中广泛讨论了解决本本特征问题的主题，因为可以将许多图像处理算法视为此类操作员。我们建议使用数字方法的替代方法，该方法可能会更强大，并具有解决更复杂问题的能力。在这项工作中，我们关注的简单问题已知分析解决方案。这样，我们就可以在给定环境中发现DNN（深神经网络）的功能和缺点时做出初步步骤。
In this work, we explore the ability of NN (Neural Networks) to serve as a tool for finding eigen-pairs of ordinary differential equations. The question we aime to address is whether, given a self-adjoint operator, we can learn what are the eigenfunctions, and their matching eigenvalues. The topic of solving the eigen-problem is widely discussed in Image Processing, as many image processing algorithms can be thought of as such operators. We suggest an alternative to numeric methods of finding eigenpairs, which may potentially be more robust and have the ability to solve more complex problems. In this work, we focus on simple problems for which the analytical solution is known. This way, we are able to make initial steps in discovering the capabilities and shortcomings of DNN (Deep Neural Networks) in the given setting.
