论文标题
机器学习回归模型的应用到逆特征值问题
Application of machine learning regression models to inverse eigenvalue problems
论文作者
论文摘要
在这项工作中，我们从机器学习的角度研究了逆特征值问题的数值解决方案。考虑了两个不同的问题：对于对称势的逆弹力符号特征值问题和球形对称折射率的反向传输特征值问题。首先，我们解决相应的直接问题，以生成所需的特征值数据集，以训练机器学习算法。接下来，我们考虑了几个反问题的示例，并比较了每个模型的性能，以分别从给定的最低特征值组中预测未知电位和折射率。我们使用的有监督回归模型是k-neartiment邻居，随机森林和多层感知器。我们的实验表明，这些机器学习方法在对其参数的适当调整下可以数值解决所检查的逆特征值问题。
In this work, we study the numerical solution of inverse eigenvalue problems from a machine learning perspective. Two different problems are considered: the inverse Strum-Liouville eigenvalue problem for symmetric potentials and the inverse transmission eigenvalue problem for spherically symmetric refractive indices. Firstly, we solve the corresponding direct problems to produce the required eigenvalues datasets in order to train the machine learning algorithms. Next, we consider several examples of inverse problems and compare the performance of each model to predict the unknown potentials and refractive indices respectively, from a given small set of the lowest eigenvalues. The supervised regression models we use are k-Nearest Neighbours, Random Forests and Multi-Layer Perceptron. Our experiments show that these machine learning methods, under appropriate tuning on their parameters, can numerically solve the examined inverse eigenvalue problems.
