发表机构
Universidad Complutense de Madrid（马德里complutense大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究用残差神经网络逼近参数依赖问题的解，基于梯度流开发收敛训练方案，利用洛雅西维茨理论保证收敛，通过求解常微分方程组逼近网络系数，经测试可正确再现简单常微分方程解的参数依赖关系，合理逼近逆问题解。
AI 中文摘要
我们基于梯度流开发了一种收敛方案来训练包含解析激活函数的神经网络。收敛性由洛雅西维茨理论保证。该方法的主要优点是实现简单。通过求解常微分方程组来逼近网络系数。我们通过构建参数问题解的残差神经网络逼近进行测试，能正确再现简单常微分方程解对几个参数的依赖关系，还能合理逼近含波约束的逆问题解，即使在问题严重不适定的区域。
英文摘要
We develop a convergent scheme to train neural networks involving analytic activation functions based on gradient flows. Convergence properties are guaranteed by Lojasiewicz theory. The main advantage of this approach is its simplicity of implementation. The coefficients of the network are approximated by solving a system of ordinary differential equations. We test the method by constructing residual neural network approximations of solutions of parametric problems. The dependence of the solutions of simple ordinary differential equations on a few parameters is correctly reproduced. The solutions of inverse problems involving wave constraints which depend on a few parameters can be reasonably approximated, even in regions in which the problem is severely ill posed.
Commentsto appear in Journal of Nonlinear, Complex and Data Science
Journal refJournal of Nonlinear, Complex and Data Science, 2026
