混合神经网络,连续和符号计算来解决非线性方程的参数系统
1INRIA Sophia-Antipolis, 2004 routes des Lucioles, 06902 Sophia-Antipolis, France.
概括
本研究介绍了非线性参数方程的新型解答器,使用机器学习来找到所有真实解决方案. 该方法训练多层感知子 (MLPs) 来预测初始解决方案,在工程应用中获得准确结果的高成功率.
科学领域:
- 计算数学 计算数学 计算数学
- 数字分析 数字分析
- 机器学习应用 机器学习应用
背景情况:
- 在各种科学和工程领域中,解决非线性参数方程F ((P,X) = 0至关重要.
- 现有的数值方法可能无法在一系列参数P的系统中找到所有真实解决方案.
- 需要强大的解决方案,保证在一个有限的参数区域内找到所有精确的解决方案是显著的.
研究的目的:
- 开发一种能够为非线性参数方程系统找到所有确切真实解的解法器.
- 利用机器学习,特别是多层感知子 (MLP),以提高数值解决器的收性和准确性.
- 在初始训练阶段后,为许多参数实例实现系统的高效解决.
主要方法:
- 从已知参数-解决方案对的初始集合生成学习集.
- 训练多层感知子 (MLPs) 来预测解决方案,优化牛顿方法的收成功率.
- 从一组MLP构建一个解决器,每个MLP指导一个本地解决器到精确的解决方案.
主要成果:
- 在使用足够多的MLP来找到学习集的确切解决方案时,取得了100%的成功率.
- 证明了解决方案在验证集上的有效性,显示了自动生成和自学能力.
- 成功地将该方法应用于机器人和化学问题,提供所有解决方案的高概率.
结论:
- 建议的解决方案,利用MLP,可以准确地找到非线性参数系统的所有真实解决方案.
- 虽然最初的解决器设计时间很长,但每个参数实例的解决时间非常低.
- 该方法非常适合在参数空间中需要频繁解决的应用程序,特别是用于减少计算时间的分布式实现.
相关概念视频
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