概率理查德森推理推理可能的理查德森推理
Chris J Oates1, Toni Karvonen2,3, Aretha L Teckentrup4
1School of Mathematics, Statistics and Physics, Newcastle University, Newcastle upon Tyne, UK.
概括
高斯-理查德森推断 (GRE) 提供了一种概率方法来改进数值方法. 这种方法处理复杂的计算机代码和不确定的融合顺序,实现了显著的加速度和精度增长.
科学领域:
- 数字分析 数字分析
- 计算科学 计算科学
- 应用数学 应用数学 应用数学
背景情况:
- 外加推算方法增强了数值方法的收顺序.
- 传统方法与现代复杂的计算机代码和不确定的趋同作斗争.
- 多忠实度建模在分析趋同订单时提出了挑战.
研究的目的:
- 介绍理查森推断的概率观点.
- 统一经典推断与多忠度建模.
- 开发一种方法来统计处理不确定的趋同订单.
主要方法:
- 使用高斯过程开发了高斯-理查德森推断 (GRE).
- 对于多项式或指数式加速度的确定的条件.
- 制定实验设计作为一个连续优化问题.
主要成果:
- 高斯-理查德森推断 (GRE) 提供了一个概率框架.
- GRE通过统计估计不确定的趋同订单.
- 在计算心脏模型中证明了实际的准确性增长.
结论:
- GRE将古典推断与多忠度建模统一起来.
- 概率方法使得统计估计的趋同订单.
- 在复杂的模拟中,GRE提供了一个强大的工具来增强数字方法.
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