在普遍微分方程中评估不确定性量化
Nina Schmid1, David Fernandes Del Pozo2, Willem Waegeman1
1Life & Medical Sciences (LIMES) Institute, University of Bonn, Bonn, Germany.
概括
这项研究正式确定了普遍微分方程 (UDEs) 的不确定性量化,这是一个强大的科学机器学习方法. 它评估贝叶斯和频率主义方法,以确保复杂系统中可靠的参数和预测性不确定性估计.
科学领域:
- 科学机器学习科学机器学习
- 计算科学 计算科学
- 应用数学 应用数学 应用数学
背景情况:
- 科学机器学习 (SciML) 将物理知识与数据驱动的方法集成在一起,以发现治理方程.
- 通用微分方程 (UDEs) 将机械模型与神经网络等通用函数近似器结合起来.
- UDEs的稳定性取决于对参数和预测的严格不确定性量化 (UQ).
研究的目的:
- 为了正式确定普遍微分方程 (UDEs) 的不确定性量化 (UQ).
- 调查和评估适用于UDE的关键频率主义和贝叶斯式UQ方法.
- 在合成示例上评估不同UQ技术的有效性和效率.
主要方法:
- 专门针对UDE框架的UQ原则的正式化.
- 集合方法,变异推理和马尔科夫链蒙特卡洛 (MCMC) 采样的实施和分析.
- 通过使用三组日益复杂的合成数据集进行评估,以测试方法的稳定性和效率.
主要成果:
- 在UDEs中展示了UQ的正式框架,这对模型可靠性至关重要.
- 对比了频率主义 (组合) 和贝叶斯式 (变量推理,MCMC) UQ方法的性能.
- 提供了对UDE不同UQ策略的有效性和计算效率的见解.
结论:
- 在科学机器学习中,UQ对于通用微分方程的可靠应用至关重要.
- 像MCMC和变异推理这样的贝叶斯方法在UDE中显示了认识学UQ的前景.
- 该研究为开发更可靠和可解释的SciML模型提供了基础.
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