贝叶斯神经网络与物理信息的 priors 与应用到边界层速度
概括
这项研究引入了以物理为基础的贝叶斯前期神经网络 (BNN),以量化物理为基础的神经网络 (PINN) 的不确定性. 新的框架将部分微分方程 (PDEs) 整合为复杂系统更准确,数据效率更高的预测的先决条件.
科学领域:
- 计算流体动力学 计算流体动力学
- 机器学习 机器学习
- 贝叶斯的推理 贝叶斯的推理
背景情况:
- 基于物理学的神经网络 (PINNs) 将部分微分方程 (PDEs) 集成到神经网络训练中.
- 目前的PINN方法缺乏正式的不确定性量化.
- 在PINNs中的最小化问题往往缺乏可靠的不确定性估计.
研究的目的:
- 开发一种新的框架,用于在基于物理学的神经网络中量化不确定性.
- 在贝叶斯神经网络 (BNN) 框架内将PDEs作为先前信息进行整合.
- 为具有有限数据的复杂系统提供物理一致的预测.
主要方法:
- 提出了一个基于物理的先前信息 (PIP) -BNN框架,其中PDEs充当先验.
- 校准了先前的平均值,使其与PDE溶液相似,并使用先前的差异来确定信心.
- 传播PDE信息到后方用于不确定性量化.
主要成果:
- PIP-BNN框架成功量化了预测中的不确定性.
- 在模拟的粘性流体流量和实验性流边界层数据上证明了有效性.
- 实现了物理一致的预测,与未知先验相比,观察次数显著减少.
结论:
- PIP-BNN方法提供了一种可靠的方法,用于在基于物理的机器学习中量化不确定性.
- 该框架通过利用数据和先前的物理知识,使复杂系统的准确预测成为可能.
- 该方法对科学建模和工程中的应用有希望,因为数据稀缺,但物理定律是已知的.
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