论文标题
有效贝叶斯推理的动力学系统的物理知识的机器学习
Physics-Informed Machine Learning of Dynamical Systems for Efficient Bayesian Inference
论文作者
论文摘要
尽管No-U-Turn采样器（螺母）是进行贝叶斯推断的广泛采用方法，但它需要许多后梯度，在实践中计算可能很昂贵。最近，人们对基于物理的动力学（或哈密顿）系统的机器学习以及哈密顿神经网络（HNNS）引起了重大兴趣。但是，这些类型的体系结构尚未应用于有效地解决贝叶斯推论问题。我们建议使用HNN进行有效进行贝叶斯推断，而无需大量后梯度。我们将潜在变量输出引入HNNS（L-HNN），以提高表达性和减少的集成误差。我们将L-HNN集成在坚果中，并进一步提出了一种在线错误监控方案，以防止L-HNNS可能几乎没有培训数据的区域进行采样堕落。考虑到几种复杂的高维后密度，我们证明了通过在线错误监测的螺母中的L-HNN，并将其性能与螺母进行比较。
Although the no-u-turn sampler (NUTS) is a widely adopted method for performing Bayesian inference, it requires numerous posterior gradients which can be expensive to compute in practice. Recently, there has been a significant interest in physics-based machine learning of dynamical (or Hamiltonian) systems and Hamiltonian neural networks (HNNs) is a noteworthy architecture. But these types of architectures have not been applied to solve Bayesian inference problems efficiently. We propose the use of HNNs for performing Bayesian inference efficiently without requiring numerous posterior gradients. We introduce latent variable outputs to HNNs (L-HNNs) for improved expressivity and reduced integration errors. We integrate L-HNNs in NUTS and further propose an online error monitoring scheme to prevent sampling degeneracy in regions where L-HNNs may have little training data. We demonstrate L-HNNs in NUTS with online error monitoring considering several complex high-dimensional posterior densities and compare its performance to NUTS.
