论文标题
Markov-Chain Monte Carlo的自适应物理信息信息网络
Adaptive Physics-Informed Neural Networks for Markov-Chain Monte Carlo
论文作者
论文摘要
在本文中，我们提出了自适应物理信息信息的神经网络（APINNS），以通过马尔可夫链蒙特卡洛（MCMC）进行准确有效的无模拟贝叶斯参数估计。我们特别关注一类参数估计问题，以计算可能性函数需要解决PDE。所提出的方法包括：（1）构建离线PINN-UQ模型作为向前模型的近似值； （2）使用从MCMC采样器生成的样品即时精制该近似模型。所提出的APINN方法不断地完善该近似模型，并确保近似误差始终小于用户定义的残余误差阈值。我们从数值上证明了所提出的APINN方法在解决由泊松方程控制的系统的参数估计问题时的性能。
In this paper, we propose the Adaptive Physics-Informed Neural Networks (APINNs) for accurate and efficient simulation-free Bayesian parameter estimation via Markov-Chain Monte Carlo (MCMC). We specifically focus on a class of parameter estimation problems for which computing the likelihood function requires solving a PDE. The proposed method consists of: (1) constructing an offline PINN-UQ model as an approximation to the forward model; and (2) refining this approximate model on the fly using samples generated from the MCMC sampler. The proposed APINN method constantly refines this approximate model on the fly and guarantees that the approximation error is always less than a user-defined residual error threshold. We numerically demonstrate the performance of the proposed APINN method in solving a parameter estimation problem for a system governed by the Poisson equation.
