论文标题
错误感知的B细节：改善贝叶斯物理信息神经网络中的不确定性定量
Error-Aware B-PINNs: Improving Uncertainty Quantification in Bayesian Physics-Informed Neural Networks
论文作者
论文摘要
物理知识的神经网络（PINN）正在流行，作为解决微分方程的一种方法。尽管在某些情况下比经典数值技术更可行，但Pinn仍然缺乏信誉。可以在不确定性量化（UQ）中找到一种补救措施，该补救措施刚刚在PINN的背景下开始出现。评估训练有素的Pinn符合施加的微分方程的程度是解决不确定性的关键，但是对于这项任务缺乏全面的方法。我们在贝叶斯钉（B-Pinns）中提出了一个UQ的框架，该框架结合了B-Pinn溶液与未知的真实溶液之间的差异。我们利用了线性动力学系统上PINN的误差界限的最新结果，并证明了一类线性ODE的预测不确定性。
Physics-Informed Neural Networks (PINNs) are gaining popularity as a method for solving differential equations. While being more feasible in some contexts than the classical numerical techniques, PINNs still lack credibility. A remedy for that can be found in Uncertainty Quantification (UQ) which is just beginning to emerge in the context of PINNs. Assessing how well the trained PINN complies with imposed differential equation is the key to tackling uncertainty, yet there is lack of comprehensive methodology for this task. We propose a framework for UQ in Bayesian PINNs (B-PINNs) that incorporates the discrepancy between the B-PINN solution and the unknown true solution. We exploit recent results on error bounds for PINNs on linear dynamical systems and demonstrate the predictive uncertainty on a class of linear ODEs.
