学术报告

       报告题目：Quantifying uncertainty in physics-informed neural networks for solving forward and inverse PDE problems with noisy data

        用于求解含噪声数据的正、逆偏微分方程问题的物理信息神经网络中的不确定性量化

       报告人：孟旭辉，华中科技大学数学与统计学院数学与应用学科交叉创新研究院

       报告时间：2022年4月26日,下午14:00

       腾讯会议：449 177 656

       摘要：Deep learning algorithms have emerged recently for solving partial differential equations (PDEs), especially in conjunction with sparse data. In particular, the recently developed physics-informed neural networks (PINNs) have shown their effectiveness in solving both forward and inverse PDE problems. Different from the classical numerical methods in which the differential operators are approximated by the data on certain discrete lattices (meshes), PINNs compute all the differential operators of a PDE using the automatic differentiation technique involved in the backward propagation. Consequently, no mesh (structured mesh or unstructured mesh used in the classical numerical methods) is required for the PINN to solve PDEs, which saves a lot of effort in grid generation. Another attractive feature is that PINNs are capable of solving the inverse PDE problems effectively and with the same code that is used for forward problems. However, the vanilla PINNs (1) lead to overfitting predictions in situations with large noise in data, and (2) do not predict uncertainty. In this talk, I will introduce three newly developed PINNs to prevent overfitting as well as quantify uncertainties in predictions: (1) Bayesian physics-informed neural networks, (2) multi-fidelity Bayesian neural networks, and (3) Generative Adversarial Networks (GANs) for learning functional priors/posteriors from data and physics.

       个人简介：孟旭辉，2017年博士毕业于华中科技大学能源与动力工程学院，2018年-2022年美国布朗大学应用数学系研究博士后，2022年3月至今华中科技大学数学与统计学院数学与应用学科交叉创新研究院副教授。主要研究方向为求解PDE正反问题的深度学习方法。截至目前已在JCP、CMAME、SIAM Review等期刊发表SCI论文20篇(3篇ESI高被引论文)，并担任SISC、JCP、CMAME、Artif. Intell. Rev.等期刊审稿人。