北京雁栖湖应用数学研究院

张晓明

胡煜中

2026年06月18日 10:00 至 11:00

A3-2-301

Zoom 204 323 0165 (BIMSA)

In this talk, I will review the optimization process in physics-informed machine learning (PIML). Training a PIML model is essentially a multi-objective optimization problem, where neural networks are required to satisfy governing equations, boundary and initial conditions, and observational data simultaneously. Therefore, the optimization process plays a crucial role in ensuring the convergence, stability, and accuracy of PIML models. The talk will emphasize on three key components of the optimization process: optimization problem, the loss function, and the optimizer. First, I will introduce several problem decomposition strategies for the optimization problem, including domain decomposition, sequential training, time decomposition, transfer learning, curriculum learning, multifidelity learning, and stacked training. Next, I will discuss the modification of the loss function, involving global loss weights, local pointwise weights, adaptive sampling strategies, and suitable residual penalty functions. Finally, I will review optimizer selection, covering first-order methods, quasi-Newton and second-order methods, as well as recent advances that address gradient conflicts, ill-conditioning, and multi-objective optimization challenges.

Hu Yuzhong is a second-year PhD student in a joint program between BIMSA and academy of mathematics and systems science, CAS, under the supervision of Professor Zhang Xiaoming.