Research

My academic research falls into three main areas:

• High dimensional partial differential equations: Our goal is to develop new adaptive sampling strategies to accelerate training efficiency for physics-informed neural networks and DeepONets. We are also interested in building novel surrogate model to deal with partial differential equations with random inputs, furthermore to solve PDE-control and Bayesian inverse problems.

• Data-driven uncertainty quantification: Our goal is to build fast, scaleable surrogate models to model the data-driven uncertainty. Recently we are interested in Gaussian process, generative model and information bottleneck, etc.

• Physics-informed generative model and model reduction based on neural networks.