| Abstract: | Solving partial differential equations (PDEs) by deep neural networks has attracted significant attentions in recent years. In this presentation, I will discuss two problems related to this topic: (1) how to capture shock waves with (high-dimensional) random inputs? (2) how to find the global optimizer of highly nonconvex objective functions arising from machine learning tasks? These are joint works with Shi Jing (SJTU) and Liyao Lyu (MSU). |
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