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PhD Exit Seminar: Self-Similar Shock Formation and Some Results in Deep Learning
Special Events| Speaker: | Kyle Chickering, UC Davis |
| Related Webpage: | https://math.ucdavis.edu/~krc |
| Location: | 1147 MSB |
| Start time: | Wed, Sep 17 2025, 11:00AM |
We review the speaker’s work on self-similar shock formation for the fractal Burgers equation, and discuss how numerics play a role in analysis. Motivated by recent work in this area, we discuss how physics-informed neural networks (PINNs) are well-suited to exploring these types of mathematical problems. We introduce a method for improving the computational efficiency of PINNs and are able to compute previously intractable self-similar profiles. Next, we introduce a novel interpretation of the mathematical theory underlying PINNs, and in the final part of this talk we apply this new framework to a problem which arises in the field of multimodal large language models. Zoom Link: https://ucdavis.zoom.us/j/92911241399?pwd=YWHHFSyFtLOpmU69wlbVzoMnzIbeqs.1