AbstractConstitutive models are widely used for modeling complex systems in science and engineering, when first-principle-based, well-resolved simulations are prohibitively expensive. For example, in fluid dynamics, constitutive models are required to describe nonlocal, unresolved physics such as turbulence and laminar-turbulent transition. However, traditional constitutive models based on PDEs...
AbstractLearning dynamics of deep neural networks is complex. While previous approaches made advances in mathematical analysis of the dynamics of two-layer neural networks, addressing deeper networks have been challenging. In this talk, I will present a mean field theory of the learning dynamics of deep networks and discuss its practical implications
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