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Abstract:

In this talk, recent continuous-time deep learning approaches will be surveyed, presenting applications in high-dimensional mean field games and optimal control while discussing efficient training and quantization techniques.  We will demonstrate how continuous-time deep learning models can address high-dimensional mean field games and optimal control problems, extending their application to state spaces with dimensions reaching the hundreds.  For these applications, we leverage neural ordinary differential equations in combination with scalable Lagrangian partial differential equations solvers to mitigate the curse of dimensionality, optimizing a neural network representation of the value function with penalty terms that enforce Hamilton-Jacobi-Bellman equations—eliminating the need for pre-computed training data.  We conclude with ongoing research on improving deep neural network training efficiency through mixed-precision computation and modified Gauss-Newton algorithms.  By dynamically adjusting the floating-point precision and leveraging advanced automatic differentiation, we achieve reductions in model size and computational cost. 

About the Speaker:

Lars Ruthotto is an applied mathematician specializing in computational methods for machine learning and inverse problems.  He is a Winship Distinguished Research Associate Professor in the Mathematics and Computer Science department at Emory University.  Ruthotto is also a member of the Scientific Computing Group and leads the Emory REU site for Computational Mathematics for Data Science.  Before joining Emory, he completed a postdoctoral assignment at the University of British Columbia and held Ph.D. positions at the University of Lübeck and the University of Münster.  His research and teaching lie at the intersection of applied mathematics and data science, with a particular focus on deep learning and inverse problems.  In deep learning, he works to generate new insights and enhance training efficiency for continuous models based on differential equations.  His work also involves machine learning approaches for high-dimensional PDEs and optimal control, with connections to active and reinforcement learning.  In the field of inverse problems, his focus on generative modeling for inference, with applications in image registration and reconstruction, and have collaborated extensively with experts in public health, geophysics, and medical imaging.