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Watch a 51-minute lecture from the CMSA Mathematics and Machine Learning Closing Workshop where Eric Vanden-Eijnden from Courant/NYU explores the mathematical foundations and applications of generative models based on dynamical transport. Delve into the construction of probability distribution maps and their evolution from image generation to scientific computing applications. Learn how improved understanding of generative models' inner workings enhances their design, particularly in structuring transport for complex target distributions while maintaining computational efficiency. Discover applications in Monte Carlo sampling for statistical mechanics and Bayesian inference, as well as the numerical integration and interpretation of random dynamical systems driven out of equilibrium. Gain insights into how these methods address problems previously considered intractable due to the curse of dimensionality, with a unique focus on applications involving models without data.
