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This is an announcement of Elena Orlova's Candidacy Exam.<br>
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Candidate: Elena Orlova<br>
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Date: Thursday, May 30, 2024<br>
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Time: 11 am CT<br>
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Location: JCL 298<br>
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Title: Deep Stochastic Mechanics<br>
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Abstract: This work introduces a novel deep-learning-based approach for numerical simulation of a time-evolving Schrödinger equation inspired by stochastic mechanics and generative diffusion models. Unlike existing approaches, which exhibit computational complexity
that scales exponentially in the problem dimension, our method allows us to adapt to the latent low-dimensional structure of the wave function by sampling from the Markovian diffusion. Depending on the latent dimension, our method may have far lower computational
complexity in higher dimensions. Moreover, we propose novel equations for stochastic quantum mechanics, resulting in quadratic or linear computational complexity with respect to the number of dimensions. Numerical simulations verify our theoretical findings
and show a significant advantage of our method compared to other deep-learning-based approaches used for quantum mechanics.<br>
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Advisors: Rebecca Willett<br>
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Committee Members: Rebecca Willett, Ian Foster, and Yuxin Chen</div>
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