Deep Stochastic Mechanics
This addresses a computational bottleneck in quantum mechanics simulations, offering a potentially scalable solution for high-dimensional problems.
The paper tackles the exponential computational complexity of simulating time-evolving Schrödinger equations by introducing a deep-learning method that adapts to latent low-dimensional structures, achieving quadratic complexity in dimensions and showing significant advantages in numerical simulations.
This paper 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 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.