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A common operator viewpoint is developed connecting generator-based partial differential equations, variational principles, Markov state models, dynamical Galerkin approximation, and neural networks with an emphasis on self-supervised methods that learn solutions of their defining dynamical equations rather than relying on labeled shooting data.
A denoiser trained solely on classical statistics can accurately reproduce quantum Boltzmann distributions without retraining, revealing a profound connection between generative modeling and quantum fluctuations.
