J. Weare

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.

AI weather models can backcast effectively, but their surprising accuracy comes at the cost of physical fidelity, raising questions about the foundations of predictability in climate science.

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.