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With this paper, we can push beyond the limitations of dynamical density functional theory. And due to the use of neural networks, we can do this much faster.
Superadiabatic forces occur in nonequilibrium and they can be very strong.
To get some training data for the neural network, we had to run a bunch of nonequilibrium many-body simulations. For this we used adaptive Brownian dynamics, which finds just the right pace for the numerical time evolution of the systems.
Our neural network also satisfies exact Noether identities. These identities determine how the different force contributions balance each other.
The adiabatic approximation in dynamical density functional theory is uncontrolled. If you plan to ride the exciting trail of nonequilibrium soft matter physics then be on the safe side and use power functional theory. Yeah!
Update 13.12.2023: Treating equilibrium via Neural functional theory for soft matter is based on machine learning deep functional relationships of statistical mechanics; see Press Release for PNAS, Review, and Tutorial.