Perspective: How to overcome dynamical density functional theory.

Area of Science:

• Soft matter physics
• Non-equilibrium statistical mechanics
• Computational physics

Background:

• Dynamical density functional theory (DDFT) offers limited insight into true time evolution of soft matter.
• Existing methods struggle with accurate prediction and design of non-equilibrium phenomena.

Purpose of the Study:

• To advocate for a comprehensive dynamical theory for non-equilibrium soft matter.
• To highlight limitations of DDFT and propose power functional theory as a superior alternative.
• To demonstrate the application of machine learning within this framework.

Main Methods:

• Critically analyze the limitations of dynamical density functional theory (DDFT).
• Introduce power functional theory for describing non-equilibrium dynamics.
• Employ machine learning to model a steady sedimentation flow of a Lennard-Jones fluid.

Main Results:

• Power functional theory provides insights into non-equilibrium dynamics, incorporating exact sum rules.
• Machine learning successfully maps mean motion to internal force fields.
• The trained model predicts and designs steady-state dynamics for various density modulations.

Conclusions:

• Power functional theory offers a promising framework for non-equilibrium many-body physics.
• Machine learning integrated with power functional theory overcomes DDFT's conceptual and practical limitations.
• This approach has significant potential for predicting and designing soft matter behavior.