EPR-Net: constructing a non-equilibrium potential landscape via a variational force projection formulation.

Area of Science:

• Biophysics
• Computational Biology
• Statistical Mechanics

Background:

• Constructing potential landscapes is vital for understanding high-dimensional non-equilibrium systems in biophysics.
• Existing methods struggle with the complexity and dimensionality of these systems.

Purpose of the Study:

• To introduce EPR-Net, a novel deep learning approach for potential landscape construction in high-dimensional non-equilibrium steady-state systems.
• To enable simultaneous estimation of steady entropy production rate (EPR).

Main Methods:

• EPR-Net utilizes the orthogonal projection of the driving force in a weighted inner-product space.
• A specialized loss function connects directly to the steady entropy production rate.
• The framework incorporates enhanced learning for low-noise systems and handles dimensionality reduction and state-dependent diffusion.

Main Results:

• EPR-Net demonstrates superior accuracy, effectiveness, and robustness compared to existing methods on benchmark problems.
• Accurate solutions and landscape insights were obtained for complex biophysical systems, including an 8D limit cycle and a 52D multi-stability problem.

Conclusions:

• EPR-Net provides a versatile and powerful solution for potential landscape construction in biophysics.
• The approach offers accurate solutions and valuable insights for diverse biophysical problems.