Lee-Yang Theory Guided Force Field Refinement Based on Phase Diagrams

What the math gives to ML

The paper offers a transferable phase-transition mechanism: Lee-Yang zeros of the complexified partition function approach the real thermodynamic axis at a physical transition, so the partition-function modulus near that axis is a universal objective that does not require hand-designed order parameters. The neural-network analogue is to train an energy-based neural potential or differentiable simulator so that its complex-field partition-function landscape develops minima at experimentally or computationally known transition points. This is most promising for neural force fields and learned Hamiltonians, where phase-diagram fidelity can constrain global thermodynamics and improve unobserved observables such as heat capacity and enthalpy.