Microscopic origin of reduced learnability in the liquid regime

Characterize the microscopic origin of the reduced learnability of dense, disordered liquid-like configurations by normalizing-flow architectures, including whether the coexistence of strong local correlations and large-scale configurational disorder produces probability manifolds that are intrinsically difficult to represent through smooth invertible transformations.

Background

The paper studies the generation efficiency of a conditional normalizing flow along nested-sampling trajectories for two-dimensional Lennard–Jones systems. At high density, the flow performs well for high-energy, gas-like configurations and again in the low-energy, ordered solid-like regime, but its efficiency decreases substantially in the intermediate dense-fluid or liquid-like regime, where strong many-body correlations coexist with substantial configurational disorder.

The authors show that the lower-density system exhibits a broader and more heterogeneous low-energy landscape, with a weaker recovery of generation efficiency. They attribute the difficulty in part to the coexistence of local packing correlations, large-scale disorder, and multiple nearly degenerate minima, but state that the microscopic mechanism responsible for the reduced learnability in the liquid regime has not been fully characterized. Resolving this issue would clarify the geometric properties of molecular probability distributions and the inductive biases of current normalizing-flow architectures.