Infusing Experimental Reality into Complex Many-Body Hamiltonians: The Observable-Constrained Variational Framework (OCVF)
Shaoliang Guo, Ziping Yang
TL;DR
This work tackles the mismatch between high-accuracy but computationally expensive quantum descriptions and physically realistic macroscopic behavior in complex materials. It introduces the Observable-Constrained Variational Framework (OCVF), a top-down method that augments a DFT-derived skeleton $H_o$ with a neural-network correction $\Delta H_\theta$ and trains it to satisfy experimental observables $\mathfrak{O}_{exp,s}$ through differentiable molecular dynamics within CEVM. The authors derive a rigorous gradient-enabled pipeline, employing a differentiable forward model $F_s$, a Jensen-Shannon–based metric $L_{JS}$, and an adjoint-sensitivity approach to backpropagate through long MD trajectories, achieving self-consistent corrections to phase-transition temperatures and lattice structures in BaTiO3, with improvements of $95.8\%$ for the C-T transition and $36.1\%$ for the O-R transition relative to the prior model, and a $55.6\%$ gain in rhombohedral lattice accuracy. By constructing a continuous effective free energy surface that stitches across thermodynamic states, the method provides a general protocol to calibrate theoretical Hamiltonians against experimental reality, enabling robust predictions of complex phase behavior in multi-component systems.
Abstract
Deep learning potentials for complex many-body systems often face challenges of insufficient accuracy and a lack of physical realism. This paper proposes an "Observable-Constrained Variational Framework" (OCVF), a general top-down correction paradigm designed to infuse physical realism into theoretical "skeleton" models (H_o) by imposing constraints from macroscopic experimental observables (\mathfrak{O}_{\text{exp},s}). We theoretically derive OCVF as a numerically tractable extension of the "Constrained-Ensemble Variational Method" (CEVM), wherein a neural network (ΔH_θ) learns the correction functional required to match the experimental data. We apply OCVF to BaTiO3 (BTO) to validate the framework: a neural network potential trained on DFT data serves as H_o, and experimental PDF data at various temperatures are used as constraints (\mathfrak{O}{\text{exp},s}). The final model, H_o + ΔH_θ, successfully predicts the complete phase transition sequence accurately (s', s \neq s'). Compared to the prior model, the accuracy of the Cubic-Tetragonal (C-T) phase transition temperature is improved by 95.8\% , and the Orthorhombic-Rhombohedral (O-R) T_c accuracy is improved by 36.1\%. Furthermore, the lattice structure accuracy in the Rhombohedral (R) phase is improved by 55.6\%, validating the efficacy of the OCVF framework in calibrating theoretical models via observational constraints.