A unified machine learning framework for ab initio multiscale modeling of liquids

Understanding and predicting the behavior of liquid matter across length scales, using only the microscopic interactions encoded in the Schrödinger equation, remains a central challenge in the physical sciences. Achieving this goal requires not only an accurate and efficient description of intermolecular forces but also a consistent framework that bridges the micro-, meso-, and macroscales. Here, by combining machine-learned interatomic potentials (MLIPs) with neural classical density functional theory (neural cDFT), we present such a framework. The underlying idea is simple: MLIPs trained on quantum-mechanical energies and forces are used to generate inhomogeneous microscopic density profiles, which in turn serve as the training data for neural cDFT. The resulting ab initio neural cDFT is not only significantly more computationally efficient than molecular simulations, but also provides a conceptually transparent route to the thermodynamics of both homogeneous and inhomogeneous systems. We demonstrate the approach for both water and carbon dioxide using several exchange-correlation functionals. Beyond accurately reproducing bulk equations of state and liquid-vapor phase diagrams, ab initio neural cDFT predicts, from first principles, how confinement modifies liquid-vapor coexistence in water. It also captures complex behavior in supercritical carbon dioxide such as the Fisher-Widom and Widom lines. Ab initio neural cDFT establishes a general first-principles route to multiscale modeling of fluids within a single unified conceptual framework.

💡 Research Summary

**
The authors present a comprehensive first‑principles multiscale modeling framework for liquids that unifies microscopic quantum‑mechanical accuracy with mesoscopic and macroscopic efficiency. The approach consists of two tightly coupled machine‑learning components. First, they train machine‑learned interatomic potentials (MLIPs) using density‑functional theory (DFT) energies and forces for water and carbon dioxide, employing a variety of exchange‑correlation (xc) functionals (SCAN, RPBE‑D3, PBE‑D3, BLYP‑D3, SCAN‑rVV10) as well as popular empirical models (TIP4P/2005, TraPPE). These MLIPs provide a fast surrogate for the true potential energy surface, enabling canonical molecular dynamics (MD) simulations of hundreds of molecules under many random external potentials V_ext(z) across a broad temperature range.

From these MD runs the authors extract planar, non‑uniform equilibrium density profiles ρ_eq(z). These profiles, together with the corresponding V_ext(z), constitute the training data for a neural‑network implementation of classical density functional theory (neural cDFT). In classical DFT the central quantity is the excess Helmholtz free‑energy functional F_ex