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 (cDFT), we present such a framework. MLIPs trained on quantum-mechanical energies and forces are used to generate inhomogeneous density profiles, which then serve as the training data for neural cDFT. The resulting ab initio neural cDFT is more computationally efficient than molecular simulations and provides a conceptually transparent route to the thermodynamics of both homogeneous and planar inhomogeneous systems. We demonstrate the approach for both water and carbon dioxide using several exchange-correlation functionals. Beyond accurately reproducing-at the level of the underlying approximate electronic structure-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. While current applications are limited to bulk fluids and planar geometries, this approach establishes a general first-principles route to multiscale modeling of fluids by unifying two independently developed machine-learning paradigms. This work represents an important step toward generalizing cDFT beyond simple empirical potentials to chemically complex systems.