Energy landscape statistics and thermodynamics of a machine-learned model of water.

Water's anomalous thermodynamic behavior arises from the presence of intricate hydrogen-bond networks that are highly sensitive to many-body interactions, challenging molecular modeling for decades. The ongoing machine learning revolution has opened the possibility of performing quantum-accurate liquid-structure calculations at affordable computational cost. Beyond reproducing water's thermodynamic properties with high fidelity, such simulations provide a stringent benchmark for theoretical models and a route to deeper physical understanding. We use the recently developed machine-learned Deep Potential Many-Body Polarizable water model to show that the free energy of supercooled water can be accurately modeled with the potential energy landscape formalism. The resulting equation of state predicts the presence of a liquid-liquid critical point in excellent agreement with recent estimates. Together with previous studies based on empirical classical water potentials, it confirms that the potential energy landscape of water is Gaussian, providing a unifying framework for extracting thermodynamic behavior across model complexity, from empirical force fields to quantum-trained neural network models.