2018/11/30 by Shang-Chun Lin, Lin Shang-Chun, Martin Oettel · 3 citations
Engineering · Materials Science · Physics and Astronomy · #Artificial neural network #Computational learning theory #Convolutional neural network #Dimension (graph theory) #Energy (signal processing) #Feature (linguistics) #Machine Learning in Materials Science #Phase Equilibria and Thermodynamics #Quantum many-body systems #State (computer science) #Training (meteorology) #cond-mat.soft
paper · pdf · doi:10.21468/scipostphys.6.2.025
published as SciPost Phys. 6, 025 (2019) · Correct some typo and minor changes
openalex created_date 2018/11/29 · openalex publication_date 2019/02/26 · arxiv created 2019/02/27 · arxiv updated 2019/03/04 · openalex updated_date 2026/08/05
We use machine learning methods to approximate a classical density functional. The functional ‘learns’ by comparing the density profile it generates with that of simulations. As a study case, we choose the model problem of a Lennard–Jones fluid in one dimension where there is no exact solution available. After separating the excess free energy functional into a “repulsive” and an “attractive” part, machine learning finds a functional for the attractive part in weighted–density form. The predictions of density profile at a hard wall shows good agreement when subject to thermodynamic conditions beyond those in the training set. This also holds for the equation of state if this is evaluated near the training temperature. We discuss the applicability to problems in higher dimensions.