SFB 1313 Publication "Classical density functional theory in three dimensions with GPU-accelerated automatic differentiation: Computational performance analysis using the example of adsorption in covalent-organic frameworks"

A new SFB 1313 publication is published in "Chemical Engineering Science". The work has been developed by researchers involved in Project A01.

Classical density functional theory in three dimensions with GPU-accelerated automatic differentiation: Computational performance analysis using the example of adsorption in covalent-organic frameworks

Authors

• Rolf Stierle (University of Stuttgart)
• Gernot Bauer (University of Stuttgart)
• Nadine Thiele (University of Stuttgart)
• Benjamin Bursik (University of Stuttgart, research project A01)  
• Philipp Rehner (ETH Zürich)
• Joachim Gross (University of Stuttgart, research project A01)  

Abstract< 1 , which indicates a strong intensity of physical processes on the boundary, described by the inhomogeneity φ ε (the cases α = 1 and α > 1 were previously studied by the same authors). A complete Puiseux asymptotic expansion is constructed for the solution u ε as ε → 0 , i.e., when the diffusion coefficients are eliminated and the thin network shrinks into a graph. Furthermore, the corresponding uniform pointwise and energy estimates are proved, which provide an approximation of the solution with a given accuracy in terms of the parameter ε .

We show how classical density functional theory can greatly benefit from algorithmic advances in machine learning, especially neural networks. By exploiting GPU-accelerated backward automatic differentiation, we overcome the often cumbersome and error-prone implementation of functional derivatives for classical density functional theory computations. This provides an efficient and straightforward solution for computing functional derivatives, opening up a wide range of applications. We show the gain in computational performance by using backward automatic differentiation to compute the functional derivatives on GPUs, and exemplify the use of this easy-to-implement and highly extensible classical density functional theory framework to predict the adsorption isotherms of a methane/ethane mixture described by a Helmholtz energy functional based on the PC-SAFT equation of state in the covalent-organic framework 2,3-DhaTph. Together with this manuscript, we provide the full classical density functional theory code as supplementary material.