Quantifying the Lennard–Jones Potential between Two Hard Ellipsoids Using Coarse-Grained Deep Learning Techniques

Equations: Eq. (1): V_LJ = 4ε_LJ[(σ/r)¹²– (σ/r)⁶]. Eq. (2): U_AB = 4ε_AB{[σ₀/(R_AB – σ_AB + σ₀)]¹² – [σ₀/(R_AB – σ_AB + σ₀)]⁶}. Eq. (3): U = ∑_{i ∈ Body 1} ∑_{j ∈ Body 2} U_LJ(r_ij)

Classical molecular dynamics is a highly intensive method for simulating the kinetics, thermodynamics, and structural properties of a many-body system over time. Such simulations require the use of energy functions describing the trajectory and momenta of the particles. We focus on the Lennard–Jones potential (LJP), which governs the van der Waals energetics between two particles. By accelerating this non-bonded energy function, we will have simplified the simulation of simple particles (e.g. platelets, nanoparticles) in materials science. We seek to modify the potential’s conventional form, (1), which fails to accurately model the vdW forces between large anisotropic particles. While (3), the current standard for calculation of the potential accurately represents such forces, it is computationally expensive.

We propose a physics-informed neural network (PINN) to learn the parameters of (2). Our goal is to replicate the accuracy of (3) by training our PINN to recognize the relationship between the coefficients of (2) and the parameters of two ellipsoids, our particle of choice. The architecture of the PINN is as follows: two neural networks were ensembled together to find the coefficients of ε_AB and σ_AB and tune for σ₀ in (2). A minimum training loss of 0.0004 over 250 epochs was achieved by implementing an adaptive learning rate algorithm.