Session: 16-01-01: Government Agency Student Poster Competition

Paper Number: 145208

145208 - Learning the Governing Equations of Diffusion in Solids From Atomistic Simulations 

Historically, constitutive laws are constructed by phenomenological observations or first-principle derivations. With atomistic simulations, we now have mechanistic insights into the fundamental physical processes, but scaling up these atomistic processes to larger-scale models remains a fundamental challenge. In this work, we use the data-driven method of Sparse Regression to discover the constitutive equations of materials by learning from atomistic simulations. We attempt to leverage spatiotemporal data obtained from molecular dynamics simulations to gain insight into the mechanism of the diffusion process in solid-state materials and derive the partial differential equation (PDE) that governs the evolution of the concentration of diffusing particles in a solid material. 

We simulated the diffusion of the Hydrogen (H) atom in Nickel (Ni) at 800K temperature using Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) with embedded atom potential. Two situations have been considered: depositing H atoms into a pristine Ni crystal and deleting H atoms from a Ni-H alloy. H concentration, C(t,x), as a function of time and spatial coordinates, are recorded, based on which the time and spatial derivatives (up to the second order) are calculated.  On the left-hand side of the equation to be determined is the time derivative of C; on the right-hand side are candidate terms, including C, its spatial derivatives, and all their possible combinations. Sparse regression uses atomistic simulation data to identify the most informative functional terms on the right-hand side and determine their coefficients. Even though data-driven methods are indispensable tools, they suffer from inherent noise associated with data obtained from experiments and simulations. Computing higher-order derivatives on these noisy discretized datasets exacerbates this problem even more. We applied the total variational regularization (TVR) differentiation scheme to attenuate the effect of noise and extract important features from the data. This method regularizes the derivative itself, effectively reducing its total variation subject to its integral being a close match to the original data, thus removing irrelevant variation while retaining important features. Through the process described above, we have identified a governing PDE for H diffusion in Ni—except for the second order spatial derivative term of C on the right-hand side as commonly seen in diffusion equation, there is a first-order derivative term and a coupling term between C and its second order spatial derivative. To validate our results, we have also applied the method of sparse regression on the data obtained from Monte Carlo random-walk simulations and successfully identified the second-order spatial derivative term on the right-hand side of the PDE with high coefficient accuracy, i.e., the diffusion equation, indicating the effectiveness of the framework.

Furthermore, we will work towards identifying the chemo-mechanics PDE for lithium diffusion in anode materials, paving the way to address the pressing issue of mechanical degradation of silicon anodes in lithium-ion rechargeable batteries. Moreover, our work contributes to a new method for constitutive modeling of materials.

Presenting Author: Wongelemengist Nadew Utah State University

Presenting Author Biography: Wongelemengist Nadew is a second-year Ph.D. student in Mechanical & Aerospace Engineering at Utah State University. He graduated with a Bachelor's degree in mechanical engineering from Addis Ababa Institute of Technology in Ethiopia in 2020. He does research in computational solid mechanics. His research focuses on developing novel models for diffusion processes in solid materials, combining machine learning techniques with traditional engineering principles.

Authors:

Wongelemengist Nadew Utah State University
Haoran Wang Utah State University