Session: 12-03-03: Data-Enabled Predictive Modeling, Scientific Machine Learning, and Uncertainty Quantification in Computational Mechanics

Paper Number: 112990

112990 - Feature Importance and Uncertainty Quantification of Machine Learning Model in Materials Science 

In the field of material science and engineering, machine learning has drawn significant amount of attentions in recent years due to their ability of accelerating the discovery of novel materials through their applications in empirical potential development and surrogate model assisted material design. Molecular dynamics simulations are becoming indispensable in material analysis and design, due to the accurate first principle methods that are free of empirical parameters and phenomenological models. However, successful application of molecular dynamics simulations comes at the expense of high computational cost that is limiting the scale of the simulation model to a limited size of atoms and the simulation time scales to the order of several hundred picoseconds. In order to overcome the limitations on the system size and time scale, empirically parameterized interatomic potentials have been developed to approximate atomic interactions through the simplification of fitting energy components from bond, angle and dihedrals interactions by using simple analytical functions, often inspired by physical interaction laws. To most empirical potentials, the computational cost scales linearly in general with the number of atoms in the simulation system, thus even for small structures that cost is several orders of magnitude lower as compared to the first principle methods. However, as the conventional empirical potentials heavily rely on the simplify analytical functions with parameters that are typically fitted to reproduce either experimental or first principle references, therefore the model complex largely correlates with the range of simulation systems for which the potential is suitable. Thus, careful parameterization of empirical potentials can become very much challenging and has to be validated for each material system to be simulated.

To address the issues with traditionally constructed potentials, efforts have been reported in the literature to utilize machine learning techniques to interpolate the first principle potential energy surface based on a set of reference calculations. As a representative, methods developed by Behler and Parrinello based on artificial neural networks (ANNs) and by Csányi and coworkers based on the Gaussian process regress are the very pioneer attempts for developing the machine learning potentials. Other promising approaches for developing machine learning potentials includes permutation invariant polynomials, the modified Shepard method using Taylor expansions and interpolating moving least squares. This new class of approaches for the interatomic potential development have the advantages that highly complex interatomic potential energy surface can be described for which physical empirical potential functions may be impossible to derive and machine learning regression can be made well automated. In addition, the flexibility of model functions in machine learning enables the developed potentials to achieve an accuracy that is comparable to the first principle reference method used in their construction. In the past decades, machine learning potentials have been constructed for various types of material systems. However, there are two major challenges in applying the new class of machine learning potentials for molecular dynamics simulations: 1) how to quantify the model uncertainty considering various uncertainty recourses and 2) how to mitigate the uncertainty and ensure the tractability and fidelity of the developed machine learning potential in an efficient manner. In order to realize the full potentials of the machine learning force field potentials, these questions need to be answered by developing efficient methodology for uncertainty quantification and management to improve the validity and predictability of their applications in atomistic simulations.

In this paper, uncertainty quantification will be conducted for machine learning potentials to investigate the influence of encoding methods on the fidelity of developed potential. In the presented study, the Behler–Parrinello (B-P) approach combined with high dimensional ANNs potential is employed for the development of machine learning potentials. Feature importance will be evaluated and uncertainty quantification will be conducted to investigate the effects of encoding methods on the quality of the developed machine learning potential. Specifically, the application of ANNs potentials and the sensitivity analysis are conducted and demonstrated with the example of 2D materials, such as graphene.

Presenting Author: Akash Singh University of Illinois at Urbana-Champaign

Presenting Author Biography: Akash Singh is a PhD. candidate at University of Illinois at Urbana Champaign

Authors:

Zhichen Liu University of Illinois at Urbana Champaign
Akash Singh University of Illinois at Urbana-Champaign
Yumeng Li University of Illinois at Urbana-Champaign