Efficient Quantum-Informed Computational Frameworks for Mechanics of Materials: Many-Body Dispersion and Machine Learning Surrogate Modeling

Accurately modeling van der Waals dispersion interactions is essential for understanding and predicting the mechanics of complex materials. Classical force fields provide computational efficiency but often fail to capture the inherently quantum mechanical nature of long-range dispersion. The many-body dispersion (MBD) model offers a more sophisticated and accurate description by explicitly accounting for collective electron correlations. However, its direct application to large-scale simulations remains severely constrained by computational cost. This thesis addresses these challenges by developing efficient computational frameworks and machine learning (ML) surrogate models that enable quantum-informed simulations of MBD at scales relevant to mechanics of materials.

The first contribution is the development of a DFTB+MBD framework, supported by an open-source repository, that balances fidelity and efficiency in quantum-informed modeling. Representative case studies, including carbon chains, carbon nanotubes, and ultra-high molecular weight polyethylene, demonstrate the critical role of MBD in accurately describing long-range interactions while exposing the limitations of simplified approaches. These insights motivates the selection of polymer melts as prototypical systems where MBD effects are both significant and computationally tractable for surrogate model development.

Building on this foundation, the thesis introduces a tailored ML surrogate model for MBD forces in polymer melts. A trimmed SchNet architecture is designed to efficiently encode atomic environments within a cutoff distance, achieving a balance between physical consistency, predictive accuracy, and computational cost. Validated across polymer systems of varying complexity and integrated into molecular dynamics simulations, the surrogate model enables direct comparisons with classical pairwise dispersion models. The results reveal distinct signatures of the collective and many-body nature of MBD in polymer dynamics, including enhanced chain mobility and broader configurational sampling.

In parallel, a theoretical reformulation of the MBD method is proposed, separating many-body correlations from pairwise contributions through a novel matrix representation. This advance provides a foundation for more interpretable and potentially more generalizable surrogate models, opening new directions for both analysis and model development.

Overall, this thesis demonstrates that incorporating high-fidelity quantum mechanical effects, specifically MBD, into large-scale soft-matter simulations is both feasible and beneficial. The theoretical insights, surrogate modeling strategies, and methodological innovations developed here establish a foundation for scalable quantum-informed simulations and pave the way towards multiscale modeling frameworks that bridge quantum accuracy with continuum-scale predictive capability.