Title: Physics-informed and ML-based Models for Inverse Problems in Multi-scale Modeling of Complex Materials

Abstract: The computational study of complex polymeric materials is a very challenging field, due to the broad spectrum of the underlying length and time scales. We present a hierarchical multi-scale methodology for predicting the macroscopic properties of polymer-based nanostructured systems, which involves ab-initio, atomistic and coarse-grained (CG) simulations, as well as homogenization approaches and continuum models. The atomistic and CG models are derived through a systematic "bottom-up" hybrid physics-based data-driven strategy, using information from the more detailed, ab-initio and atomistic respectively, scale without adjustable parameters [1-2]. In all cases the "bridging" of different scales involves high dimensional inverse problems that are addressed via advanced optimization methods. Moreover, Deep Learning algorithms are developed to reintroduce atomic detail on the CG scale and obtain atomistic configurations of long polymer chains [3].

Here, we first provide an overview of the above hierarchical approach that allows the study of macromolecular systems over a broad range of time scales, from a few fs up to ms and the prediction of their properties (structural, dynamical, rheological, etc.) [2]. Next, we discuss a few examples of the proposed computational methodology concerning the fundamental study, and the prediction of structure-property relationships, of polymer based nanostructured materials, including polymer films and polymer nanocomposites [3-5].

1. N. Patsalidis, et al., J. Chem. Inf. & Model., (2025), 65, 9009, https://doi.org/10.1021/acs.jcim.5c01193; J. Phys. Chem. C, 2022, 126, 16792−16803, https://doi.org/10.1021/acs.jpcc.2c03630
2. G. Baxevani, et al., SIAM Multiscale Modeling & Simulation, (2023), 4, 1746 https://doi.org/10.1137/23M1548451; Kalligiannaki, et al. Europ. Phys. J. Special Topics, (2016), 225, 1347., http://dx.doi.org/10.1140/epjst/e2016-60145-x
3. E. Christofi, et al., J. Chem. Inf. & Model., (2024), 64, 1853, https://doi.org/10.1021/acs.jcim.3c01870; J. Chem. Phys. 2022, 157, 184903, https://doi.org/10.1063/5.0110322
4. P. Bačová, et al., ACS Nano, (2019), 13, 2, 2439 https://doi.org/10.1021/acs.nanolett.2c04213; A. F. Behbahani, et al., Macromolecules, (2021), 54, 6, 274, https://dx.doi.org/10.1021/acs.macromol.0c02583
5. H. Reda et al., Nano Letters, (2024), 24, 1, 148, https://pubs.acs.org/doi/10.1021/acs.nanolett.3c03491; H. Reda et al., Comput. Methods Appl. Mech. Engrg. (2022), 395, 114905, https://doi.org/10.1016/j.cma.2022.114905