The main scientific topic of this direction is to use, and develop new as well, multi-scale computational (*HPC + data-driven*) methodologies in order to construct more accurate quantitative models of complex materials across different scales. To achieve this a *hybrid physics-based data-driven paradigm* is proposed, that links together high-performance computing (large-scale simulations) and AI technologies. In more detail, we envisioned work along the following directions:

*Data-driven coarse-graining strategies*: The development of data-driven systematic CG techniques is a very important and still unexplored area of multi-scale modelling. In systematic “bottom-up” strategies the effective CG interactions are derived as follows: Assume a microscopic system, composed of*N*atoms/particles in the canonical ensemble, described by a Hamiltonian*H*in the microscopic_{N}**q**(3*N*) configuration (positions of all atoms), and a mesoscopic CG description of this system with*M*“superatoms” (*M*<*N*), and Hamiltonian*H*, in the mesoscopic_{M}**Q**(3*M*) phase space.

The observable can be distribution functions (e.g. bonded distributions, pair correlation functions, g(r)), the total force acting on a CG particle, or the relative entropy, or Kullback-Leibler divergence, between the microscopic and the coarse space Gibbs measure [??]. Despite the success of such methods, they become problematic for multi-component nanostructured systems (e.g. blends, interfaces, crystals, etc.) due to the complex heterogeneous structure, at the atomic level, of such systems. One of the reasons the above techniques fail is that the set of *basis functions* used to *approximate the exact, but not computable, many-body PMF* is not large enough.

To overcome the above limitations here we combine the existing schemes with *deep learning-based* approaches to provide more accurate, and more transferable as well, approximations of the CG model (free energy surface, FES) under a broad range of conditions. For this, we propose to use neural networks, NNs, which can, in principle, be used to fit any continuous function on compact subsets of R^{n} (see universal approximation theorem). However, their application to describe the interaction between atoms or molecular is not straightforward, since NNs do not obey the required symmetries (such as permutation, translation, etc) followed by physical laws in nature. Thus here the NNs will be combined with proper transformations of the original data [??]. We anticipate that new CG force fields will be a more accurate approximation of the “exact” many-body PMF thus deriving in more powerful and transferable CG models. In addition, we will explore CG *density-dependent potentials* in which density-dependent terms are used to approximate the exact many-body PMF in an analogous manner to classical density functional theory. Recently we’ve developed such CG models for homopolymer bulk systems. Here we will extend such potentials to complex nanostructured systems, also comparing against the data-driven (NNs-based) approximations.

*Linking microscopic and mesoscopic scales*: The main challenge in the multi-scale modelling of complex materials is the systematic linking of the models across the different scales. For these algorithms that either eliminate (dimensionality reduction) or re-introduce degrees of freedom (back-mapping process) are required. Recently, we’ve developed hierarchical back-mapping strategies incorporating generic different scales of description from blob-based models and moderate coarse-grained up to all-atom models (see Figure 3). The central idea is to efficiently equilibrate CG polymers and then to re-insert atomistic degrees of freedom via*geometric and Monte Carlo approaches*. Furthermore, more recently we introduce a general image-based approach for structural back-mapping from coarse-grained to atomistic models using*adversarial neural networks*.

The above methods have been extensively tested for polymer melts of high molecular weight. Here, we will extend these methods to provide large all-atom configurations for heterogeneous nanostructured systems. This is a particularly challenging area, due to the inherent complexities of such systems, that has not been addressed in the literature so far. The new methods will be thoroughly examined and validated by comparing their structural and conformational properties of the back-mapped model configurations with reference data from smaller systems, which are obtained directly from long atomistic simulations.