Gustavo Ramirez-Hidalgo

Abhiram Badrinarayanan, Davor Davidovic, Edoardo Di Napoli et al.

Simulating large molecular systems comprising thousands of atoms requires highly scalable methodologies. While modern Density Functional Theory (DFT) codes exhibit linear scaling, solving the associated large, sparse generalized eigenproblems remains a critical computational bottleneck on exascale architectures. In the context of the LimitX project, we propose a data-driven framework to accelerate these calculations. By shifting the machine learning target from discrete eigenvalues to the coefficients of an interpolating Chebyshev polynomial, and by comparing both all-atom and fragment-based structural representations, we successfully overcome the dimensionality constraints of large-scale spectral prediction. We investigate three machine learning models (Kernel Ridge Regression, Graph Neural Networks, and Random Forests) trained on a novel 2 TB dataset of protein dimers. The predicted spectra provide initial guesses that effectively bypass early Self-Consistent Field (SCF) iterations in BigDFT. Ultimately, these spectral predictors will be deployed to dynamically optimize upcoming rational filter-based eigensolvers, such as FrASE, which is currently in initial development.

Edoardo Di Napoli, Alessandro Pecchia, Gustavo Ramirez-Hidalgo

The simulation of quantum transport in nanodevices requires the solution of the Dyson and Keldysh equations, a task dominated by the inversion of massive, block-tridiagonal matrices. While the Recursive Green's Function (RGF) method has long been the standard $O(N)$ solver for quasi-1D systems, its formulation has typically been restricted to sequential execution and nearest-neighbor interactions. In this work, we carefully reformulate RGF through the lens of Domain Decomposition and Schur Complement theory. This allows us to extend the recursive formalism to block $n$-diagonal systems (handling higher-order stencils) and to derive a parallel algorithm, Domain-Decomposition based RGF (DDRGF), which stitches macroscopic domains via reduced interface systems. We explore data dependencies in DDRGF in detail, by means of block-sparse structures and tracing back to the desired output as a block tridiagonal approximation, giving a clear, reproducible and extensible formulation. We validate these algorithms using \texttt{LibNEGF.jl}, a Julia-based implementation, demonstrating that the structural insights of domain decomposition provide a robust pathway for high-performance quantum transport simulations on modern multi-core clusters. The theory presented here lays down the base for tackling the Keldysh problem, to be similarly handled in future stages of our work. Although the target here is the acceleration of kernels in the non-equilibrium Green's function method, the algorithms and the implementations presented can be immediately used in any application involving block $n$-diagonal systems.