The aim of this special issue in Geoscientific Model Development is to collate contributions from the EGU General Assembly 2024, specifically the session titled "Advances in Numerical Modelling of Geological Processes". This session explores the complex multi-physics nature of geological processes, which often involve the interaction of different physical phenomena. Such interactions can generate nonlinear responses, leading to the spontaneous localization of flow and deformation.

In addition to physics-based models, geological and geophysical datasets serve as another vital source of information, while recent technological advancements have significantly enhanced spatial and temporal resolutions.

Understanding the interplay between different physical processes necessitates the development of advanced numerical tools and methodologies. Effective new models should utilize various types of parallel hardware efficiently and in a backend-agnostic manner. These models must also balance conciseness with the capability to bridge portability and performance, thereby addressing the challenge of the two-language barrier. Furthermore, new applications that incorporate high-quality data into physics-based predictive numerical simulations are crucial. These applications facilitate workflows that further refine key unknown parameters within the models. The integration of innovative inversion strategies, which connect forward dynamic models with observable data, and the combination of partial differential equation (PDE) solvers with machine learning (ML) through differentiable programming, represent significant areas of research within this field.

This special issue comprises contributions from the following two complementary themes also featured in the EGU session:

1. The first of these themes entails computational advances associated with alternative spatial and/or temporal discretization for existing forward/inverse models, scalable high-performance computing implementations of new and existing methodologies (GPUs/multi-core), solver and preconditioner developments, combining PDEs with AI- or ML-based approaches (physics-informed ML), automatic differentiation and differentiable programming, and significant performance increases by using new algorithms or code and methodology comparisons (benchmarks).
2. The second area of interest comprises physics advances associated with the development of PDEs to describe geological processes, inversion strategies and adjoint-based modelling, numerical model validation through comparison with observables (data), scientific discovery enabled by 2D and 3D modelling, and utilization of coupled models to explore nonlinear interactions.

Review process: all papers of this special issue underwent the regular interactive peer-review process of Geoscientific Model Development handled by members of the GMD editorial board.