Numerical models are central to understanding the multi-physics processes governing the Earth's evolution, from mantle convection and lithospheric deformation to magmatic systems, faulting, and natural and engineered reservoirs. These processes couple hydrological, thermal, chemical and mechanical effects whose nonlinear interactions lead to spontaneous localisation of flow and deformation, posing persistent challenges for discretisation, solvers and computational resources.

The way such models are built is changing rapidly. Heterogeneous HPC architectures, differentiable programming and machine learning increasingly allow forward models to be tightly integrated with observations for inversion and uncertainty quantification. At the same time, AI-assisted and agent-based software development is reshaping how scientific codes are written, ported, tested and maintained. This raises new questions about verification, reproducibility and trust.

We invite contributions from three complementary themes:

1/ Computational advances
- Novel spatial and/or temporal discretisations for forward and inverse models
- Scalable, performance-portable HPC implementations (multi-vendor GPUs, multi-core), including energy efficiency
- Solver and preconditioner developments
- Hybrid physics–ML approaches: surrogates, neural operators, learned closures and ML-accelerated solvers
- Automatic differentiation (AD) and differentiable programming

2/ Theoretical and applied advances
- Development of PDEs describing geological processes
- Adjoint-based, Bayesian and ensemble inversion; uncertainty quantification
- Model validation against observables and data assimilation
- Coupled models exploring nonlinear interactions, and scientific discovery enabled by new modelling approaches

3/ Research software and development practices
- AI-assisted and agentic workflows for code development, porting of legacy codes, testing and documentation, including lessons learnt and limitations
- Verification of scientific software, AI-generated or not: benchmarks, manufactured solutions, convergence studies
- Code and methodology comparisons (community benchmarks)
- Open, reproducible and sustainable modelling software ecosystems