Differentiable multi-physics solvers for extreme-scale geophysics simulations on GPUs

Although geodynamics and ice flow dynamics address distinct physical systems, they share significant computational and modelling challenges. Both require vast, data-intensive simulations on next-generation high-performance computing (HPC) platforms. With limited observational data, these models must be rigorously constrained to improve their predictive power. Our work focuses on differentiable modelling of Earth’s largest ice sheets and high-resolution 3D geodynamic processes, such as magmatic systems and the formation of the Alps.

We are developing differentiable multi-physics solvers for extreme-scale geophysical simulations on GPUs - ∂GPU4GEO. These high-performance, scalable tools leverage advanced programming techniques, particularly automatic differentiation (AD) within the Julia programming language. Using Enzyme.jl, an AD tool integrated with the LLVM compiler, we combine differentiation with compiler optimisations. This approach enables highly efficient reverse-mode AD, achieving near-theoretical peak performance.

Building on the GPU4GEO PASC project (2020–2024), we are extending pseudo-transient solvers with differentiable modelling capabilities. The modular GPU4GEO software stack, composed of specialised Julia packages, provides solvers for diverse physical systems and customisable building blocks. By integrating Enzyme.jl into the entire stack, we enable high-performance AD on GPUs while maintaining support for distributed-memory parallelism via MPI. These developments ensure scalability on flagship supercomputers and facilitate efficient exploration of geophysical processes.

This collaborative effort targets applications requiring large-scale simulations to address critical scientific challenges. The resulting computational tools are optimised for next-generation GPU architectures, offering transformative potential for geodynamics and glaciology research.