We present an efficient and scalable approach to inverse PDE-based modelling with the adjoint method. We use automatic differentiation (AD) with Enzyme to automaticaly generate the buidling blocks for the inverse solver. We utilize the efficient pseudo-transient iterative method to achieve performance that is close to the hardware limit for both forward and adjont problems. We demonstrate close to optimal parallel efficiency on GPUs in series of benchmarks.

We present an efficient approach for the development of 3-D partial differential equation solvers that are able to tackle the hardware limit of modern GPUs and scale to the world's largest supercomputers. The approach relies on the accelerated pseudo-transient method and on the automatic generation of on-chip memory usage-optimized computation kernels for the implementation. We report performance and scaling results on LUMI and Piz Daint, an AMD-GPU and a NVIDIA-GPU supercomputer.