An exact finite-state representation of viscoelastic memory for accelerated sea-level modeling: SLEvolve v1.0

Abstract

Glacial Isostatic Adjustment (GIA) models solve the gravitationally self-consistent sea-level equation for the response of the solid Earth and the oceans to changing ice loads. As these models are increasingly embedded in coupled ice-sheet simulations, glacial-cycle calculations, and large ensembles, standard pseudo-spectral 1-D solvers face a steep computational barrier: they evaluate the viscoelastic response by explicitly re-summing every past load increment, scaling quadratically with time steps as $O(N^2)$. Here we show that this computational penalty is an artifact of algorithmic formulation rather than Earth physics. By exploiting the exponential form of the viscoelastic relaxation kernel, we reformulate the viscous response as an exact recursive update of a finite set of modal states, without re-summing the load history. This exact reformulation alone reduces the cost of a run to $O(N)$, yielding a 20.6-fold speed-up relative to a standard full-history 1-D GIA solver for a case study involving a 550-step Antarctic future sea-level projection. Implemented in our open-source solver SLEvolve v1.0, this formulation---combined with fewer, table-free and multithreaded spherical-harmonic transforms, improved file handling, and physics-inspired iteration starts---achieves an end-to-end speed-up of over three orders of magnitude (up to 4,000-fold) against the same 1-D GIA solver, reducing day-long simulations to under thirty seconds on a workstation. Beyond this solid-Earth application, SLEvolve illustrates how human-derived analytical reformulations can be combined with benchmark-harnessed AI-assisted engineering to modernize scientific software. In particular, Numerical regression tests and performance profiling guided the AI agents'implementation choices and helped reject ineffective optimizations.