Axions are hypothetical particles that may explain the observed dark matter (DM) density and the non-observation of a neutron electric dipole moment. An increasing number of axion laboratory searches are underway worldwide, but these efforts are made difficult by the fact that the axion mass is largely unconstrained. If the axion is generated after inflation, a unique mass gives rise to the observed DM abundance; due to nonlinearities and topological defects known as strings, computing this mass accurately has been a challenge for four decades. Recent works using large static lattice simulations have led to largely disparate predictions for the axion mass, spanning the range from 25 microelectronvolts to over 500 microelectronvolts. However, static lattices are intrinsically limited for studies of axion cosmology, which requires both large simulation volumes and good spatial resolution of strings to accurately capture the relevant physics. As I will show, simulations using adaptive mesh refinement, a technique for solving systems of partial differential equations on a dynamic non-uniform lattice, are better suited for this context since only the string cores require high spatial resolution. Using dedicated AMR simulations, we achieve an over three-order-of-magnitude leap in dynamic range and provide evidence that axion strings radiate their energy with a scale-invariant spectrum, leading to a mass prediction in the range (40,180) microelectronvolts.