Stable adaptive time-stepping for large-scale tVMC dynamics

Develop a stable adaptive Runge–Kutta–Fehlberg time-stepping scheme for time-dependent variational Monte Carlo (tVMC) that accurately simulates real-time dynamics of neural-network quantum states for large two-dimensional disordered transverse-field Ising models, avoiding the instabilities encountered by the authors for large system sizes.

Background

The authors used time-dependent variational Monte Carlo to simulate nonequilibrium dynamics with neural-network quantum states. Fixed time steps are computationally costly, motivating adaptive strategies (e.g., Runge–Kutta–Fehlberg) to accelerate early-time evolution and refine steps near critical points.

Although attractive in principle, their adaptive attempts were not stable at larger sizes. A stable, accurate adaptive scheme would reduce computational cost while preserving fidelity to the target dynamics across the studied quench regimes.