Adaptive Online Emulation for Accelerating Complex Physical Simulations

Complex physical simulations often require trade-offs between model fidelity and computational feasibility. We introduce Adaptive Online Emulation (AOE), which dynamically learns neural network surrogates during simulation execution to accelerate expensive components. Unlike existing methods requiring extensive offline training, AOE uses Online Sequential Extreme Learning Machines (OS-ELMs) to continuously adapt emulators along the actual simulation trajectory. We employ a numerically stable variant of the OS-ELM using cumulative sufficient statistics to avoid matrix inversion instabilities. AOE integrates with time-stepping frameworks through a three-phase strategy balancing data collection, updates, and surrogate usage, while requiring orders of magnitude less training data than conventional surrogate approaches. Demonstrated on a 1D atmospheric model of exoplanet GJ1214b, AOE achieves 11.1× speedup (91\% time reduction) across 200,000 timesteps while maintaining accuracy, potentially making previously intractable high-fidelity time-stepping simulations computationally feasible.