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Adaptive Online Emulation for Accelerating Complex Physical Simulations

Tara P. A. Tahseen, Nikolaos Nikolaou, Luís F. Simões, Kai Hou Yip, João M. Mendonça, Ingo P. Waldmann

TL;DR

This work introduces Adaptive Online Emulation (AOE), a framework that dynamically learns neural surrogates during time-stepping simulations using a numerically stable Online Sequential Extreme Learning Machine (OS-ELM). By maintaining cumulative statistics for online updates and employing a three-phase integration strategy, AOE achieves substantial speedups (11.1×) on a high-fidelity 1D radiative-transfer model of an exoplanet while preserving high accuracy (≈0.01% error in $p$–$T$ profiles). The approach minimizes offline training requirements and enables efficient exploration of parameter regimes where traditional surrogates falter. The results suggest broad applicability for accelerating complex physics simulations without sacrificing reliability, with future work targeting adaptive control, active learning, and uncertainty quantification.

Abstract

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 times speedup (91% time reduction) across 200,000 timesteps while maintaining accuracy, potentially making previously intractable high-fidelity time-stepping simulations computationally feasible.

Adaptive Online Emulation for Accelerating Complex Physical Simulations

TL;DR

This work introduces Adaptive Online Emulation (AOE), a framework that dynamically learns neural surrogates during time-stepping simulations using a numerically stable Online Sequential Extreme Learning Machine (OS-ELM). By maintaining cumulative statistics for online updates and employing a three-phase integration strategy, AOE achieves substantial speedups (11.1×) on a high-fidelity 1D radiative-transfer model of an exoplanet while preserving high accuracy (≈0.01% error in – profiles). The approach minimizes offline training requirements and enables efficient exploration of parameter regimes where traditional surrogates falter. The results suggest broad applicability for accelerating complex physics simulations without sacrificing reliability, with future work targeting adaptive control, active learning, and uncertainty quantification.

Abstract

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 times speedup (91% time reduction) across 200,000 timesteps while maintaining accuracy, potentially making previously intractable high-fidelity time-stepping simulations computationally feasible.

Paper Structure

This paper contains 9 sections, 2 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Methodology: Adaptive Online Emulation
  3. Extreme Learning Machines
  4. Numerically Stable Variant of OS-ELM
  5. Integration with Time-Stepping Frameworks
  6. Results
  7. Discussion
  8. Future Work
  9. Code Availability

Figures (2)

  • Figure 1: AOE performance on GJ1214b atmospheric simulation. (Left) Pressure-temperature profiles showing strong agreement between numerical (black) and AOE (red dashed) solutions after 200,000 timesteps ($\Delta t = 0.5s$). (Right) Prediction error remains below $\sim0.01$% throughout the simulation.
  • Figure 2: Fixed initialization costs (warmup + training) are amortized over longer simulations enabling a larger speedup. While this speedup factor is unique to this particular simulation and the chosen AOE hyperparameters ($N_\text{update}, N_\text{cycle}, H)$, the overall trend is simulation-agnostic.