# Efficient Learning of Accurate Surrogates for Simulations of Complex Systems

arXiv: https://arxiv.org/abs/2207.12855 · HTML: https://mlsanity.com/paper/2207.12855/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 0 of its 100 references that are in the map.
- First posted on arXiv 11 Jul 2022.

## Built on by (most cited first, 7 of 7)

- [Physics-consistent machine learning: output projection onto physical manifolds](https://mlsanity.com/paper/2502.15755/) (2025)
- [SMRS: advocating a unified reporting standard for surrogate models in the artificial intelligence era](https://mlsanity.com/paper/2502.06753/) (2025)
- [Frugal Machine Learning for Energy-efficient, and Resource-aware Artificial Intelligence](https://mlsanity.com/paper/2506.01869/) (2025)
- [Predictive Scale-Bridging Simulations through Active Learning](https://mlsanity.com/paper/2209.09811/) (2022)
- [APS: Bias-Controlled Adaptive Prototype Simulation for Population-Scale LLM Agents](https://mlsanity.com/paper/2605.27419/) (2026)
- [Cycle-Consistent and Uncertainty-Aware Neural Surrogates for Tokamak Edge Plasmas](https://mlsanity.com/paper/2607.21407/) (2026)
- [Wrong-Physics Backdoors in Neural PDE Operators](https://mlsanity.com/paper/2608.20439/) (2026)

## Abstract (arXiv)

Machine learning methods are increasingly used to build computationally inexpensive surrogates for complex physical models. The predictive capability of these surrogates suffers when data are noisy, sparse, or time-dependent. As we are interested in finding a surrogate that provides valid predictions of any potential future model evaluations, we introduce an online learning method empowered by optimizer-driven sampling. The method has two advantages over current approaches. First, it ensures that all turning points on the model response surface are included in the training data. Second, after any new model evaluations, surrogates are tested and "retrained" (updated) if the "score" drops below a validity threshold. Tests on benchmark functions reveal that optimizer-directed sampling generally outperforms traditional sampling methods in terms of accuracy around local extrema, even when the scoring metric favors overall accuracy. We apply our method to simulations of nuclear matter to demonstrate that highly accurate surrogates for the nuclear equation of state can be reliably auto-generated from expensive calculations using a few model evaluations.