# Learning From Simulators: A Theory of Simulation-Grounded Learning

arXiv: https://arxiv.org/abs/2509.18990 · HTML: https://mlsanity.com/paper/2509.18990/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 21 references that are in the map.
- First posted on arXiv 23 Sep 2025.

## Builds on (most cited first, 9 of 9)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [TabPFN: A Transformer That Solves Small Tabular Classification Problems in a Second](https://mlsanity.com/paper/2207.01848/) (2022)
- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [Transformers Can Do Bayesian Inference](https://mlsanity.com/paper/2112.10510/) (2021)
- [Universal Differential Equations for Scientific Machine Learning](https://mlsanity.com/paper/2001.04385/) (2020)
- [Statistical Foundations of Prior-Data Fitted Networks](https://mlsanity.com/paper/2305.11097/) (2023)
- [Simulation as Supervision: Mechanistic Pretraining for Scientific Discovery](https://mlsanity.com/paper/2507.08977/) (2025)
- [Mantis: A Foundation Model for Mechanistic Disease Forecasting](https://mlsanity.com/paper/2508.12260/) (2025)

## Built on by (most cited first, 1 of 1)

- [In-Context Learning Under Regime Change](https://mlsanity.com/paper/2604.16988/) (2026)

## Abstract (arXiv)

Simulation-Grounded Neural Networks (SGNNs) are predictive models trained entirely on synthetic data from mechanistic simulations. They have achieved state-of-the-art performance in domains where real-world labels are limited or unobserved, but lack a formal underpinning. We place SGNNs in a unified statistical framework. Under standard loss functions, they can be interpreted as amortized Bayesian predictors trained under a simulator-induced prior. Empirical risk minimization then yields convergence to the Bayes-optimal predictor under the synthetic distribution. We employ classical results on distribution shift to characterize how performance degrades when the simulator diverges from reality. Beyond these consequences, we develop SGNN-specific results: (i) conditions under which unobserved scientific parameters are learnable via simulation, and (ii) a back-to-simulation attribution method that provides mechanistic explanations of predictions by linking them to the simulations the model deems similar, with guarantees of posterior consistency. We provide numerical experiments to validate theoretical predictions. SGNNs recover latent parameters, remain robust under mismatch, and outperform classical tools: in a model selection task, SGNNs achieve half the error of AIC in distinguishing mechanistic dynamics. These results establish SGNNs as a principled and practical framework for scientific prediction in data-limited regimes.