Learning From Simulators: A Theory of Simulation-Grounded Learning

Abstract: 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 present the foundational theory of simulation-grounded learning. We show that SGNNs implement amortized Bayesian inference under a simulation prior and converge to the Bayes-optimal predictor. We derive generalization bounds under model misspecification and prove that SGNNs can learn unobservable scientific quantities that empirical methods provably cannot. We also formalize a novel form of mechanistic interpretability uniquely enabled by SGNNs: by attributing predictions to the simulated mechanisms that generated them, SGNNs yield posterior-consistent, scientifically grounded explanations. We provide numerical experiments to validate all 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.