Comparing computational models and intertemporal choice data in a shared latent space

Simulation-based scientific inference is constrained both by the adequacy and distinguishability of the candidate models as well as their connections to real data. To facilitate testing these models, we propose a shared latent-space framework that embeds model-simulated and empirical data in a common representational space, providing a geometric basis for analyzing relationships among models, experimental designs, and real observations. We compare four ways of constructing this space: model classification, parameter decoding, reconstruction-based Neural Processes, and a hybrid reconstruction--classification objective. Using intertemporal choice as a testbed, we show that the learned geometry recovers relationships among computational-model simulators, characterizes how their distinguishability changes across data-collection designs, and tests whether empirical observations are covered by simulator-supported regions, enabling detection of simulator--data mismatch (model mis-specification). Reconstruction-based learning provides access to uncertainty in latent representations, offers a data-driven way to discover heterogeneity in observed data, and provides a space that can be re-used in further model development. Shared latent geometry therefore provides a framework for quantifying and diagnosing the performance of computational models in relation to real data, paving the way for automated theory development.