Scalable Simulation-Based Model Inference with Test-Time Complexity Control

Simulation plays a central role in scientific discovery. In many applications, the bottleneck is no longer running a simulator—it is choosing among large families of plausible simulators, each corresponding to different forward models/hypotheses consistent with observations. Over large model families, classical Bayesian workflows for model-selection are impractical. Furthermore, amortized model-selection methods typically hard-code a fixed model prior—or complexity penalty—at training time, requiring users to commit to a particular parsimony assumption before seeing the data. We introduce PRISM, a simulation-based encoder-decoder that infers a joint posterior over both discrete model structures and associated continuous parameters, while enabling test-time control of model complexity via a tunable model prior that the network is conditioned on. We show that PRISM scales to families with combinatorially many (up to billions of) model instantiations on a synthetic symbolic regression task. As a scientific application, we evaluate PRISM on biophysical modeling for diffusion MRI data, showing the ability to perform model selection across several multi-compartment models, on both synthetic and in-vivo neuroimaging data.

Scientists build mathematical models — of brains, epidemics, tissue, physics — to explain noisy measurements. The hard part is rarely running one model: it's choosing among the many plausible ones that could all explain the same data. Standard Bayesian model comparison fits each candidate separately and weighs them by how well they predict the data, but this becomes hopeless when there are millions or billions of possible model structures. We introduce PRISM, a neural network that, after a single training run, can take a new observation and instantly answer two coupled questions: which mechanistic model best explains this data, and what are the parameters of that model — together with calibrated uncertainty over both. PRISM works on combinatorially large model families that classical methods cannot touch, and lets users dial a "simplicity knob" at test time to favor simpler or richer explanations without ever retraining. We demonstrate this on a synthetic equation-discovery task with billions of candidate formulas, and on a real scientific application: inferring the microscopic structure of brain tissue from diffusion MRI. In the brain-imaging case, PRISM identifies which biophysical tissue model is supported by each voxel's measurement, matches gold-standard MCMC quality, and reveals where modeling choices genuinely change the conclusions — a step toward more honest, evidence-driven scientific inference.