Simulation-based inference
A class of machine learning methods that infer the parameters of a scientific model by learning from simulations rather than requiring a tractable likelihood function — particularly useful in physics and cosmology.
Simulation-based inference (SBI), also called likelihood-free inference, solves a common problem in scientific modeling: you have a complex simulator that can generate realistic data given a set of parameters, but you can’t write down a mathematical formula for the probability of observing your data given those parameters (the likelihood). Classical Bayesian inference requires that formula. SBI doesn’t.
Instead, SBI trains a neural network on many simulator runs — each with a different set of input parameters — to learn the relationship between parameters and observed data. That learned relationship can then be used to infer which parameter values are most consistent with your real observations, producing a posterior distribution over parameters.
Where it’s used in physics and astronomy:
- Cosmology: inferring dark matter density, Hubble constant, and other cosmological parameters from galaxy survey data — simulations of large-scale structure are expensive but tractable; computing the likelihood directly is not
- Gravitational wave analysis: inferring properties of merging black holes or neutron stars from LIGO/Virgo signals
- Particle physics: estimating parameters of the Standard Model from collision data where the full likelihood is intractable
- Neuroscience and climate: any field where you have a high-fidelity simulator but complex, high-dimensional observations
Common SBI methods:
Neural Posterior Estimation (NPE), Neural Likelihood Estimation (NLE), and Sequential Neural Posterior Estimation (SNPE) are the main algorithmic families, implemented in packages like sbi (Python).
Key limitation: SBI results are only as good as the simulator. If the simulator doesn’t accurately capture the real data-generating process, the inferred posteriors will be biased — a concern called “model misspecification.”
Related terms: Ensemble Forecasting
Related guide: Physics & Astronomy