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Many domains of science have developed complex simulations to describe phenomena of interest. While these simulations provide high-fidelity models, they are poorly suited for inference and lead to challenging inverse problems. We review the rapidly developing field of simulation-based inference and identify the forces giving additional momentum to the field. Finally, we describe how the frontier is expanding so that a broad audience can appreciate the profound influence these developments may have on science. 

An important part of the Large Hadron Collider (LHC) legacy will be precise limits on indirect effects of new physics, framed for instance in terms of an effective field theory. These measurements often involve many theory parameters and observables, which makes them challenging for traditional analysis methods. We discuss the underlying problem of “likelihood-free” inference and present powerful new analysis techniques that combine physics insights, statistical methods, and the power of machine learning. We have developed MadMiner, a new Python package that makes it straightforward to apply these techniques. In example LHC problems we show that the new approach lets us put stronger constraints on theory parameters than established methods, demonstrating its potential to improve the new physics reach of the LHC legacy measurements. While we present techniques optimized for particle physics, the likelihood-free inference formulation is much more general, and these ideas are part of a broader movement that is changing scientific inference in fields as diverse as cosmology, genetics, and epidemiology. 

Simulators often provide the best description of real-world phenomena. However, the probability density that they implicitly define is often intractable, leading to challenging inverse problems for inference. Recently, a number of techniques have been introduced in which a surrogate for the intractable density is learned, including normalizing flows and density ratio estimators. We show that additional information that characterizes the latent process can often be extracted from simulators and used to augment the training data for these surrogate models. We introduce several loss functions that leverage these augmented data and demonstrate that these techniques can improve sample efficiency and quality of inference.