Derivative-Free Ensemble Transform Langevin Dynamics: Robust Inference for Misspecified Simulators

Scientific simulators are widely used for parameter inference in climate, epidemiology, systems biology, and engineering, but they are often likelihood-free, imperfect, stochastic, and unavailable in differentiable form. This makes simulation-based inference challenging: likelihood-based methods are inapplicable, while many generalized Bayesian samplers require simulator derivatives or backpropagation through complex models. We propose derivative-free ensemble transform Langevin dynamics (DF-ETLD) for likelihood-free inference with maximum mean discrepancy generalized posteriors. By replacing simulator derivatives with ensemble parameter--output cross-covariances, the proposed method approximates the posterior without requiring gradients of the forward model, making it applicable to a broader class of likelihood-free simulators. We evaluate DF-ETLD on stochastic Lorenz '96, contaminated location, and misspecified SIR benchmarks, comparing against gradient-based scoring rule samplers and ABC baselines. Across these settings, DF-ETLD achieves comparable or better performance while avoiding simulator derivatives and reducing computational cost. These results suggest ensemble transform posterior inference as a practical route to robust simulation-based inference with imperfect scientific simulators.