Differentiable emulation for high-dimensional Bayesian calibration of nuclear reaction models

Full Bayesian calibration of expensive nuclear models has been blocked not by the cost of any single solve, but by the absence of exact likelihood gradients in legacy parameter-dependent operators, which forces gradient-free samplers to spend $\mathcal{O}(10^5)$ evaluations exploring high-dimensional correlated posteriors. I introduce DREAM, a differentiable calibration strategy in which the parameter-dependent operator is sampled offline by any legacy code, compressed by singular value decomposition, and reconstructed online in a differentiable framework so that automatic differentiation delivers exact likelihood gradients through the full forward solve at the cost of one additional evaluation per Hamiltonian Monte Carlo step. The construction is operator-level and depends only on smooth, compressible parameter dependence; the underlying physics solver is treated as a black box. As a representative demonstration, DREAM is applied to a continuum-discretized coupled-channels (CDCC) analysis of $d$+$^{58}$Ni elastic scattering at $20$~MeV with eighteen optical-potential parameters, for which No-U-Turn Sampling converges on a single GPU in under ten minutes from a cold start with zero divergent transitions, yielding a full Bayesian posterior for a breakup reaction. The mean emulator error is more than an order of magnitude below the inferred model discrepancy, so the posterior is set by the reaction model rather than the surrogate. Treating the Koning-Delaroche systematics as an informative prior, the data update the well-determined parameter combinations, raising the mean deuteron surface absorption about $36\%$ above the Koning-Delaroche value, while the under-determined directions remain at the prior; this is a representative payoff that the multi-energy datasets DREAM is designed to accommodate can sharpen into a full physics interpretation.