Gradient-Informed Monte Carlo Fine-Tuning of Diffusion Models for Low-Thrust Trajectory Design

A new study introduces Neural Surrogate Hamiltonian Monte Carlo (HMC), which leverages neural likelihoods to enhance Bayesian inference methods, particularly Markov Chain Monte Carlo (MCMC). This approach addresses the computational challenges associated with likelihood function evaluations by employing machine learning techniques to streamline the process. The method demonstrates significant advantages, including improved efficiency and robustness in simulations.

A new variational method for canonical ensembles with differentiable temperature has been proposed, addressing the challenge of accurately computing thermodynamic quantities in many-body systems at thermal equilibrium. This method allows for direct sampling and provides thermodynamic quantities as continuous functions of temperature, akin to analytical solutions. Validation was achieved through phase transition calculations in the Ising and XY models.

A novel particle-based algorithm for mean-field variational inference, named PArticle VI (PAVI), has been introduced, providing a nonparametric mean-field approximation and establishing non-asymptotic error bounds. This marks a significant advancement in variational inference, traditionally reliant on parametric assumptions through coordinate ascent variational inference (CAVI).