Accelerating Nonlinear MPC by Behavior Cloning with Separated Timescales: Application to Nuclear Reactor Load-Following

Abstract

Behavior Cloning (BC) of expert controllers for multiscale dynamical systems is challenging: state variables evolving at widely separated timescales induce highly nonlinear couplings that a shared latent space may fail to adequately represent, degrading closed-loop generalization. We propose Structured Representation Learning for Behavior Cloning (SRLBC), an architecture designed to leverage the physical knowledge of multiscale systems in which slow state variables, fast (stiff) state variables, and predictable exogenous inputs evolve at different timescales. On 500 long-horizon roll-outs of a pressurized water reactor (PWR) load-following benchmark -a high-dimensional, stiff industrial system with challenging safety constraints -and across 20 training seeds, separated embeddings systematically outperform shared embedding baselines on cumulative cost, imitation accuracy and constraint satisfaction. The resulting standalone policies approach NMPC closed-loop performance at a computational cost 15 times lower on average. Since standalone policies still leave a few percent of trajectories infeasible, we embed the learned policies in a safety-augmented approximate NMPC framework, in which the optimizer is only called when the predicted input sequence is not certified as safe. This yields controllers still 6.8 times faster than the NMPC controller on average, with a feasibility (i.e., constraint satisfaction) of at least 99.8% for all architectures, SRLBC retaining the lowest closed-loop cost. Under distribution shift, standalone BC policies degrade sharply: SRLBC degrades the least, and once safety-augmented, it retains a feasibility above 98% with the lowest closed-loop cost. Beyond the quantitative results, Jacobian-based sensitivity analysis shows that the resulting controller relies on a sparse and less redundant set of latent features, each attributable to a single group of physical variables, and aligned with the physical timescale decomposition of the system.