Embedding Bayesian optimization in a multi-agent large language model framework for critical heat flux modeling with uncertainty quantification

Large language model (LLM) agents can automate engineering modeling, but self-generated hyperparameter searches often trail expert baselines and vary across runs. We present OPTIMA (Orchestrated, Physics-driven, Tool-Integrated Multi-Agent), an optimization-integrated multi-agent framework that delegates numerical search to a validated ensemble optimization tool rather than asking agents to generate optimization code. A supervisor coordinates coding, execution, repair, and optimization agents through explicit invocation, error-detection, and termination protocols, confining LLM stochasticity to recoverable workflow steps while keeping Bayesian optimization deterministic and reproducible. OPTIMA is evaluated on the OECD/NEA critical heat flux (CHF) benchmark of 24,579 measurements using five measured inputs. The automatically produced 15-member deep ensemble achieves a root mean square percentage error of 12.6% over all data, close to a human-expert Bayesian-optimization pipeline using the same search (12.4%), while providing decomposed aleatory and epistemic uncertainty with conservative calibrated coverage. It also tracks the 2006 look-up table and reproduces physically consistent trends across blind slice datasets. These results suggest that LLM agents are most effective as orchestrators of validated scientific tools rather than generators of numerical code.