Engineering predictions require physical mechanisms to be translated consistently into equations, discretization, code, and validation, yet errors can propagate despite local checks. Artificial-intelligence (AI) agents automate scientific tasks, but coordinating and independently auditing the theory-to-solver process under physical constraints and human oversight remains unresolved. We introduce a human-in-the-loop, physics-constrained multi-agent workflow where human experts define admissible physics and modeling boundaries, while agents retrieve evidence, derive equations, implement solvers, and audit the theory-to-code chain. Applied to soil-plug evolution during suction-caisson installation, the workflow generated and audited 6 formulations in 2.9 h of agent execution once physical knowledge and inputs were prepared. Among these formulations, adding seepage-driven soil void-ratio evolution to the geometric baseline reduced mean absolute final-heave error from 58.4% to 9.0% across 14 profiles; the selected model further incorporated near-wall dilation and achieved mean absolute percentage errors of 12.4% across 9 final-state cases and 4.2% at the endpoints of 5 process histories. Beyond predictive performance, blinded replay recovered all 9 target problems, while an independent audit uncovered 5 implementation problems after 36 predefined checks had passed. Overall, this work extends multi-agent AI beyond task automation toward human-governed engineering solvers.

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