Autonomous Physics-Informed Multi-Phase Optimization of Data Center Cold Plates Using 3D Lattice Boltzmann Simulation

The escalating power density of modern AI accelerators demands liquid cold plate designs that simultaneously maximize convective heat transfer and satisfy stringent pressure drop constraints. Traditional design workflows rely on computationally expensive 3D CFD iterations or surrogate-based optimization that sacrifices physical fidelity. This paper presents a physics-informed multi-phase search framework that directly couples Lattice Boltzmann Method (LBM) simulations with a structured multi-phase exploration strategy. The framework automatically generates parametric pin-fin cold plate geometries with circle pin-fin topology across varying pin radius and inlet velocity, executes 3D LBM simulations under constant heat flux boundary conditions, and evaluates a composite objective function incorporating Nusselt number maximization and pressure drop penalty. The multi-phase search discovers a high-performance configuration with Nu = 258.7 (radius-based), Δ P = 0.0143 (lattice units), Score = 258.7) within 300 evaluations. Comparative benchmarking against Gaussian process Bayesian optimization (Matérn 5/2 kernel, Expected Improvement acquisition) reveals complementary strengths: the multi-phase strategy provides superior design space coverage and physical interpretability, while Bayesian optimization converges to the highest peak score (258.7 (3D)), demonstrating effective convergence to the best configuration found within the searched bounds. Top-view (XY-plane) LBM simulations of the full 130 mm × 70 mm cold plate domain demonstrate significant flow maldistribution effects for corner inlet configurations, highlighting the importance of inlet placement in practical cold plate design. The complete pipeline is open-source and deployable on commodity hardware, providing an accessible methodology for pin-fin thermal design optimization in data center cooling applications.