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Hydrogen can support carbon-free distributed power in micro gas turbines, but its high reactivity makes combustor design difficult because flashback, pressure loss, outlet-temperature uniformity, and NOx emissions must be balanced. This thesis develops a computational fluid dynamics (CFD)-surrogate optimization framework for a swirl-stabilised hydrogen micro gas turbine combustor with six design variables: swirler blockage, central fuel-lance protrusion, secondary-hole pattern, axialchannel blockage, global equivalence ratio, and central-lance fuel split. A validated steady RANS model with Flamelet Generated Manifold chemistry generated 165 labelled design points. Gaussian-process surrogates predicted the CFD responses with calibrated uncertainty, while a logistic response surface identified flashback with a cross-validated receiver-operating-characteristic area of 0.99. A trust-region NSGA-III search constrained by flashback probability, data support, and prediction uncertainty produced thirty trusted Pareto designs. Additional CFD simulations confirmed eight selected designs; all were non-flashback and met the acceptance criteria. The balanced minimax design achieved 4.60% total-pressure loss, 562.6 K mean exit temperature, 27.1 ppmv NOx, and a 0.319 pattern factor at the prescribed very-lean study condition, ???? = 0.0431. This combustor-exit temperature is not a nominal full-load turbine inlet temperature. The results show that flashback-aware, uncertainty-calibrated CFD-surrogate optimization can identify practical hydrogen combustor compromises at much lower cost than direct CFD search.