This work aims to develop a scalable surrogate modelling framework for robust multidisciplinary design optimisation (RMDO) in complex engineering systems. Focusing on gas-bearing supported rotors, it addresses the need to maintain system performance under manufacturing deviations and uncertain operating conditions. A large dataset was generated via space-filling sampling in dimensional and operating parameter spaces for herringbone grooved journal bearings. Dimensionless transformation was then applied, converting extrapolation problems into manageable interpolation tasks. Ensemble artificial neural networks (EANNs) were hyperparameter-optimized using genetic algorithms. The resulting EANN surrogate model was validated against a high-fidelity baseline model and further corroborated through experimental tests on a compressor rotor. The EANNs exhibited over 99.5% in F1-score in classifying stability modes and predicted key rotordynamic parameters (whirl speed ratio, logarithmic decrement) with relative errors under 2% for at least 80% of the test data. In multi-objective robust optimisation, the surrogate model produced a Pareto front statistically equivalent to the baseline solution, while cutting computational cost by three orders of magnitude. Experimental validation confirmed reliable forecasts of stability limits and identified the onset of instabilities. The proposed EANN-based framework significantly reduces computational burden without compromising accuracy. Its dimensionless formulation enhances generalizability, offering a powerful pathway to efficient, robust designs in turbomachinery and beyond.