An integrated computational framework is introduced to study complex engineering systems through physics-based ensemble simulations on heterogeneous supercomputers. The framework is primarily designed for the quantitative assessment of laser-induced ignition in rocket engines. We develop and combine an implicit programming system, a compressible reacting flow solver, and a data generation/management strategy on a robust and portable platform. We systematically present this framework using test problems on a hybrid CPU/GPU machine. Efficiency, scalability, and accuracy of the solver are comprehensively assessed with canonical unit problems. Ensemble data management and autoencoding are demonstrated using a canonical diffusion flame case. Sensitivity analysis of the ignition of a turbulent, gaseous fuel jet is performed using a simplified, three-dimensional model combustor. Our approach unifies computer science, physics and engineering, and data science to realize a cross-disciplinary workflow. The framework is exascale-oriented and can be considered a benchmark for future computational science studies of real-world systems.