The object of research the development of surrogate and reduced-order models for engineering systems based on machine-learning techniques. The study focuses on replacing time-consuming high-fidelity numerical simulations with computationally efficient models that preserve the accuracy of prediction. The approach is verified using a technical system for which reduced models are built from hydrodynamic simulation data. Method. The proposed methodology combines neural networks trained with the Levenberg–Marquardt algorithm and Gaussian process regression with the Matérn kernel. Singular value decomposition is employed to form reduced-order representations of the system. The Levenberg–Marquardt algorithm demonstrated faster convergence and higher stability compared to conventional gradient descent, while Gaussian process regression ensured accurate interpolation of nonlinear dependencies. Results. The integration of singular value decomposition with Gaussian process regression enables rapid reconstruction of the system state vector within seconds while maintaining adequate model fidelity. The developed surrogate models provide reliable approximation of high-fidelity simulation results and significantly reduce computational time. The obtained results confirm the effectiveness of the proposed approach for accelerating engineering analysis and creating digital-twin-based predictive models.