Over the past decades, the application of Markov Chain Monte Carlo (MCMC) to Multi-Observable Thermochemical Tomography (MTT) has become increasingly popular for inferring the thermochemical structure of the Earth, thanks to its ability to sample the highly nonlinear posterior Probability Distribution Functions (PDFs) that lack closed-form expressions [1]. Applying such algorithms requires a comprehensive numerical model of the Earth’s interior that solves and integrates a set of intricate forward problems while ensuring consistency with fundamental principles of thermodynamics. One such solver is Dynamic Topography Evolution (DTE), which can be modeled by simulating the movement of highly viscous creeping geofluids (Stokes-like fluids) and capturing the elastoplastic interactions between different layers of the Earth’s interior. However, such simulations entail exceptionally high computational demands [2], especially when extreme material nonlinearities, three-dimensional complexities, and intricate interfacial interactions are considered. As a result, their use in large-scale studies is constrained, emphasizing the necessity for novel and efficient Reduced-Order Model (ROM) methodologies [3]. Results from linear model reduction techniques suggest that the complexity of the problem surpasses the capabilities of projection-based approaches, due to the slow decay of the Kolmogorov n-width and the complexity of the nonlinear behavior. Consequently, our work aims to develop and exploit novel approaches in Scientific Machine Learning (SciML) to build a hybrid ROM framework capable of efficiently reducing the nonlinear 3D problem while preserving the required levels of accuracy and fidelity. Furthermore, applying such a non-intrusive approach to obtain fast evaluation of the forward problem within the inversion process could enable seamless model updates as the inversion progresses through the parameter space exploration.