Learning accurate and computationally cheap data-driven surrogate models is a fundamental challenge in Scientific Machine Learning (SciML), especially when dealing with problems requiring multiple queries, such as model forecasts, uncertainty quantification, scenario analyses and inverse problems. Indeed, many physical systems, ranging from fluid dynamics and epidemiology to genetic transcriptomics, are governed by highly detailed models whose numerical solution is computationally expensive and often requires delicate, problem-dependent parameter calibration. Impaired tuning at this stage can severely compromise the reliability of the resulting predictions. SciML approaches based on latent representations constitute powerful tools to deal with data representing extremely high-dimensional dynamics and limited knowledge of the hidden model [2]. However, purely data-driven models often suffer from limited interpretability and poor extrapolation capabilities. These limitations motivate the systematic integration of physics-based constraints and topological information of the data-manifold into the latent space. By embedding this prior knowledge, we improve robustness to noise and keep the dimension of the latent space controlled. In this talk, we present a class of autodecoder-based neural architectures driven by physical and topological characteristics of the input data, designed to learn efficient surrogate models for complex dynamical systems. In particular, we focus on an innovative hybrid model-learning framework developed for epidemiological forecasts, where the time evolution of the transmission rate in a prescribed compartmental model is learned by available data [3]. The proposed architecture couples a data-driven differential model, represented by a neural network that incorporates external covariates, with a physics-based layer that propagates the epidemic dynamics. Numerical experiments in realistic settings prove that the proposed approach yields reliable and interpretable predictions even when dealing with realistic noisy data. These results pave the way for the adoption of this class of hybrid approaches as reliable surrogates in a wide range of applications.