Learning accurate and stable surrogate models for nonlinear partial differential equations (PDEs) remains a central challenge in computational mechanics, particularly for long-time integration and multi-physics problems. Recently, operator-learning approaches have emerged as a promising alternative to traditional reduced-order models by learning mappings between infinite-dimensional function spaces rather than discrete solution representations [1,2]. In this work, a class of neural operator models is introduced and evaluated for the long-time prediction of nonlinear PDEs, with a particular focus on multispecies diffusion–reaction systems. High-fidelity numerical simulations are used to generate a challenging reference dataset featuring heterogeneous coefficients, nonlinear reaction kinetics, and long temporal horizons. Several operator-learning architectures, including integral-operator-based and latent-space formulations, are trained to advance the solution in time. The proposed models are assessed in terms of accuracy, stability, and error accumulation over extended time horizons. The results suggest that integral operator formulations provide performance comparable to existing neural operator models for long-time prediction in nonlinear and reaction-dominated regimes [3]. To assess generalization beyond the training configuration, the proposed models are further validated on standard benchmark datasets, including diffusion–reaction and Navier–Stokes problems [4]. Results on these benchmark problems indicate that the proposed operator-learning framework is applicable to a broader class of nonlinear PDEs. Overall, this work explores operator-learning architectures and provides a systematic evaluation across custom and benchmark datasets, offering insights into the design of neural operators for long-time PDE prediction.