Process modeling is a cornerstone for design-technology co-optimization, especially in achieving high-volume manufacturing. Data-driven process models are susceptible to overfitting due to a lack of comprehensive understanding of the underlying process mechanisms. Semi-physical process models often fall short in accurately pre-dicting advanced nodes, primarily due to oversimplified process mechanisms. To address these challenges, we propose a generic process modeling approach based on neural ordinary differential equations. This scheme integrates ODEs to enable time-evolution prediction of process topography while incorporating neural net-works to depict process mechanisms in a data-driven manner. We apply the generic modeling scheme to chemical mechanical pol-ishing and copper electroplating processes, considering they serve as quintessential representations of process modeling challenges. Through silicon data on 28/32/40 nm nodes, the accuracy of our pro-posed models outperforms traditional semi-physical models and can effectively compete with data-driven approaches. These findings underscore the considerable advantages of our proposed modeling scheme in terms of accuracy enhancement for existing models, au-tomated model construction, more accurate modeling of complex mechanisms than the phenomenological modeling strategy and re-ducing the risk of overfitting. Moreover, the successful application of our method to diverse processes underscores its generality and potential for extension to other manufacturing processes.