ASAS-NANP SYMPOSIUM: Mathematical modeling in animal nutrition-modeling in the agriculture 4.0 era and beyond: merging mechanistic knowledge and artificial intelligence with hybrid modeling.

With the arrival of the 4th Agricultural Revolution (Agriculture 4.0) and the influsion of animal production systems with sensors, automation, and advanced analytics, new opportunities have arisen to improve sustainability, efficiency, and the precision with which we feed animals. It is possible that the barriers of the past such as lack of automation, efficient means of data capture, and appropriate analytical tools with which to drive decision support and system optimization will be mitigated in our lifetime. Increasingly, we will see the blending of mechanistic understanding with technological advancement to guide decision-making. The emerging frontier of hybrid models representing frameworks that integrate mechanistic understanding with the pattern recognition of machine learning, offers considerable promise for application in animal systems. As an illustrative case study, research conducted in other fields where modeling approaches have been successfully integrated will be explored (for example, bioprocess engineering, weather, human health), as well as recent research in agriculture. Several architectures for hybrid modeling may be considered for application in animal biosciences: 1) Serial hybridization, where a machine learning (ML) model provides inputs into a white box model (could be mechanistic or empirical), or vice versa, 2) Parallel hybridization, where models act in parallel and ML and white box model outputs are aggregated or weighted to enhance model performance, 3) Physical constraint hybridization, where domain knowledge (such as conservation laws) typically embedded in mechanistic models are integrated into the structure, parameters or outputs of a ML model, and 4) mechanistic learning, where ML model(s) are embedded within a mechanistic model to predict specific pools or fluxes. Key challenges including data quality and integration, model interpretability, and computational efficiency are discussed alongside practical strategies to overcome them. This review examines how hybrid models can bridge the gap between data-driven insights and biological causality to support real-time decision-making in feed formulation, emissions management, and health monitoring. By positioning hybrid modeling as a cornerstone of precision livestock farming, Agriculture 4.0, and beyond, this review outlines a vision for next-generation tools that are scientifically grounded, causally robust, and prepared to support digital decision-making.