A physics-informed long short-term memory (LSTM) model for estimating ammonia emissions from dairy manure during storage

Manure management on dairy farms impacts how farmers maximize its value as fertilizer, reduce operating costs, and minimize environmental pollution potential. A persistent challenge on many farms is minimizing ammonia losses through volatilization during storage to maintain manure nitrogen content. Knowing the quantities of emitted pollutants is at the core of designing and improving mitigation strategies for livestock operations. Although process-based models have improved the accuracy of estimating ammonia emissions, complex systems such as manure storage still need to be solved because some underlying science still needs work. This study presents a novel physics-informed long short-term memory (PI-LSTM) modeling approach combining traditional process-based with recurrent neural networks to estimate ammonia loss from dairy manure during storage. The method entails inverse modeling to optimize hyperparameters to improve the accuracy of estimating physicochemical properties pertinent to ammonia's transport and surface emissions. The study used open data sets from two on-farm studies on liquid dairy manure storage in Switzerland and Indiana, U.S.A. The root mean square errors were 1.51 g m−2 h−1 for the PI-LSTM model, 3.01 g m−2 h−1 for the base compartmental process-based (Base-CPBM) model, and 2.17 g m−2 h−1 for the hyperparameter-tuned compartmental process-based (HT-CPBM) model. In addition, the PI-LSTM model outperformed the Base-CPBM and the HT-CPBM models by 20 to 80 % during summer and spring, when most annual ammonia emissions occur. The study demonstrated that incorporating physical knowledge into machine learning models improves generalization accuracy. The outcomes of this study provide the scientific basis to improve policymaking decisions and the design of suitable on-farm strategies to minimize manure nutrient losses on dairy farms during storage periods.