# Physics-Informed Neural Networks for Modeling Postprandial Plasma Amino Acids Kinetics in Pigs

## TL;DR

This paper introduces a new AI method that improves modeling of amino acid digestion in pigs using fewer blood samples, making nutritional studies more efficient.

## Contribution

The novel contribution is a Physics-Informed Neural Network (PINN) that integrates biological laws into AI modeling for digestive kinetics.

## Key findings

- The PINN model maintained high accuracy with sparse data, outperforming traditional methods.
- PINN reduced RMSE in key amino acid profiles under sparse sampling conditions.
- The model successfully used physical laws as regularization, improving parameter stability.

## Abstract

Understanding the dynamics of amino acid absorption in pigs is crucial for optimizing animal nutrition and growth efficiency. However, traditional mathematical models used to analyze these digestive processes often struggle when data is scarce, requiring researchers to perform frequent and invasive blood sampling to ensure accurate results. This study aimed to overcome these limitations by developing a Physics-Informed Neural Network, an advanced artificial intelligence approach that integrates established biological laws of digestion into the learning process. We compared this new method against standard techniques using data from pigs fed various protein diets. Our results demonstrated that the PINN-based model was significantly more robust, maintaining high predictive accuracy even when the number of blood samples was drastically reduced. Unlike traditional methods, it successfully reconstructed complete digestive profiles from sparse data without requiring manual adjustments. We concluded that this technology offers an alternative for nutritional modeling. By adopting this method, high-precision analysis can be achieved with minimal samples in future, reducing the frequency of blood sampling while ensuring data quality.

Postprandial plasma amino acid (AA) kinetics serve as essential indicators of digestive efficiency and systemic metabolic status in pigs. Traditional kinetic analysis relies on Non-Linear Least Squares (NLS) regression using compartmental models, yet these methods typically demand repeated blood sampling and precise initialization to ensure convergence. In this study, we developed a Physics-Informed Neural Network (PINN) framework by integrating mechanistic Ordinary Differential Equations (ODEs) directly into the deep learning loss function. The framework was evaluated using a benchmark dataset. Specifically, we performed a retrospective analysis by downsampling the original high-frequency data to simulate dense and sparse sampling strategies. The results demonstrate that while both models exhibit high fidelity under dense sampling, PINN maintains superior robustness and predictive accuracy under data-constrained conditions. Under the sparse sampling scenario, PINN reduced the Root Mean Square Error (RMSE) compared to NLS in key metabolic profiles, such as Methionine in the FAA group (p < 0.01) and Lysine in the HYD group (p < 0.05). Unlike NLS, which is sensitive to initial guesses, PINN successfully utilized physical laws as a regularization term to robustly solve the inverse problem, demonstrating superior parameter identification stability and predictive consistency under data-constrained conditions compared to NLS. We concluded that the PINN framework provides a reliable and consistent alternative for modeling the AA dynamics. In the future, it may be possible to reconstruct highly accurate physiological trajectories under optimized sparse sampling conditions.