# Nutrient–response modeling with a single and interpretable artificial neuron

## TL;DR

A new interpretable machine learning model using a single artificial neuron improves nutrient-response modeling in nutritional sciences.

## Contribution

A single artificial neuron with hyperbolic tangent activation provides a flexible and interpretable alternative to classical nonlinear regression for nutrient modeling.

## Key findings

- The model matches or exceeds classical methods in performance across 12 datasets from poultry and fish studies.
- Modern ML practices like Bayesian regularization and bootstrap resampling enhance robustness and uncertainty quantification.
- The method captures essential nutrient dynamics with analytical transparency and small data efficiency.

## Abstract

Precise estimation of nutrient requirements and utilization efficiency is fundamental to nutritional sciences, yet it is mainly performed using classical nonlinear regression models. These models are interpretable but require careful selection of the functional form and initial parameter values. Flexible machine learning (ML) methods are seemingly disliked due to their perceived “black box” nature, which can obscure biological insight. A minimal and interpretable ML framework addresses this gap in nutrient–response modeling. The proposed approach uses a single artificial neuron with a hyperbolic tangent activation. Mathematically, this resembles a four-parameter sigmoidal function but with greater flexibility and distinct parameter definitions, allowing capture of the monotonic, saturating dynamics typical of essential nutrient responses. The method is enhanced with modern ML best practices, including data augmentation, Bayesian regularization, and bootstrap resampling, providing robust, uncertainty-quantified estimates of key nutritional metrics—such as asymptotic response, inflection point, and nutrient requirements—even from small datasets. Evaluations across 12 diverse datasets from poultry and fish studies, including amino acids and phosphorus, demonstrated that the single artificial neuron matches or exceeds the performance of classical models while providing full analytical transparency. The framework is implemented as a no-code graphical application, ‘NutriCurvist’, offering an easy-to-use alternative tool for nutrient-response modeling to support data-driven, precision nutrition.

The online version contains supplementary material available at 10.1038/s41598-025-29267-w.