A likelihood-based framework for simultaneously learning both noise and growth dynamics using biologically-informed neural networks
Abstract
In recent years, neural ordinary differential equation frameworks such as Biologically-Informed Neural Networks (BINNs) have shown promise for learning mechanistic laws from sparse data. However, most existing approaches implicitly assume homoscedastic Gaussian noise, and therefore do not account for potentially meaningful structure in biological variability. Here, we present an extension to the existing BINNs framework that includes a learnable noise model, allowing discovery of the noise model directly from data. Using population growth as an example, we demonstrate that the framework accurately recovers the underlying noise structure and improves predictions of the underlying growth laws compared to existing approaches. As such, this work establishes a general likelihood-based framework for jointly learning dynamics and heteroscedastic noise within mechanistic neural network approaches.
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BibTeX
@misc{crossley2026likelihoodbased,
title = {{A likelihood-based framework for simultaneously learning both noise and growth dynamics using biologically-informed neural networks}},
author = {Rebecca M. Crossley and Ruth E. Baker},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.13475},
eprint = {2606.13475},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.13475},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A likelihood-based framework for simultaneously learning both noise and growth dynamics using biologically-informed neural networks
AU - Rebecca M. Crossley
AU - Ruth E. Baker
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2606.13475
UR - https://arxiv.org/abs/2606.13475
AB - In recent years, neural ordinary differential equation frameworks such as Biologically-Informed Neural Networks (BINNs) have shown promise for learning mechanistic laws from sparse data. However, most existing approaches implicitly assume homoscedastic Gaussian noise, and therefore do not account for potentially meaningful structure in biological variability. Here, we present an extension to the existing BINNs framework that includes a learnable noise model, allowing discovery of the noise model directly from data. Using population growth as an example, we demonstrate that the framework accurately recovers the underlying noise structure and improves predictions of the underlying growth laws compared to existing approaches. As such, this work establishes a general likelihood-based framework for jointly learning dynamics and heteroscedastic noise within mechanistic neural network approaches.
ER -