A likelihood-based framework for simultaneously learning both noise and growth dynamics using biologically-informed neural networks

Journal article

In recent years, neural ordinary differential equation frameworks such as BiologicallyInformed 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.

Authors: Crossley, RM; Baker, RE

• Publication status: Accepted
• Peer review status: Peer reviewed
• Publisher: Springer
• Journal: Bulletin of Mathematical Biology
• Acceptance date: 2026-09-03
• EISSN: 1522-9602
• ISSN: 0092-8240
• Language: English