Reliable mechanistic operator recovery with biologically-informed neural networks: principles for architecture and optimisation design

Research Approach

This study investigates the reliability of Biologically-Informed Neural Networks (BINNs) in recovering mechanistic operators from sparse, noisy biological data. Unlike standard neural networks that focus solely on data interpolation, BINNs embed differential equations into the training process to learn the underlying constitutive operators (e.g., diffusion, advection, and reaction terms). The authors systematically evaluate how network architecture, learning rates, loss weighting, and batch sizes influence the recovery of these mechanisms across a suite of one-dimensional advection-diffusion-reaction (ADR) benchmark problems.

Key Findings

The researchers demonstrate that successful mechanistic inference is a delicate balancing act. Key insights include:

• Architecture: Moderately expressive networks consistently outperform overly complex models, which are prone to overfitting and noise sensitivity.
• Optimization: Intermediate learning rates and batch sizes provide the best stability, preventing the optimization process from either stalling or failing to converge on the correct physical parameters.
• Loss Balancing: Accurate operator recovery requires a careful weighting between data-fitting losses (which ensure the model matches observations) and PDE residual losses (which enforce physical consistency). Neglecting this balance often leads to models that interpolate data well but fail to capture the true governing biological mechanisms.

Practical Diagnostics

A significant contribution of this work is the identification of practical diagnostics for failure modes. The authors provide guidelines for recognizing when a BINN is under-fitting, over-fitting, or suffering from unstable optimization. These diagnostics are particularly valuable for researchers working with experimental data where the ground truth is unknown, allowing for more credible model discovery.