Exploring accuracy and uncertainty quantification in physics-informed neural networks for inferring microbial community dynamics

Abstract

Physics-Informed Neural Networks (PINNs) have become a popular way to infer interpretable interaction parameters from noisy microbial time series, but practitioners face many tunable design choices (loss weights, regularisers, scaling, training schedules) with little guidance, and uncertainty is rarely quantified. We present a two-part study using a DeepXDE PINN for a six-species generalised Lotka-Volterra (gLV) model with a known step input and fixed, species-specific step amplitudes, under synthetic noise. Part A: Accuracy ablation. Starting from a broad-init baseline, we systematically vary constrained initialisation, parameter scaling, L2 regularisation with loss-weighting, split training with auxiliary observations, function constraints, adaptive collocation, hyperparameter tuning, and optimisers (Adam,L-BFGS). The largest gains come from simple parameter scaling. Hyperparameter tuning and adaptive collocation achieve competitive pairwise interaction errors. Part B: Uncertainty quantification. We benchmark deep ensembles and Monte Carlo (MC) dropout and report multi-replicate fits with different initial conditions. An N=10 deep ensemble yields the best single-trajectory growth-rate accuracy, while MC-dropout provides predictive bands. Overall, scaling plus either tuning or ensembles delivers robust interaction inference; our loss-weight sweep and additional regularisation settings offer practical defaults. We release code, metrics, and figures to serve as baselines for accuracy and uncertainty quantification in microbiome PINNs.