Data-driven discovery of dynamical models in biology If you train a model to forecast a biological time series, you get predictions. What you often don't get is the equation behind them. For applied ML, that gap matters: a network that nails the next time step can still drift into negative concentrations, and a sparse-regression fit that looks clean on synthetic data can collapse the moment you add real noise. In a new review, Bartosz Prokop and Lendert Gelens map out the full landscape of data-driven model discovery, and they organize it through a lens that unifies the whole field: Koopman operator theory. The framing is elegant. Most nonlinear systems can't be diagonalized, but Koopman theory says you can lift them into a space of observables where the dynamics become linear. Almost every data-driven method is then just a different way of approximating that operator. Regression methods (SINDy, symbolic regression, Granger causality) build it explicitly. Neural nets (FFNNs, RNNs, autoencoders, neural ODEs) learn the observables implicitly. Decomposition methods (DMD, eDMD, HAVOK) extract them spectrally. To make the comparison concrete, they stress-test representatives from each family on the Oregonator, a three-species chemical oscillator with a known ground truth. Under ideal conditions everything works. Then they degrade the data the way biology actually degrades it: measurement noise, partial observability, too few oscillation periods, an impoverished basis library. A shared failure hierarchy emerges. SINDy breaks because it differentiates noisy signals. FFNNs fail to generalize past the training window. DMD collapses when the lifting is too coarse to capture a Koopman-invariant subspace. Same root cause, three symptoms. Their measured conclusion is that no single method wins. The way forward is hybrids: universal differential equations that wrap a neural net around known mechanism, SINDy-plus-autoencoder pipelines, and nullcline-learning methods like CLINE that turn forecasting into geometry. For drug discovery, metabolic engineering, and synthetic biology, the takeaway is concrete: method choice has to be matched to your data's observability and noise, not to benchmark leaderboards. A pipeline that recovers interpretable kinetics from sparse, noisy assay data is worth more than one that forecasts beautifully but explains nothing, because only the former lets you run what-if experiments in silico before committing wet-lab budget. Paper: Prokop et al., Nature Reviews Physics (2026), journal license | doi.org/10.1038/s42254-026-0…