A physics-informed neural network framework for inferring infinitesimal phase response curves from finite-pulse circadian recordings

Biological clocks reset and entrain to external cues in a phase-dependent manner. The infinitesimal phase response curve (iPRC) provides the local dynamical rule underlying this process by quantifying how an input changes the instantaneous phase velocity of an oscillator. Inferring iPRCs would make it possible to predict how rhythms respond to new stimulus timings and durations, but existing approaches often require detailed mechanistic models, long perturbation recordings, or specialized population-level resetting experiments. Here we introduce Physics-informed neural network for iPRC inference (PINN-iPRC), a physics-informed neural network framework for inferring iPRCs from standard finite-pulse stimulus-response recordings. PINN-iPRC represents the unknown iPRC as a neural network and embeds the phase equation into the loss function, identifying the iPRC that leads to the observed transient phase trajectory under the known stimulus. In synthetic oscillators, PINN-iPRC accurately recovered iPRCs from finite-pulse recordings, including complex ones that are difficult to capture with simpler parametric reconstructions. Applied to existing experimental Arabidopsis circadian recordings, PINN-iPRC recovered iPRCs comparable to those obtained from specialized population-level resetting experiments, while requiring only conventional stimulus-response trajectories. The inferred iPRCs were further used to predict finite-duration PRCs and circadian peak phases across photoperiods. In particular, the predicted near-invariance of the prr7 peak phase across 8-16 h of darkness was consistent with independently published prr7-11 root recordings. These results support PINN-iPRC as a practical physics-informed approach for extracting interpretable phase-sensitivity functions from routine biological oscillator recordings, with potential applications in experimental design, entrainment prediction, and chronotherapeutic or pharmacological schedule optimization.