Structurally corrected invariant-preserving neural networks for conservative dynamical systems: a statistically validated approach

In this paper a structural correction in neural network architecture for the long-time integration of conservative dynamical systems is used to overcome uncontrolled invariant drift existing in standard physics-informed formulations. The Structurally Corrected IP-PINN is used to solve the Lotka–Volterra predator–prey system where the multiplicative architectural correction to the invariant manifold demonstrates from a statistical significance perspective improvements beyond both baseline and soft-constraint methods (Welch’s t-test, $$p < 10^{-11}$$ , Cohen’s $$d = 5.03$$ ). Also our structurally corrected neural network (SC-PINN) reaches a 72.2% reduction in invariant drift (mean $$9.54\times 10^{-2}$$ vs. $$3.43\times 10^{-1}$$ ) contrasted to the baseline, and a 66.9% improvement over soft penalty techniques.