Hybrid Physics-Informed Neural Network Correction of the Lotka–Volterra Model Under Noisy Conditions: Sensitivity Analysis of the λ Parameter

In recent years, hybrid systems combining data-driven and physics-based approaches have gained increasing attention for solving complex real-world problems where deterministic modeling alone is insufficient. Within this framework, Physics-Informed Neural Networks and related hybrid models have been successfully applied across physics, engineering, and biological systems to improve predictive accuracy under uncertainty. However, their stability and sensitivity to noise and model misspecification remain open questions. This study investigates a hybrid Lotka–Volterra population dynamics model augmented with a neural correction term, aiming to analyze how the strength of the neural contribution, controlled by the coupling parameter λ (0≤λ ≤1), affects model performance under noisy and distorted conditions. Here, λ=0 corresponds to the purely physical Lotka–Volterra system, whereas λ=1 represents the fully neural-corrected model. Three experimental setups were implemented: (1) evaluation on noisy data, (2) analysis of the λ sensitivity and its stabilizing effect, and (3) compensation of parameter distortion through neural adaptation. The results indicate that, in the absence of parameter-induced distortions, relying solely on noisy data, moderate neural correction provides the most accurate and stable model behavior, whereas excessive neural influence may distort the original system dynamics. Conversely, when the underlying Lotka–Volterra model incorporates biased parameters, neural correction with a higher λ effectively compensates for structural inaccuracies, enhancing predictive robustness.