Physics-informed kernel mixtures for structural dynamics

The effective integration of physical prior knowledge and measured data is critical for developing robust physics-informed machine learning frameworks. Calibrating the balance between structured physical approximations and data-driven flexibility is a key challenge of model development, particularly when physical models are only valid within specific operational regimes. In such cases, a global reliance upon a physical approximation can lead to model misspecification. This paper introduces a physics-informed kernel mixture framework for Gaussian process regression, capable of dynamically varying the reliance upon available physical knowledge based on identifiable switching variables. This ensures that physical understanding is prioritised in valid regimes and relaxed in favour of flexible data-driven components elsewhere. Rather than relying on soft constraints or loss-based penalties, known physics is explicitly embedded within the construction of kernels, enforcing desirable properties within predictions (e.g. quadratic lift force, localised behaviours). This allows model structure to mimic available physical intuition in an interpretable manner. Furthermore, the framework incorporates regime-dependent heteroscedastic noise to accurately capture varying uncertainty across different operational states. The versatility of the physics-informed kernel mixture framework is demonstrated through two distinct engineering case studies: the aerodynamic directional loading of a long-span suspension bridge and the prediction of aircraft wing strain during in-flight manoeuvres. The proposed kernel structures improve predictive accuracy and extrapolation whilst recovering an interpretable representation of regime-dependent system behaviour.