A Kernel-based Resource-efficient Neural Surrogate for Multi-fidelity Prediction of Aerodynamic Field

Surrogate models provide fast alternatives to costly aerodynamic simulations and are extremely useful in design and optimization applications. This study proposes a new kernel-based neural surrogate, KHRONOS. KHRONOS blends sparse high - fidelity (HF) data with arbitrary low - fidelity (LF) information to accurately predict aerodynamic fields under constrained computational resources. Unlike traditional approaches, KHRONOS is built upon variational principles, interpolation theory, and tensor decomposition. These elements provide a mathematical basis for hyper-reduction of the neural networks. Using the AirfRANS dataset as a high- fidelity benchmark and NeuralFoil to generate low- fidelity counterparts, this article compares the performance of KHRONOS with three contemporary model architectures: multi- layer perceptron (MLP), a graph neural network (GNN), and a physics -informed neural network (PINN). We consider varying levels of high -fidelity data availability (0%, 10%, and 30%) and increasingly complex geometry parameterizations. These are used to predict the surface pressure coefficient distribution over the airfoil. Results indicate that, while all models eventually achieve comparable predictive accuracy when unlimited data and resources are provided, their computational demands differ markedly. KHRONOS consistently requires orders of magnitude fewer trainable parameters and delivers much faster training and inference than conventional neural networks without sacrificing accuracy. These findings highlight the potential of KHRONOS and similar architectures to balance accuracy and efficiency in multi-fidelity aerodynamic field prediction.