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

TL;DR

This paper introduces KHRONOS, a kernel-based neural surrogate model that efficiently combines high- and low-fidelity data for aerodynamic prediction, excelling in resource-limited scenarios with fewer parameters and faster training.

Contribution

The study presents KHRONOS, a novel kernel-based neural surrogate leveraging variational principles and tensor decomposition, offering significant efficiency improvements over traditional dense neural networks.

Findings

KHRONOS outperforms in resource-constrained settings.

Requires fewer trainable parameters and trains faster.

Achieves comparable accuracy to other models.

Abstract

Surrogate models provide fast alternatives to costly aerodynamic simulations and are extremely useful in design and optimization applications. This study proposes the use of a recent kernel-based neural surrogate, KHRONOS. In this work, we blend sparse high-fidelity (HF) data with low-fidelity (LF) information to predict aerodynamic fields under varying constraints in computational resources. Unlike traditional approaches, KHRONOS is built upon variational principles, interpolation theory, and tensor decomposition. These elements provide a mathematical basis for heavy pruning compared to dense neural networks. Using the AirfRANS dataset as a high-fidelity benchmark and NeuralFoil to generate low-fidelity counterparts, this work compares the performance of KHRONOS with three contemporary model architectures: a multilayer 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, whilst all models eventually achieve comparable predictive accuracy, KHRONOS excels in resource-constrained conditions. In this domain, KHRONOS consistently requires orders of magnitude fewer trainable parameters and delivers much faster training and inference than contemporary dense neural networks at comparable accuracy. These findings highlight the potential of KHRONOS and similar architectures to balance accuracy and efficiency in multi-fidelity aerodynamic field prediction.