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

arXiv: https://arxiv.org/abs/2512.10287 · HTML: https://mlsanity.com/paper/2512.10287/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 48 references that are in the map.
- First posted on arXiv 11 Dec 2025.

## Builds on (most cited first, 8 of 8)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [AirfRANS: High Fidelity Computational Fluid Dynamics Dataset for Approximating Reynolds-Averaged Navier-Stokes Solutions](https://mlsanity.com/paper/2212.07564/) (2022)
- [Multi-fidelity reduced-order surrogate modeling](https://mlsanity.com/paper/2309.00325/) (2023)
- [Multi-Fidelity Residual Neural Processes for Scalable Surrogate Modeling](https://mlsanity.com/paper/2402.18846/) (2024)
- [NeuralFoil: An Airfoil Aerodynamics Analysis Tool Using Physics-Informed Machine Learning](https://mlsanity.com/paper/2503.16323/) (2025)
- [Multi-fidelity surrogate modeling for temperature field prediction using deep convolution neural network](https://mlsanity.com/paper/2301.06674/) (2023)
- [KHRONOS: a Kernel-Based Neural Architecture for Rapid, Resource-Efficient Scientific Computation](https://mlsanity.com/paper/2505.13315/) (2025)
- [Manifold Alignment-Based Multi-Fidelity Reduced-Order Modeling Applied to Structural Analysis](https://mlsanity.com/paper/2206.06920/) (2022)

## Built on by (most cited first, 3 of 3)

- [Agile Reinforcement Learning through Separable Neural Architecture and Applications](https://mlsanity.com/paper/2601.23225/) (2026)
- [Separable neural architectures as a primitive for unified predictive and generative intelligence](https://mlsanity.com/paper/2603.12244/) (2026)
- [Separable Neural Architectures as Physical World Models: from Mathematical Theory to Applications](https://mlsanity.com/paper/2606.14934/) (2026)

## Abstract (arXiv)

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.