Taylor series error correction network for super-resolution of discretized fluid solutions*

High-fidelity fluid simulations can impose an enormous computational burden, thus bringing up the need for an effective up-sampling method for generating high-resolution data. However, conventional up-sampling methods encounter challenges when estimating results based on low-resolution meshes due to the often non-linear behavior of discretization error induced by the coarse mesh [1]. In this study, we present TEECNet (Taylor Expansion Error Correction Network), designed to efficiently super-resolve partial differential equations (PDEs) solutions via graph representations. We use neural networks to learn high-dimensional non-linear mappings between low- and high-fidelity solution spaces to mitigate the effects of discretization error. Building upon the notion that discretization error can be expressed as a Taylor series expansion based on the mesh size, we directly encode approximations of the numerical error in the network design. This novel approach is capable of calibrating point-wise evaluations and emulating physical laws in infinite-dimensional solution spaces. Additionally, computational experiment results verify that the proposed method exhibits favorable generalization across diverse physics domains including heat transfer and simplified Navier-Stokes equations, achieving over 96% accuracy by mean squared error and close to 2% better performance than state-of-the-art measures.