HybriNet-Hybrid Neural Network-based framework for Multi-Parametric Database Generation, Enhancement, and Forecasting

TL;DR

HybriNet introduces a unified hybrid deep-learning reduced-order model that couples high-order SVD (HOSVD) with Gaussian Process Regression and LSTM-based forecasting to generate, enhance, and predict multi-parametric fluid-dynamics databases. The framework performs parametric interpolation across $Re$ and $AoA$, spatial upscaling, and time-accurate forecasting while maintaining a compact representation through HOSVD, achieving $<2\%$ relative error compared to high-fidelity references. Validation on 2D laminar flow around a square cylinder demonstrates accurate reconstruction, missing-data completion, and robust extrapolation to unseen flow conditions. The approach offers a scalable, modular workflow for efficient CFD database generation, digital-twin development, and rapid online simulations with quantified uncertainty.

Abstract

In this work, we introduce HybriNet an innovative and robust framework capable of enhancing spatial resolution, generating fluid dynamics databases for specific flow parameters, and predicting their temporal evolution. The methodology is based on the development of a reduced-order model (ROM) by integrating high-order singular value decomposition (HOSVD) with machine learning (ML) and deep learning (DL) techniques. The ROM enables the generation of multi-parametric fluid dynamics databases concerning varying flow conditions, increases the spatial resolution, and predicts the behaviour of the fluid dynamics problem in terms of time. This helps to accelerate numerical simulations and generate new data efficiently. The performance of the proposed approach has been validated using a collection of 30 two-dimensional laminar flow simulations over a square cylinder at different Reynolds numbers and angles of attack. The databases reconstructed using the proposed methodology exhibited a relative root mean square error below 2% when compared to ground-truth high-resolution data, demonstrating the robustness, accuracy, and efficiency of the proposed framework.

Figures (31)

• Figure 1: Sketch of the methodology applied for the SVD-based alignment of the databases obtained through numerical simulations.
• Figure 2: Sketch of the methodology applied for the development of the proposed HybriNet. Here, ncomp denotes the number of velocity components, nRe and nAoA represent the number of Reynolds numbers and angles of attack in the database, respectively. nx and ny refer to the number of points along each spatial dimension, and t indicates the number of temporal snapshots. $W^{(i)}$ are the mode matrices associated with each dimension of the tensor, $\sigma$ are the singular values, and $\mathcal{S}$ denotes the core tensor.
• Figure 3: Sketch of the methodology applied for the generation of databases unseen flow conditions.
• Figure 4: Sketch of the methodology applied for the resolution enhancement using GPR.
• Figure 5: Sketch of the methodology used for forecasting.