Data-driven reduced order modelling based on deep learning
Authors:   , Fu Rui 
Published: September 2024

Reduced Order Modelling (ROM) has become a powerful tool in computational simulations, especially for complex ﬂuid dynamics. ROM-based models (ROMs) oﬀer signiﬁcant reductions in computational cost while maintaining acceptable accuracy. These models rely on dimensional reduction to simplify complex dynamic systems into lower-dimensional representations. It is essential for large simulations and real-time analysis when computational eﬃciency is crucial. The Parametric Reduced Order Models (PROMs) extend the capabilities of traditional ROMs by considering changes in physical parameters or system conﬁgurations that aﬀect the variability of dynamic system responses. This parametric feature enables PROMs to adapt to various dynamic environments, enhancing their ﬂexibility and applicability. In recent years, deep learning has performed excellently in handling large datasets and complex systems. Integrating deep learning methods into ROMs and PROMs has opened up new areas for improving the performance and applicability of ROMs and PROMs. With deep learning methods, ROMs are signiﬁcantly enhanced in robust capabilities for feature extraction, pattern recognition, and the ability to learn complex relationships in data. For PROMs, deep learning helps achieve higher accuracy, better generalisation and faster adaptation to new conditions. In ﬁelds such as ﬂuid dynamics and climate modelling, dynamic systems always have signiﬁcant challenges with their ﬁeld complexity and high dimensionality. The ROMs/PROMs with deep learning applied in these ﬁelds not only enable more eﬃcient computations for simulations but also the extraction of deeper insights from simulation data, enabling improvements in predictive modelling and decision-making. This thesis presents several advancements in the ﬁeld of Reduced Order Modeling (ROM)for ﬂuid ﬂow problems. The primary contributions are threefold: 1. Non-Linear Non-Intrusive ROM(NL-NIROM): A novel nonlinear non-intrusive ROM(NL-NIROM) is introduced for ﬂuid dynamic ﬁeld time-series prediction, which is based on an Autoencoder network and the self-attention mechanism. Additionally, a linear non-intrusive reduced order model(L-NIROM) is also developed on proper orthogonal decomposition (POD) and self-attention mechanism. The advantage of this NL-NIROM is that it can capture more non-linearity information than POD-based L-NIROM. 2. Parametric Non-Linear Non-Intrusive ROM (P-NLNIROM): A new parametric non-linear non-intrusive reduced-order model (P-NLNIROM) for the ﬂuid ﬂow system simulations on diﬀerent parameter sets is presented. This model is constructed by the Stacked Auto-Encoder(DAE) and Deep Residual Learning Neural network(ResNet). In addition, transfer learning(TL) is employed to extend the prediction range within the parametric space, thereby greatly improving the predictive capabilities of the P-NLNIROM. 3. Error Estimate Parametric ROM: Building upon the P-NLNIROM, an error estimate parametric ROM is implemented to correct the predicted simulations caused by P-NLNIROM for higher accuracy and reliability in simulation outputs. To evaluate the eﬀectiveness of this ROM, a numerical experiment on the lock exchange scenarios is presented. It serves as an example case to demonstrate the performance and practical applicability of the error estimate parametric ROM with ﬂuid dynamics simulations.