[Paper Review] ModelFLOWs-app: data-driven post-processing and reduced order modelling tools

Ashton Hetherington, Adrián Corrochano+7 more|arXiv (Cornell University)|May 26, 2023

Model Reduction and Neural Networks4 citations

TL;DR

ModelFLOWs-app is an open-source Python software that integrates modal decomposition and deep learning to create data-driven reduced order models (ROMs) for complex nonlinear dynamical systems. By combining proper orthogonal decomposition and deep neural networks, it enables accurate reconstruction of sparse data, prediction of system dynamics, and physics-informed modeling—offering a computationally efficient alternative to full numerical simulations with demonstrated success across fluid dynamics, aerospace, and medical imaging applications.

ABSTRACT

This article presents an innovative open-source software named ModelFLOWs-app, written in Python, which has been created and tested to generate precise and robust hybrid reduced order models (ROMs) fully data-driven. By integrating modal decomposition and deep learning methods in diverse ways, the software uncovers the fundamental patterns in dynamic systems. This acquired knowledge is then employed to enrich the comprehension of the underlying physics, reconstruct databases from limited measurements, and forecast the progression of system dynamics. These hybrid models combine experimental and numerical database, and serve as accurate alternatives to numerical simulations, effectively diminishing computational expenses, and also as tools for optimization and control. The ModelFLOWs-app software has demonstrated in a wide range of applications its great capability to develop reliable data-driven hybrid ROMs, highlighting its potential in understanding complex non-linear dynamical systems and offering valuable insights into various applications. This article presents the mathematical background, review some examples of applications and introduces a short tutorial of ModelFLOWs-app.

Motivation & Objective

• To develop a robust, open-source software tool for constructing fully data-driven hybrid reduced order models (ROMs) that integrate physical insights with machine learning.
• To address the high computational cost of traditional numerical simulations by enabling accurate, fast predictions using limited data.
• To enhance understanding of complex nonlinear systems through pattern identification in spatio-temporal data, particularly in turbulent and reactive flows.
• To support diverse industrial applications—from aerospace and wind energy to medical imaging—by enabling data reconstruction and dynamic forecasting from sparse measurements.
• To provide a unified, extensible framework for researchers and engineers to build, calibrate, and deploy hybrid ROMs using modular, configurable deep learning architectures.

Proposed method

• Employs modal decomposition techniques such as Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD) to extract dominant spatio-temporal patterns from high-dimensional data.
• Integrates these extracted modes as input features into deep learning architectures (e.g., RNNs, CNNs) to build hybrid ROMs that preserve physical consistency while enabling data-driven learning.
• Utilizes a two-module framework: Module 1 applies modal decomposition for pattern identification and data reconstruction; Module 2 combines modal features with deep neural networks for forecasting and system behavior prediction.
• Supports multiple deep learning models (RNN, CNN) with configurable hyperparameters including batch size, number of epochs, learning rate, and layer architecture, with automated hyperparameter tuning via a 'Hyper' flag.
• Applies custom loss functions (e.g., $\text{custom}_{\text{loss}}$) and activation functions (e.g., ReLU, Sigmoid) to optimize model performance for specific tasks like temporal forecasting or reconstruction.
• Enables end-to-end modeling workflows including data preprocessing, model training, validation, and testing, with configurable splits for training (80%), validation (20%), and full test sets.

Figure 1: General distribution of ModelFLOWs-app software.

Experimental results

Research questions

• RQ1 Can a hybrid data-driven framework combining modal decomposition and deep learning effectively reconstruct high-dimensional dynamical systems from sparse measurements?
• RQ2 To what extent can such a framework predict future system states in nonlinear, complex systems like compressible flows or reactive flows with high accuracy and low computational cost?
• RQ3 How well can the software identify and characterize instabilities and coherent structures in turbulent or unsteady flows using only data?
• RQ4 Can the same framework be generalized across diverse domains such as fluid dynamics, wind energy, medical imaging, and flight test data?
• RQ5 What is the impact of automated hyperparameter tuning on model robustness and performance in different application scenarios?

Key findings

• ModelFLOWs-app successfully reconstructs full-field data from sparse measurements in complex flow systems, achieving high fidelity even with limited input data.
• The software enables accurate temporal forecasting of system dynamics in reactive flows, compressible flows with buffeting, and wind turbine behavior, with prediction horizons extending up to 2 time steps ahead.
• In wind velocity prediction using LiDAR data, the framework demonstrated reliable reconstruction and forecasting, supporting real-time control applications.
• The hybrid ROMs developed with ModelFLOWs-app reduced computational costs significantly compared to full numerical simulations, while maintaining high accuracy in capturing instabilities such as flutter in flight test data.
• The framework achieved stable and robust performance across diverse applications, including identification of cross-flow instabilities and pattern reconstruction in medical imaging, validating its cross-domain generalizability.
• Hyperparameter automation (via the 'Hyper' flag) improved model convergence and reduced tuning effort, particularly in RNN and CNN architectures, without compromising predictive accuracy.

Figure 2: The fibers of a third order tensor.