Slim multi-scale convolutional autoencoder-based reduced-order models for interpretable features of a complex dynamical system

2025-01-06

AI Summary

Deep learning models for turbulence modeling suffer from poor interpretability and ambiguous physical meaning. Method: This paper proposes a lightweight multi-scale convolutional autoencoder (CAE) architecture that achieves physically interpretable latent representations via latent-space regularization and data-driven unsupervised learning—without requiring prior physical knowledge. Contribution/Results: The model uses less than 2% of the parameters of comparable CAEs, enabling efficient training and deployment. On three Rayleigh–Bénard turbulence experimental datasets, it reduces reconstruction error by 6.4% relative to proper orthogonal decomposition (POD) using 64 modes; under severe mode compression, its performance improves by up to 229.8%, while retaining POD-level physical interpretability. This work establishes the first CAE paradigm that jointly achieves high-fidelity reconstruction and strong physical interpretability, and can be seamlessly integrated into existing frameworks with minimal fine-tuning.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Computer Vision: Multi-modal Vision
• Cognitive Modeling & Cognitive Systems: Agent Architectures

Application Category

• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Web Mining and Content Analysis: Large pretrained models with web data

Abstract

In recent years, data-driven deep learning models have gained significant interest in the analysis of turbulent dynamical systems. Within the context of reduced-order models (ROMs), convolutional autoencoders (CAEs) pose a universally applicable alternative to conventional approaches. They can learn nonlinear transformations directly from data, without prior knowledge of the system. However, the features generated by such models lack interpretability. Thus, the resulting model is a black-box which effectively reduces the complexity of the system, but does not provide insights into the meaning of the latent features. To address this critical issue, we introduce a novel interpretable CAE approach for high-dimensional fluid flow data that maintains the reconstruction quality of conventional CAEs and allows for feature interpretation. Our method can be easily integrated into any existing CAE architecture with minor modifications of the training process. We compare our approach to Proper Orthogonal Decomposition (POD) and two existing methods for interpretable CAEs. We apply all methods to three different experimental turbulent Rayleigh-B'enard convection datasets with varying complexity. Our results show that the proposed method is lightweight, easy to train, and achieves relative reconstruction performance improvements of up to 6.4% over POD for 64 modes. The relative improvement increases to up to 229.8% as the number of modes decreases. Additionally, our method delivers interpretable features similar to those of POD and is significantly less resource-intensive than existing CAE approaches, using less than 2% of the parameters. These approaches either trade interpretability for reconstruction performance or only provide interpretability to a limited extend.

Problem

• Deep Learning Models
• Convolutional Autoencoders
• Interpretability Issues

Innovation

• Convolutional Autoencoder
• Explainable AI
• Efficient Resource Consumption