Leveraging reduced-order models for state estimation using deep learning

Abstract

State estimation is key to both analyzing physical mechanisms and enabling real-time control of fluid flows. A common estimation approach is to relate sensor measurements to a reduced state governed by a reduced-order model (ROM). (When desired, the full state can be recovered via the ROM). Current methods in this category nearly always use a linear model to relate the sensor data to the reduced state, which often leads to restrictions on sensor locations and has inherent limitations in representing the generally nonlinear relationship between the measurements and reduced state. We propose an alternative methodology where a neural network architecture is used to learn this nonlinear relationship. Neural network is a natural choice for this estimation problem, as a physical interpretation of the reduced state-sensor measurement relationship is rarely obvious. The proposed estimation framework is agnostic to the ROM employed, and can be incorporated into any choice of ROMs derived on a linear subspace (e.g., proper orthogonal decomposition) or a nonlinear manifold. The proposed approach is demonstrated on a two-dimensional model problem of separated flow around a flat plate, and is found to outperform common linear estimation alternatives.

References in corpus (5)

• Machine Learning for Fluid Mechanics
• Data-Driven Sparse Sensor Placement for Reconstruction
• Shallow Neural Networks for Fluid Flow Reconstruction with Limited Sensors
• Sparse reduced-order modeling : Sensor-based dynamics to full-state estimation
• Robust flow field reconstruction from limited measurements via sparse representation

Cited by in corpus (17)

• Uncovering near-wall blood flow from sparse data with physics-informed neural networks
• Convolutional neural network based hierarchical autoencoder for nonlinear mode decomposition of fluid field data
• Super-Resolution Analysis via Machine Learning: A Survey for Fluid Flows
• Experimental velocity data estimation for imperfect particle images using machine learning
• Data-Driven Reduced-Order Modeling of Spatiotemporal Chaos with Neural Ordinary Differential Equations
• Model fusion with physics-guided machine learning
• State estimation with limited sensors -- A deep learning based approach
• Interpreted machine learning in fluid dynamics: Explaining relaminarisation events in wall-bounded shear flows
• A DeepONet multi-fidelity approach for residual learning in reduced order modeling
• Identifying key differences between linear stochastic estimation and neural networks for fluid flow regressions
• Velocity Reconstruction in Puffing Pool Fires with Physics-Informed Neural Networks
• Machine-learned control-oriented flow estimation for multiactuator multi-sensor systems exemplified for the fluidic pinball
• Gappy AE: A Nonlinear Approach for Gappy Data Reconstruction using Auto-Encoder
• Reconstructing three-dimensional bluff body wake from sectional flow fields with convolutional neural networks
• Reduced Order Modeling with Shallow Recurrent Decoder Networks
• Inadequacy of Linear Methods for Minimal Sensor Placement and Feature Selection in Nonlinear Systems; a New Approach Using Secants
• Super-resolution reconstruction of turbulent flows from a single Lagrangian trajectory