scholarly journals Leveraging reduced-order models for state estimation using deep learning

2020 ◽  
Vol 897 ◽  
Author(s):  
Nirmal J. Nair ◽  
Andres Goza
Keyword(s):  
Deep Learning ◽  
State Estimation ◽  
Reduced Order Models ◽  
Reduced Order ◽  
Image Position

scholarly journals POD-Enhanced Deep Learning-Based Reduced Order Models for the Real-Time Simulation of Cardiac Electrophysiology in the Left Atrium

2021 ◽  
Vol 12 ◽  
Author(s):  
Stefania Fresca ◽  
Andrea Manzoni ◽  
Luca Dedè ◽  
Alfio Quarteroni
Keyword(s):  
Neural Networks ◽  
Deep Learning ◽  
Left Atrium ◽  
Real Time ◽  
Cardiac Electrophysiology ◽  
Front Propagation ◽  
Reduced Order Models ◽  
Reduced Order ◽  
Training Costs ◽  
Speed Up

The numerical simulation of multiple scenarios easily becomes computationally prohibitive for cardiac electrophysiology (EP) problems if relying on usual high-fidelity, full order models (FOMs). Likewise, the use of traditional reduced order models (ROMs) for parametrized PDEs to speed up the solution of the aforementioned problems can be problematic. This is primarily due to the strong variability characterizing the solution set and to the nonlinear nature of the input-output maps that we intend to reconstruct numerically. To enhance ROM efficiency, we proposed a new generation of non-intrusive, nonlinear ROMs, based on deep learning (DL) algorithms, such as convolutional, feedforward, and autoencoder neural networks. In the proposed DL-ROM, both the nonlinear solution manifold and the nonlinear reduced dynamics used to model the system evolution on that manifold can be learnt in a non-intrusive way thanks to DL algorithms trained on a set of FOM snapshots. DL-ROMs were shown to be able to accurately capture complex front propagation processes, both in physiological and pathological cardiac EP, very rapidly once neural networks were trained, however, at the expense of huge training costs. In this study, we show that performing a prior dimensionality reduction on FOM snapshots through randomized proper orthogonal decomposition (POD) enables to speed up training times and to decrease networks complexity. Accuracy and efficiency of this strategy, which we refer to as POD-DL-ROM, are assessed in the context of cardiac EP on an idealized left atrium (LA) geometry and considering snapshots arising from a NURBS (non-uniform rational B-splines)-based isogeometric analysis (IGA) discretization. Once the ROMs have been trained, POD-DL-ROMs can efficiently solve both physiological and pathological cardiac EP problems, for any new scenario, in real-time, even in extremely challenging contexts such as those featuring circuit re-entries, that are among the factors triggering cardiac arrhythmias.

scholarly journals Deep Learning-Based Accuracy Upgrade of Reduced Order Models in Topology Optimization

2021 ◽  
Vol 11 (24) ◽  
pp. 12005
Author(s):  
Nikos Ath. Kallioras ◽  
Alexandros N. Nordas ◽  
Nikos D. Lagaros
Keyword(s):  
Deep Learning ◽  
Topology Optimization ◽  
Large Scale ◽  
Optimization Problems ◽  
Computational Effort ◽  
Reduced Order Models ◽  
Reduced Order ◽  
Learning Techniques ◽  
Complex Models ◽  
Scale Design

Topology optimization problems pose substantial requirements in computing resources, which become prohibitive in cases of large-scale design domains discretized with fine finite element meshes. A Deep Learning-assisted Topology OPtimization (DLTOP) methodology was previously developed by the authors, which employs deep learning techniques to predict the optimized system configuration, thus substantially reducing the required computational effort of the optimization algorithm and overcoming potential bottlenecks. Building upon DLTOP, this study presents a novel Deep Learning-based Model Upgrading (DLMU) scheme. The scheme utilizes reduced order (surrogate) modeling techniques, which downscale complex models while preserving their original behavioral characteristics, thereby reducing the computational demand with limited impact on accuracy. The novelty of DLMU lies in the employment of deep learning for extrapolating the results of optimized reduced order models to an optimized fully refined model of the design domain, thus achieving a remarkable reduction of the computational demand in comparison with DLTOP and other existing techniques. The effectiveness, accuracy and versatility of the novel DLMU scheme are demonstrated via its application to a series of benchmark topology optimization problems from the literature.

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