Reduced order modeling for parameterized time-dependent PDEs using spatially and memory aware deep learning

Mücke, Nikolaj Takata; Bohté, Sander M.; Oosterlee, Cornelis W.

doi:10.1016/j.jocs.2021.101408

Cited by 32 publications

(18 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The CNN model reached AUROC 0.92 while the traditional models, such as KNN, got AUROC only 0.84 ( Perng et al., 2019 ). This is because deep learning algorithms can remove many redundant dimensions by self-learning ( Kamand Kim,2017 ; Mücke et al.,2021 ), and multiclass classification problem can be resolved with SoftMax. We also noted that Ke Li et al.…”

Section: Discussionmentioning

confidence: 99%

Evaluating machine learning models for sepsis prediction: A systematic review of methodologies

Deng

Sun

et al. 2022

iScience

View full text Add to dashboard Cite

Summary Studies for sepsis prediction using machine learning are developing rapidly in medical science recently. In this review, we propose a set of new evaluation criteria and reporting standards to assess 21 qualified machine learning models for quality analysis based on PRISMA. Our assessment shows that (1.) the definition of sepsis is not consistent among the studies; (2.) data sources and data preprocessing methods, machine learning models, feature engineering, and inclusion types vary widely among the studies; (3.) the closer to the onset of sepsis, the higher the value of AUROC is; (4.) the improvement in AUROC is primarily due to using machine learning as a feature engineering tool; (5.) deep neural networks coupled with Sepsis-3 diagnostic criteria tend to yield better results on the time series data collected from patients with sepsis. The new evaluation criteria and reporting standards will facilitate the development of improved machine learning models for clinical applications.

show abstract

Section: Discussionmentioning

confidence: 99%

Evaluating machine learning models for sepsis prediction: A systematic review of methodologies

Deng

Sun

et al. 2022

iScience

View full text Add to dashboard Cite

show abstract

“…One particular class of dimension reduction techniques is represented by autoencoders, and more generally by other architectures that rely on NNs. In the recent literature many achievements are brought by CAEs, and by extension Generative Adversarial Networks (GANS), Variational Autoencoders (VAEs), bayesian convolutional autoencoders [26]: in [40] convolutional autoencoders are utilized for dimensionality reduction and long-short Term Memory (LSTM) NNs or causal convolutional neural networks are used for time-stepping; in [24] the evolution of the dynamics and the parameter dependency is learned at the same time of the latent space with a forward NN and a CNNs on randomized SVD compressed snapshots, respectively; and in [55] spatial and temporal features are separately learned with a multi-level convolutional autoencoder.…”

Section: Manifold Learningmentioning

confidence: 99%

Non-linear manifold ROM with Convolutional Autoencoders and Reduced Over-Collocation method

Romor¹,

Stabile²,

Rozza³

2022

Preprint

View full text Add to dashboard Cite

Non-affine parametric dependencies, nonlinearities and advection-dominated regimes of the model of interest can result in a slow Kolmogorov n-width decay, which precludes the realization of efficient reduced-order models based on linear subspace approximations. Among the possible solutions, there are purely data-driven methods that leverage autoencoders and their variants to learn a latent representation of the dynamical system, and then evolve it in time with another architecture. Despite their success in many applications where standard linear techniques fail, more has to be done to increase the interpretability of the results, especially outside the training range and not in regimes characterized by an abundance of data. Not to mention that none of the knowledge on the physics of the model is exploited during the predictive phase. In order to overcome these weaknesses, we implement the non-linear manifold method introduced by Carlberg et al [37] with hyper-reduction achieved through reduced overcollocation and teacher-student training of a reduced decoder. We test the methodology on a 2d non-linear conservation law and a 2d shallow water models, and compare the results obtained with a purely data-driven method for which the dynamics is evolved in time with a long-short term memory network.

show abstract

“…ROMs have been constructed without availability of a FOM by inferring the ROM from data using operator inference methods [64,78,11,52]. Machine learning methods like convolutional autoencoders have been used in a projective sense [47,66] and also inference methods [58,51] have been applied to obtain nonlinear low-dimensional approximations. Other nonlinear dimensionality reduction methods like quadratic manifolds [9,32] and diffusion maps [80] have also been leveraged.…”

Section: Introductionmentioning

confidence: 99%

Structure-Preserving Hyper-Reduction and Temporal Localization for Reduced Order Models of Incompressible Flows

Klein¹,

Sanderse

2023

Preprint

View full text Add to dashboard Cite

Reduced order modeling for parameterized time-dependent PDEs using spatially and memory aware deep learning

Cited by 32 publications

References 12 publications

Evaluating machine learning models for sepsis prediction: A systematic review of methodologies

Evaluating machine learning models for sepsis prediction: A systematic review of methodologies

Non-linear manifold ROM with Convolutional Autoencoders and Reduced Over-Collocation method

Structure-Preserving Hyper-Reduction and Temporal Localization for Reduced Order Models of Incompressible Flows

Contact Info

Product

Resources

About