Towards a Machine Learning Pipeline in Reduced Order Modelling for Inverse Problems: Neural Networks for Boundary Parametrization, Dimensionality Reduction and Solution Manifold Approximation

Ivagnes, Anna; Demo, Nicola; Rozza, Gianluigi

doi:10.1007/s10915-023-02142-4

Cited by 6 publications

(1 citation statement)

References 40 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Instead of combining data from heterogeneous models, ROM builds a simplified model, typically from some high-fidelity information. Also, in this case, the capabilities of ROM led to its diffusion in several industrial contexts [4,25,26], especially for optimization tasks [27][28][29][30][31][32] or inverse problems [33,34]. In the ROM community, proper orthogonal decomposition (POD) is one of the most employed methods to build the reduced model [35][36][37][38][39].…”

Section: Introductionmentioning

confidence: 99%

A DeepONet multi-fidelity approach for residual learning in reduced order modeling

Demo

Tezzele

Rozza

2023

Adv. Model. and Simul. in Eng. Sci.

Self Cite

View full text Add to dashboard Cite

In the present work, we introduce a novel approach to enhance the precision of reduced order models by exploiting a multi-fidelity perspective and DeepONets. Reduced models provide a real-time numerical approximation by simplifying the original model. The error introduced by the such operation is usually neglected and sacrificed in order to reach a fast computation. We propose to couple the model reduction to a machine learning residual learning, such that the above-mentioned error can be learned by a neural network and inferred for new predictions. We emphasize that the framework maximizes the exploitation of high-fidelity information, using it for building the reduced order model and for learning the residual. In this work, we explore the integration of proper orthogonal decomposition (POD), and gappy POD for sensors data, with the recent DeepONet architecture. Numerical investigations for a parametric benchmark function and a nonlinear parametric Navier-Stokes problem are presented.

show abstract

Section: Introductionmentioning

confidence: 99%

A DeepONet multi-fidelity approach for residual learning in reduced order modeling

Demo

Tezzele

Rozza

2023

Adv. Model. and Simul. in Eng. Sci.

Self Cite

View full text Add to dashboard Cite

show abstract

Disease Spread Control in Cruise Ships: Monitoring, Simulation, and Decision Making

Triantafyllou,

Kalozoumis,

Cholopoulou

et al. 2024

The Blue Book

View full text Add to dashboard Cite

Enhancing non-intrusive reduced-order models with space-dependent aggregation methods

Ivagnes,

Tonicello,

Cinnella

et al. 2024

Acta Mech

View full text Add to dashboard Cite

In this manuscript, we combine non-intrusive reduced-order models (ROMs) with space-dependent aggregation techniques to build a mixed-ROM, able to accurately capture the flow dynamics in different physical settings. The flow prediction obtained using the mixed formulation is derived from a convex combination of the predictions of several previously trained reduced-order models (ROMs), with each model assigned a space-dependent weight. The ROMs incorporated in the mixed model utilize different reduction methods, such as proper orthogonal decomposition and autoencoders, and various approximation techniques, including radial basis function interpolation (RBF), Gaussian process regression, and feed-forward artificial neural networks. Each model’s contribution is given higher weights in regions where it performs best and lower weights where its accuracy is lower compared to the other models. Additionally, a random forest regression technique is used to determine the weights for previously unseen conditions. The performance of the aggregated model is assessed through two test cases: the 2D flow past a NACA 4412 airfoil at a 5-degree angle of attack, with the Reynolds number ranging between $$1 \times 10^{5}$$ 1 × 10 5 and $$1 \times 10^{6}$$ 1 × 10 6 , and a transonic flow over a NACA 0012 airfoil, with the angle of attack as the varying parameter. In both scenarios, the mixed-ROM demonstrated improved accuracy compared to each individual ROM technique, while providing an estimate for the predictive uncertainty.

show abstract

Towards a Machine Learning Pipeline in Reduced Order Modelling for Inverse Problems: Neural Networks for Boundary Parametrization, Dimensionality Reduction and Solution Manifold Approximation

Cited by 6 publications

References 40 publications

A DeepONet multi-fidelity approach for residual learning in reduced order modeling

A DeepONet multi-fidelity approach for residual learning in reduced order modeling

Disease Spread Control in Cruise Ships: Monitoring, Simulation, and Decision Making

Enhancing non-intrusive reduced-order models with space-dependent aggregation methods

Contact Info

Product

Resources

About