An efficient and robust method for parameterized nonintrusive reduced‐order modeling

Kostorz, Wawrzyniec; Muggeridge, Ann; Jackson, Matthew D.

doi:10.1002/nme.6461

Cited by 8 publications

(5 citation statements)

References 18 publications

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“…This can be performed by classical interpolation methods such as cubic splines [ 36 ] or radial basis functions (RBF) [ 4 ]. The RBF approach was extended by [ 65 ] who used a Smolyak grid to sample the parameter space; by [ 34 ] who interpolated values of model parameters and time levels using one parametrisation; and by [ 2 ] who used adaptive sampling in time. Recently, neural networks have been used to perform the interpolation, and examples of this for steady-state parametrised problems can be found in [ 16 , 26 ], both of whom use POD and multi-layer perceptrons, and in [ 59 ], who use POD and compare a number of different networks.…”

Section: Introductionmentioning

confidence: 99%

Data Assimilation Predictive GAN (DA-PredGAN) Applied to a Spatio-Temporal Compartmental Model in Epidemiology

Silva

Heaney

et al. 2022

J Sci Comput

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We propose a novel use of generative adversarial networks (GANs) (i) to make predictions in time (PredGAN) and (ii) to assimilate measurements (DA-PredGAN). In the latter case, we take advantage of the natural adjoint-like properties of generative models and the ability to simulate forwards and backwards in time. GANs have received much attention recently, after achieving excellent results for their generation of realistic-looking images. We wish to explore how this property translates to new applications in computational modelling and to exploit the adjoint-like properties for efficient data assimilation. We apply these methods to a compartmental model in epidemiology that is able to model space and time variations, and that mimics the spread of COVID-19 in an idealised town. To do this, the GAN is set within a reduced-order model, which uses a low-dimensional space for the spatial distribution of the simulation states. Then the GAN learns the evolution of the low-dimensional states over time. The results show that the proposed methods can accurately predict the evolution of the high-fidelity numerical simulation, and can efficiently assimilate observed data and determine the corresponding model parameters.

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Section: Introductionmentioning

confidence: 99%

Data Assimilation Predictive GAN (DA-PredGAN) Applied to a Spatio-Temporal Compartmental Model in Epidemiology

Silva

Heaney

et al. 2022

J Sci Comput

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show abstract

“…Finally, we demonstrate the use of our methods on a number of toy and realistic test cases. This article is a natural continuation of our previous work 18 where an efficient method for parameterized NIROM was given; the latter was motivated by geometric arguments discussed in much greater depth in this article.…”

Section: Introductionmentioning

confidence: 94%

“…The well‐behaved nature of u for later times is represented by the high value of C (1) (near 1) and the low value of B (near 0 in magnitude). Apart from the initial relaxation period of the nonsmooth initial condition the system is well‐behaved and a NIROM is expected to be accurate, as demonstrated in Reference 18.…”

Section: Examplesmentioning

confidence: 99%

“…In this section, we summarize the mathematics by which the outputs from a discretized, high fidelity, forward model are converted into a reduced dimensionality surrogate model (following 18 ) and introduce a geometrical framework to better interpret the process of reduction and the surrogate system behavior in reduced space. We start by recapping the MoL as this is used in building the geometrical framework.…”

Section: Geometrical Frameworkmentioning

confidence: 99%

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Non‐intrusive reduced order modeling: Geometrical framework, high‐order models, and a priori analysis of applicability

Kostorz

Muggeridge

Jackson

2021

Numerical Meth Engineering

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We present an intuitive geometrical framework for non‐intrusive model reduction. Based on simple low‐dimensional geometry that is easy to visualize and interpret, the approach enables one to predict model features a priori and explain them a posteriori. Two simple a priori methods for analyzing the suitability of non‐intrusive model reduction are consequently presented and discussed. As a natural consequence of the interpretation proposed a method extension is proposed, namely, higher‐order temporal discretization. It is also demonstrated that some generic properties of the physical system modeled such as periodicity or convergence towards a steady state are easily represented in the framework proposed. The approaches are illustrated using a number of representative test problems including a three‐dimensional case of the Saffman–Taylor instability and an example exhibiting a propagating discontinuity. It is shown that this property makes the underlying non‐intrusive reduced order modeling nonsmooth meaning it will provide a poor representation of the system dynamics.

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“…They require little or no access to the used simulation code, are straightforward to implement, and can handle black‐box models. Accordingly, they are acknowledged as frequently investigated topic, 3 for example, in the field of parametrized MOR 4 …”

Section: Introductionmentioning

confidence: 99%

A nonintrusive nonlinear model reduction method for structural dynamical problems based on machine learning

Kneifl

Grunert

Fehr

2021

Numerical Meth Engineering

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Model order reduction (MOR) has become one of the most widely used tools to create efficient surrogate models for time-critical applications. For nonlinear models, however, linear MOR approaches are only practicable to a limited extent. Nonlinear approaches, on the contrary, often require intrusive manipulations of the used simulation code. Hence, non-intrusive MOR approaches using classic model order reduction along with machine learning (ML) algorithms can provide remedy. Such approaches have drawn a lot of attention in the recent years. They rely on the idea to learn the dynamics not in a high-dimensional but in a reduced space, i.e., they predict the discrete sequence of reduced system states successively. Open questions are the suitability of such methods in the field of structural dynamics and the best choice of the used ML algorithm. Both are addressed in this paper in addition to the integration of the methodology into a modular and flexible framework that can effortless be adapted to various requirements. By applying the methodology to a dynamic mechanical system, accurate surrogate models are received, which can speed up the simulation time significantly, while still providing high-quality state approximations.

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An efficient and robust method for parameterized nonintrusive reduced‐order modeling

Cited by 8 publications

References 18 publications

Data Assimilation Predictive GAN (DA-PredGAN) Applied to a Spatio-Temporal Compartmental Model in Epidemiology

Data Assimilation Predictive GAN (DA-PredGAN) Applied to a Spatio-Temporal Compartmental Model in Epidemiology

Non‐intrusive reduced order modeling: Geometrical framework, high‐order models, and a priori analysis of applicability

A nonintrusive nonlinear model reduction method for structural dynamical problems based on machine learning

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