ATHENA: Advanced Techniques for High dimensional parameter spaces to Enhance Numerical Analysis

Romor, Francesco; Tezzele, Marco; Rozza, Gianluigi

doi:10.1016/j.simpa.2021.100133

Cited by 11 publications

(15 citation statements)

References 5 publications

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“…In this section we are going to present the results obtained with the NARGP-AS and the NARGP-NLL method over two benchmark test problems, and over a more complex car aerodynamics problem. The library employed to implement the NARGP model is Emukit [34] while for the active subspace and NLL response surface design we used the open source Python package 1 called ATHENA [42] and GPy [16].…”

Section: Numerical Resultsmentioning

confidence: 99%

Multi-fidelity data fusion through parameter space reduction with applications to automotive engineering

Romor¹,

Tezzele²,

Mrosek³

et al. 2021

Preprint

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Multi-fidelity models are of great importance due to their capability of fusing information coming from different simulations and sensors. Gaussian processes are employed for nonparametric regression in a Bayesian setting. They generalize linear regression embedding the inputs in a latent manifold inside an infinite-dimensional reproducing kernel Hilbert space. We can augment the inputs with the observations of low-fidelity models in order to learn a more expressive latent manifold and thus increment the model's accuracy. This can be realized recursively with a chain of Gaussian processes with incrementally higher fidelity. We would like to extend these multi-fidelity model realizations to case studies affected by a high-dimensional input space but with low intrinsic dimensionality. In these cases physical supported or purely numerical low-order models are still affected by the curse of dimensionality when queried for responses. When the model's gradient information is provided, the existence of an active subspace, or a nonlinear transformation of the input parameter space, can be exploited to design low-fidelity response surfaces and thus enable Gaussian process multi-fidelity regression, without the need to perform new simulations. This is particularly useful in the case of data scarcity. In this work we present a new multi-fidelity approach involving active subspaces and nonlinear level-set learning method. We test the proposed numerical method on two different high-dimensional benchmarks, and on a more complex car aerodynamics problem. We show how a low intrinsic dimensionality bias can increase the accuracy of GP response surfaces.

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Section: Numerical Resultsmentioning

confidence: 99%

Multi-fidelity data fusion through parameter space reduction with applications to automotive engineering

Romor¹,

Tezzele²,

Mrosek³

et al. 2021

Preprint

Self Cite

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“…For the actual computations of the AS we have used the open source Python package called ATHENA [39].…”

Section: Active Subspacesmentioning

confidence: 99%

“…In order to implement and construct the reduced version of the convolutional neural network presented in the previous sections, we employed PyTorch [34] as development environment. We then used the open-source Python library SciPy [48] for scientific computing and the open source Python package ATHENA [39] for the actual computation of the active subspaces.…”

Section: Softwarementioning

confidence: 99%

A Dimensionality Reduction Approach for Convolutional Neural Networks

Meneghetti¹,

Demo²,

Rozza³

2021

Preprint

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The focus of this paper is the application of classical model order reduction techniques, such as Active Subspaces and Proper Orthogonal Decomposition, to Deep Neural Networks. We propose a generic methodology to reduce the number of layers of a pre-trained network by combining the aforementioned techniques for dimensionality reduction with input-output mappings, such as Polynomial Chaos Expansion and Feedforward Neural Networks. The necessity of compressing the architecture of an existing Convolutional Neural Network is motivated by its application in embedded systems with specific storage constraints. Our experiment shows that the reduced nets obtained can achieve a level of accuracy similar to the original Convolutional Neural Network under examination, while saving in memory allocation.

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“…All the algorithms used in this work are implemented in open source software libraries [47,34,7,18], which we will briefly introduce in the discussions of the corresponding numerical methods. In Figure 1 we depicted an outline of the whole numerical pipeline we are going to present, emphasizing the methods and the softwares used.…”

Section: Self-learning Mesh Morphingmentioning

confidence: 99%

“…The active subspaces technique and several other methods for parameter spaces reduction are implemented in the ATHENA 1 Python package [34].…”

Section: Active Subspacesmentioning

confidence: 99%

Hull shape design optimization with parameter space and model reductions, and self-learning mesh morphing

Demo,

Tezzele,

Mola

et al. 2021

Preprint

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In the field of parametric partial differential equations, shape optimization represents a challenging problem due to the required computational resources. In this contribution, a data-driven framework involving multiple reduction techniques is proposed to reduce such computational burden. Proper orthogonal decomposition (POD) and active subspace genetic algorithm (ASGA) are applied for a dimensional reduction of the original (high fidelity) model and for an efficient genetic optimization based on active subspace property. The parameterization of the shape is applied directly to the computational mesh, propagating the generic deformation map applied to the surface (of the object to optimize) to the mesh nodes using a radial basis function (RBF) interpolation. Thus, topology and quality of the original mesh are preserved, enabling application of POD-based reduced order modeling techniques, and avoiding the necessity of additional meshing steps. Model order reduction is performed coupling POD and Gaussian process regression (GPR) in a data-driven fashion. The framework is validated on a benchmark ship.

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ATHENA: Advanced Techniques for High dimensional parameter spaces to Enhance Numerical Analysis

Cited by 11 publications

References 5 publications

Multi-fidelity data fusion through parameter space reduction with applications to automotive engineering

Multi-fidelity data fusion through parameter space reduction with applications to automotive engineering

A Dimensionality Reduction Approach for Convolutional Neural Networks

Hull shape design optimization with parameter space and model reductions, and self-learning mesh morphing

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