ADMOS 2023

Clustering-based Parametric Surrogate Modeling of Vibroacoustic Problems Assisted by Neural Networks and Active Subspace Method

  • Sreekumar, Harikrishnan (Technische Universität Braunschweig)
  • Outzen, Lukas (Technische Universität Braunschweig)
  • Römer, Ulrich (Technische Universität Braunschweig)
  • Langer, Sabine (Technische Universität Braunschweig)

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Parametric reduced order modelling delivers significant advantages in computational costs for multi-query problems, where the expensive high-fidelity simulations are replaced with the low-fidelity solutions obtained from the respective reduced order model representing the desired parameter domain (pROM). However, the convergence of the pROM depends on the difficulty to capture the characteristics of the underlying system. Practical problems in structural dynamics and vibroacoustics, for instance the simulation of an aircraft, possess difficult system responses that are challenging for existing parametric model order reduction (PMOR) techniques. Also, the higher the number of parameters and the range of each parametric dimension, the more effort is required to produce an accurate pROM. In this contribution, we address the above issue for vibroacoustic problems by adopting an existing clustering-based PMOR modelling approach thereby producing pROMs for each of the identified clusters. With this approach, we produce local ROMs at a number of parameter sample points to train the pROM and clusters are formed according to the dissimilarity of the underlying Krylov subspace using the Grassmannian metric. Once the clusters are established, a subset of local ROMs that can represent the entire region of the cluster is iteratively identified using a classical Greedy algorithm. Finally in the PMOR online phase, the desired system response at any parametric setting can be obtained from the respective valid cluster pROM in real time by interpolation of the identified local ROMs. In addition, neural networks are deployed to learn and predict the expensive cluster assignment thereby yielding a faster online phase. The major contribution of this paper is the formulation and extension of the above approach to a high-dimensional parametric setting. The curse of dimensionality is addressed using the dimensionality reduction technique of the active subspace method (ASM). The clustering-based PMOR approach is applied to the low-dimensional parametric subspace computed by the gradient-based ASM. As a result, we propose a combined framework of PMOR training in active subspaces and clustering-based PMOR assisted by a neural network to accelerate the convergence of PMOR procedures for complex problems. In this paper, we present the adaptive algorithms of the proposed combined framework and demonstrate its efficiency using generic examples from vibroacoustics.