Introducing a microstructure-embedded autoencoder approach for reconstructing high-resolution solution field data from a reduced parametric space

Computational Mechanics, vol. 75, pp. 1377–1406

Abstract

Abstract In this study, we develop a novel multi-fidelity deep learning approach that transforms low-fidelity solution maps into high-fidelity ones by incorporating parametric space information into an autoencoder architecture. This method’s integration of parametric space information significantly reduces the amount of training data needed to effectively predict high-fidelity solutions from low-fidelity ones. In this study, we examine a two-dimensional steady-state heat transfer analysis within a heterogeneous materials microstructure. The heat conductivity coefficients for two different materials are condensed from a 101 $$\times $$ × 101 grid to smaller grids. We then solve the boundary value problem on the coarsest grid using a pre-trained physics-informed neural operator network known as Finite Operator Learning (FOL). The resulting low-fidelity solution is subsequently upscaled back to a 101 $$\times $$ × 101 grid using a newly designed enhanced autoencoder. The novelty of the developed enhanced autoencoder lies in the concatenation of heat conductivity maps of different resolutions to the decoder segment in distinct steps. Hence the developed algorithm is named microstructure-embedded autoencoder (MEA). We compare the MEA outcomes with those from finite element methods, the standard U-Net, and an interpolation approach as an upscaling technique. Our analysis shows that MEA outperforms these methods in terms of computational efficiency and error on representative test cases. As a result, the MEA serves as a potential supplement to neural operator networks, effectively upscaling low-fidelity solutions to high-fidelity while preserving critical details often lost in traditional upscaling methods, such as sharp interfaces features lost in the context of interpolation approaches.

Authors 5

1. Rasoul Najafi Koopas corresponding

   Helmut Schmidt University

   Affiliation as printed

   Chair of Solid Mechanics, Institute of Mechanics, Helmut-Schmidt University/University of the Federal Armed Forces, Holstenhofweg 85, Hamburg, 22043, Germany

2. Shahed Rezaei Aachen Access e.V

   Access

   Affiliation as printed

   Access e.V., Aachen, Germany

3. Natalie Rauter

   Helmut Schmidt University

   Affiliation as printed

   Chair of Solid Mechanics, Institute of Mechanics, Helmut-Schmidt University/University of the Federal Armed Forces, Holstenhofweg 85, Hamburg, 22043, Germany

4. Richard Ostwald

   Paderborn University

   Affiliation as printed

   Chair of Structural and Material Mechanics, Institute for Lightweight Design with Hybrid Systems, Faculty of Mechanical Engineering, Paderborn University, Pohlweg 47-49, 33098, Paderborn, Germany

5. Rolf Lammering

   Helmut Schmidt University

   Affiliation as printed

   Chair of Solid Mechanics, Institute of Mechanics, Helmut-Schmidt University/University of the Federal Armed Forces, Holstenhofweg 85, Hamburg, 22043, Germany