Domain adaptation based transfer learning approach for solving PDEs on complex geometries

  • In machine learning, if the training data is independently and identically distributed as the test data then a trained model can make an accurate predictions for new samples of data. Conventional machine learning has a strong dependence on massive amounts of training data which are domain specific to understand their latent patterns. In contrast, Domain adaptation and Transfer learning methods areIn machine learning, if the training data is independently and identically distributed as the test data then a trained model can make an accurate predictions for new samples of data. Conventional machine learning has a strong dependence on massive amounts of training data which are domain specific to understand their latent patterns. In contrast, Domain adaptation and Transfer learning methods are sub-fields within machine learning that are concerned with solving the inescapable problem of insufficient training data by relaxing the domain dependence hypothesis. In this contribution, this issue has been addressed and by making a novel combination of both the methods we develop a computationally efficient and practical algorithm to solve boundary value problems based on nonlinear partial differential equations. We adopt a meshfree analysis framework to integrate the prevailing geometric modelling techniques based on NURBS and present an enhanced deep collocation approach that also plays an important role in the accuracy of solutions. We start with a brief introduction on how these methods expand upon this framework. We observe an excellent agreement between these methods and have shown that how fine-tuning a pre-trained network to a specialized domain may lead to an outstanding performance compare to the existing ones. As proof of concept, we illustrate the performance of our proposed model on several benchmark problems.show moreshow less

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Metadaten
Document Type:Article
Author: Ayan Chakraborty, Cosmin AnitescuORCiD, Xiaoying Zhuang, Prof. Dr.Ing. Timon RabczukORCiDGND
DOI (Cite-Link):https://doi.org/10.1007/s00366-022-01661-2Cite-Link
URN (Cite-Link):https://nbn-resolving.org/urn:nbn:de:gbv:wim2-20220811-46776Cite-Link
URL:https://link.springer.com/article/10.1007/s00366-022-01661-2
Parent Title (English):Engineering with Computers
Language:English
Date of Publication (online):2022/07/22
Date of first Publication:2022/05/23
Release Date:2022/08/11
Publishing Institution:Bauhaus-Universität Weimar
Institutes and partner institutions:Fakultät Bauingenieurwesen / Institut für Strukturmechanik
Volume:2022
Pagenumber:20
First Page:1
Last Page:20
Tag:Domain Adaptation; NURBS geometry; Navier–Stokes equations; Transfer learning
GND Keyword:Maschinelles Lernen; NURBS
Dewey Decimal Classification:600 Technik, Medizin, angewandte Wissenschaften
BKL-Classification:31 Mathematik / 31.80 Angewandte Mathematik
Licence (German):License Logo Creative Commons 4.0 - Namensnennung (CC BY 4.0)