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Deep neural network enabled corrective source term approach to hybrid analysis and modeling.

Sindre Stenen Blakseth1, Adil Rasheed2, Trond Kvamsdal3

  • 1Department of Physics, Norwegian University of Science and Technology, Norway.

Neural Networks : the Official Journal of the International Neural Network Society
|December 11, 2021
PubMed
Summary

The Corrective Source Term Approach (CoSTA) integrates physics-based modeling with deep learning. This hybrid method significantly improves predictive accuracy and model explainability for complex systems.

Keywords:
Corrective source term approach (CoSTA)Deep neural networksDigital twinsExplainable AIHybrid analysis and modelingPhysics-based modeling

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Area of Science:

  • Computational Science and Engineering
  • Artificial Intelligence
  • Applied Mathematics

Background:

  • Hybrid Analysis and Modeling (HAM) seeks to combine Physics-Based Modeling (PBM) and Data-Driven Modeling (DDM) for enhanced model performance.
  • Existing models often face limitations in accuracy, generalizability, or computational efficiency.
  • There is a need for robust frameworks that can leverage the strengths of both PBM and DDM.

Purpose of the Study:

  • To introduce and validate the Corrective Source Term Approach (CoSTA) as a novel HAM technique.
  • To demonstrate CoSTA's ability to create accurate, trustworthy, and self-evolving models.
  • To enhance the explainability of deep neural network (DNN) components within scientific models.

Main Methods:

  • CoSTA augments PBM governing equations with a corrective source term derived from a DNN.
  • Numerical experiments were conducted on a one-dimensional heat diffusion problem.
  • The approach was compared against standalone PBM and DDM models.

Main Results:

  • CoSTA significantly outperformed comparable PBM and DDM models in predictive accuracy, reducing errors by several orders of magnitude.
  • The proposed method demonstrated superior generalization capabilities compared to pure DDM.
  • CoSTA facilitated the interpretation of the DNN-generated source term within the PBM context, improving explainability.

Conclusions:

  • CoSTA offers a flexible and theoretically sound framework for integrating PBM and DDM.
  • The approach is applicable to any system governed by deterministic partial differential equations.
  • CoSTA has the potential to enable the use of data-driven techniques in high-stakes applications traditionally dominated by PBM.