Back to Search
Start Over
Variational Embedding of Measured Data in Physics-Constrained Data-Driven Modeling.
- Source :
-
Journal of Applied Mechanics . Dec2022, Vol. 89 Issue 12, p1-15. 15p. - Publication Year :
- 2022
-
Abstract
- This paper presents a physics-constrained data-driven method that variationally embeds measured data in the modeling and analysis framework. The physics-based model is augmented with sparse but high-fidelity data through a variationally derived loss function. The structure of the loss function is analyzed in the context of variational correction to the modeled response wherein loss function penalizes the difference in the modeled response from the measured data that represents the local response of the system. The variationally embedded measured data (VEMD) method results in forward simulations that are not only driven by boundary and initial conditions but are also augmented by real measurements taken at only a small number of observation points. In the context of forward simulations, the proposed approach can be seen as inducing inductive biases that exploit the difference between the computed and measured quantities in the parametric space. With the help of a model problem, we show that the proposed method learns from the sparse high-fidelity datasets while preserving conservation properties of the balance laws. Method is applied to a non-smooth model problem and the mathematical attributes of the formulation are investigated in the context of high-fidelity sparse datasets. [ABSTRACT FROM AUTHOR]
- Subjects :
- *MATHEMATICAL models
*DATA modeling
*DATA analysis
Subjects
Details
- Language :
- English
- ISSN :
- 00218936
- Volume :
- 89
- Issue :
- 12
- Database :
- Academic Search Index
- Journal :
- Journal of Applied Mechanics
- Publication Type :
- Academic Journal
- Accession number :
- 175664175
- Full Text :
- https://doi.org/10.1115/1.4055256