Abstract
The Empirical Interpolation Method (EIM) and its generalized version (GEIM) can be used to approximate a physical system by combining data measured from the system itself and a reduced model representing the underlying physics. In presence of noise, the good properties of the approach are blurred in the sense that the approximation error no longer converges but even diverges. We propose to address this issue by a least-squares projection with constrains involving some a priori knowledge of the geometry of the manifold formed by all the possible physical states of the system. The efficiency of the approach, which we will call Constrained Stabilized GEIM (CS-GEIM), is illustrated by numerical experiments dealing with the reconstruction of the neutron flux in nuclear reactors. A theoretical justification of the procedure will be presented in future works.
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Notes
- 1.
We omit here the technical details on the meaning of k eff and refer to general references like [5].
- 2.
In the following part of this work, we directly assume that the value ϕ i (x) at point x is σ(ϕ i , x) as measurement.
- 3.
We replace the synthetic neutron problem here by the above analytical function so as to be able to have a more thorough and extensive numerical analysis
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Argaud, J.P., Bouriquet, B., Gong, H., Maday, Y., Mula, O. (2017). Stabilization of (G)EIM in Presence of Measurement Noise: Application to Nuclear Reactor Physics. In: Bittencourt, M., Dumont, N., Hesthaven, J. (eds) Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2016. Lecture Notes in Computational Science and Engineering, vol 119. Springer, Cham. https://doi.org/10.1007/978-3-319-65870-4_8
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DOI: https://doi.org/10.1007/978-3-319-65870-4_8
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