Stabilization of (G)EIM in presence of measurement noise: application to nuclear reactor physics
For practitioners of reduced-order modeling in nuclear reactor physics, this work provides a stabilization method for (G)EIM under noise, though it is incremental as it builds on existing techniques and lacks theoretical proof.
The paper addresses the divergence of (G)EIM approximation error under measurement noise by proposing a constrained least-squares projection (CS-GEIM) that leverages a priori knowledge of the manifold geometry. Numerical experiments on neutron flux reconstruction in nuclear reactors demonstrate improved stability.
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 a 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.