Surrogate Modeling of Resonant Behavior in Scattering Problems Through Adaptive Rational Approximation and Sketching.

Area of Science:

• Computational physics
• Numerical analysis
• Wave scattering

Background:

• Resonant behavior in scattering problems is crucial for understanding wave phenomena.
• Existing methods for identifying resonance can be computationally intensive and complex.
• Field amplification, defined as the norm of the solution operator, is a key indicator of resonance.

Purpose of the Study:

• To develop novel, efficient algorithms for identifying (almost-)resonant behavior in scattering problems.
• To build accurate surrogate models for field amplification using rational approximation.
• To provide theoretical foundations for the proposed rational approximation techniques.

Main Methods:

• Utilizing rational approximation to build surrogate models of field amplification.
• Deriving theoretical results linking field amplification to spectral properties of the scattering operator.
• Developing standard rational approximation methods and innovative hybrid approaches combining root-finding with radial basis functions.
• Employing adaptive sampling strategies for flexibility.

Main Results:

• Two algorithms, one standard and one hybrid, demonstrated superior performance in numerical experiments.
• The choice between the two best-performing methods depends on whether accuracy or efficiency is prioritized.
• The proposed methods are agnostic to discretization strategies and do not require non-real wavenumber computations.

Conclusions:

• Novel rational approximation-based algorithms effectively identify resonant behavior in scattering problems.
• The developed surrogate models offer a computationally efficient alternative for analyzing field amplification.
• The hybrid approaches show particular promise, balancing accuracy and computational cost.