3 papers
math.NA2025
Machine learning on manifolds for inverse scattering: Lipschitz stability analysis
Mahadevan Ganesh, Stuart C. Hawkins, Darko Volkov
Establishing Lipschitz stability estimates is crucial for ensuring the mathematical robustness of neural network (NN) approximations in machine learning (ML)-based parameter estima…
math.NA2024
An all-frequency stable integral system for Maxwell's equations in 3-D penetrable media: continuous and discrete model analysis
Mahadevan Ganesh, Stuart C. Hawkins, Darko Volkov
We introduce a new system of surface integral equations for Maxwell's transmission problem in three dimensions. This system has two remarkable features, both of which we prove. Fir…
math.FA2023
Optimal decay rates in Sobolev norms for singular values of integral operators
Darko Volkov
The regularity of integration kernels forces decay rates of singular values of associated integral operators. This is well-known for symmetric operators with kernels defined on $(a…