A note on identifiability for inverse problem based on observations

TL;DR

This paper discusses methods for addressing inverse problems, focusing on Morse theory and analyticity to establish solution uniqueness and isolation in certain dynamical systems.

Contribution

It introduces two approaches—Morse Lemma and analyticity—for analyzing the identifiability and solution structure of inverse problems.

Findings

Solutions are generically isolated for specific dynamical systems.

Morse Lemma provides a framework for understanding solution structure.

Analyticity ensures solution uniqueness in certain cases.

Abstract

In this paper we cover a few topics on how to treat inverse problems. There are two different flows of ideas. One approach is based on Morse Lemma. The other is based on analyticity which proves that the number of solutions to the inverse problems is generically isolated for some particular class of dynamical systems.