Some Technical Thoughts on Modeling

TL;DR

This paper discusses various issues in modeling, emphasizing the use of steepest descent methods for developing models at different levels, including functions, ODEs, and PDEs, with illustrative examples.

Contribution

It provides a conceptual overview of modeling challenges and demonstrates how steepest descent methods can be used to develop models from data at multiple levels.

Findings

Steepest descent methods can be effectively used for model development.

Different modeling levels (functions, ODEs, PDEs) require tailored approaches.

The paper offers practical examples illustrating these modeling techniques.

Abstract

This paper is more an essay than a report. There is a gentle introduction to some issues in modeling, followed by the use of steepest descent methods to develop a model as contrasted to using such methods to solve one already in hand, as in [1]. Three levels are discussed: fitting functions to model given data, fitting an ODE to model given data, and more briefly, fitting a PDE to model given data. Specific examples are discussed.