Discussion Overview
The discussion revolves around the challenge of parameter fitting for a numerical solution of a partial differential equation (PDE) related to the diffusion of a concentrate into a cylindrical medium. Participants explore methods to efficiently determine unknown parameters such as initial concentration and diffusion constant using experimental data.
Discussion Character
- Exploratory, Technical explanation, Debate/contested
Main Points Raised
- One participant describes an initial approach involving a parameter sweep followed by least squares fitting and optimization using fminsearch, expressing concerns about its inefficiency.
- Another participant suggests using the Global Optimization Toolbox to selectively calculate solutions of the PDE, refining initial parameters based on previous results, although this suggestion is not applicable to all participants.
- A later reply indicates that the participant ultimately resorted to a parameter sweep with a double loop, storing square differences to find a minimum, while acknowledging it may not be the most efficient method.
- One participant recommends the Levenberg-Marquardt algorithm for fitting the data and determining unknown parameters, noting that the derivative is known.
Areas of Agreement / Disagreement
There is no consensus on the best method for parameter fitting, with multiple competing views on approaches and techniques remaining unresolved.
Contextual Notes
Participants express uncertainty about the efficiency of their methods and the applicability of suggested tools, indicating limitations in their current approaches and available resources.
Who May Find This Useful
Researchers or practitioners dealing with parameter fitting in numerical solutions of PDEs, particularly in the context of diffusion processes and optimization techniques.