Parameter space compression underlies emergent theories and predictive models.

Area of Science:

• Physics
• Statistical Mechanics
• Complex Systems Modeling

Background:

• Real-world systems, though microscopically complex, often have simple, accurate descriptions.
• Accurate predictions are achievable even with significant uncertainties in microscopic parameters across various scientific fields.

Purpose of the Study:

• To connect the predictability of complex systems with parameter space structure.
• To analyze parameter sensitivities in continuum theories and critical points.
• To demonstrate a general principle for predictive modeling in diverse scientific areas.

Main Methods:

• Analysis of parameter sensitivities in a prototypical continuum theory (diffusion).
• Investigation of parameter sensitivities at a self-similar critical point (Ising model).
• Quantification of parameter space compression using eigenvalues of the Fisher Information Matrix.

Main Results:

• Identified parameter space compression as key to effective theories for long-scale observables.
• Demonstrated this compression in both diffusion and the Ising model.
• Observed similar compression patterns across diverse scientific models.

Conclusions:

• Parameter space compression is a fundamental aspect enabling effective and universal theories.
• The structure of parameter space in effective continuum and universal theories facilitates predictive modeling.
• This principle suggests broader applicability for predictive modeling in science.