physics-fitting

name	physics-fitting
description	Nonlinear curve fitting for physics data with proper error propagation, chi-squared analysis, residual diagnostics, confidence intervals, and model comparison (AIC/BIC). Use for any parameter extraction from experimental or simulation data.
category	physics
version	1.0.0
author	Synthetic Sciences
license	MIT
tags	["Curve Fitting","Regression","Chi-Squared","Error Propagation","Parameter Estimation","Physics"]
dependencies	["scipy>=1.11.0","numpy>=1.24.0","matplotlib>=3.7.0","lmfit>=1.2.0"]

Physics Data Fitting

Overview

Extract physical parameters from data using nonlinear least squares, chi-squared minimization, and Bayesian inference. Proper error propagation, residual analysis, confidence intervals, and model comparison included.

When to Use

• Fitting a model function to experimental data
• Extracting physical constants from measurements
• Comparing competing models (which theory fits better?)
• Propagating measurement uncertainties to derived quantities
• Any parameter estimation with proper error bars

Do NOT Use When

• You need MCMC / full posterior distributions (use bayesian-inference with emcee/PyMC)
• You're discovering the model itself (use symbolic-regression)
• Data is a time series from an ODE (use ode-solver + this skill)

Core Workflows

1. Basic Nonlinear Fit (scipy)

import numpy as np
from scipy.optimize import curve_fit
import matplotlib.pyplot as plt

# Model function
def exponential_decay(t, A, tau, C):
    """y = A * exp(-t/tau) + C"""
    return A * np.exp(-t / tau) + C

# Data with uncertainties
t_data = np.array([0.5, 1, 2, 3, 5, 7, 10, 15, 20])
y_data = np.array([9.8, 8.1, 5.5, 3.9, 2.1, 1.3, 0.7, 0.35, 0.22])
y_err = np.array([0.3, , , , , , , , ])


popt, pcov = curve_fit(exponential_decay, t_data, y_data,
                       sigma=y_err, absolute_sigma=,
                       p0=[, , ])  


perr = np.sqrt(np.diag(pcov))
A, tau, C = popt
dA, dtau, dC = perr
()
()
()


residuals = (y_data - exponential_decay(t_data, *popt)) / y_err
chi2 = np.(residuals**)
ndof = (t_data) - (popt)
chi2_red = chi2 / ndof
()