Python拟合时如何自定义步长？基于lmfit模块的技术问询

Great question—this is such a relatable pain point when working with rough, low-resolution models where those tiny default step sizes just don’t cut it! Let’s break down how you can take control of step sizes in lmfit and Python fitting more broadly:

1. Global Step Size for Numerical Differentiation (Minimizer eps Parameter) #

lmfit’s Minimizer class lets you set a global step size for calculating partial derivatives right when you initialize it. This will apply to all varying parameters by default:

from lmfit import Minimizer, Parameters

def residual(params, x, data):
    # Your residual calculation logic here
    model = params['param1'] * x + params['param2']
    return model - data

params = Parameters()
params.add('param1', value=1.0, vary=True)
params.add('param2', value=2.0, vary=True)

# Set global differential step size to 0.01 (tweak based on your model scale)
minimizer = Minimizer(residual, params, fcn_args=(x, data), eps=0.01)
result = minimizer.minimize()

2. Per-Parameter Custom Step Sizes #

If different parameters need different step sizes (e.g., one parameter has a much larger scale than another), you can define individual eps values when adding each parameter:

# Param1 needs a larger step size, param2 can stay smaller
params.add('param1', value=100.0, vary=True, eps=5.0)
params.add('param2', value=2.0, vary=True, eps=0.01)

This overrides the global eps for that specific parameter during derivative calculations.

3. Step Sizes for Brute-Force Grid Search #

If you’re using lmfit’s brute-force fitting method, use the brute_step parameter to set the grid step for each parameter:

params.add('param1', value=1.0, vary=True, brute_step=0.2)
params.add('param2', value=2.0, vary=True, brute_step=0.1)

# Run brute-force search with your custom steps
result = minimizer.brute()

4. Pass Step Size Parameters to Scipy Optimizers #

Since lmfit wraps scipy’s optimizers, you can pass step-related arguments directly to the underlying optimizer via kwargs in the minimize method. For example:

• For BFGS, use the epsilon parameter to set derivative step size:

  result = minimizer.minimize(method='bfgs', epsilon=0.02)
  

• For Nelder-Mead, you can control initial step size with initial_simplex (define a simplex where each edge length is your desired step):

  import numpy as np
  initial_simplex = np.array([[1.0, 2.0], [1.1, 2.0], [1.0, 2.1]])  # Step sizes of 0.1 for each param
  result = minimizer.minimize(method='nelder-mead', initial_simplex=initial_simplex)
  

Check scipy’s optimizer docs for the exact parameter names for your chosen method.

5. Manual Step Control (Advanced) #

If you want full control over chi-squared calculations with custom steps, you could implement your own numerical differentiation logic in the residual function. This is more work, but useful for edge cases where built-in methods don’t fit your model’s behavior.

For your specific issue where chi-squared stays constant: start by setting eps to ~1% of your parameter’s current value (scaled to your model’s scale) and adjust from there. This should give enough parameter variation to make chi-squared change detectable.

内容的提问来源于stack exchange，提问作者Stéphane