3. Model Selection¶

This chapter covers how to choose and define models for curve fitting.

3.1. Built-in Models
3.2. Custom Models
3.3. Model Validation

3.4. Chapter Overview¶

Built-in Models (10 min): Use NLSQ’s library of common mathematical models.
Custom Models (10 min): Write your own model functions with JAX.
Model Validation (5 min): Check that your model is correct before fitting.

3.5. Quick Reference¶

# Built-in exponential decay
from nlsq.functions import exponential_decay

popt, pcov = fit(exponential_decay, x, y, p0=[1, 0.5])

# Custom model
import jax.numpy as jnp

def my_model(x, a, b, c):
    return a * jnp.sin(b * x) + c

popt, pcov = fit(my_model, x, y, p0=[1, 1, 0])

3.6. Key Rule¶

Important

All model functions must use jax.numpy (not numpy) for mathematical operations. This enables automatic differentiation and GPU acceleration.

import jax.numpy as jnp  # Use this!
import numpy as np  # Not for model math


def model(x, a, b):
    return a * jnp.exp(-b * x)  # jnp, not np