Concepts & Explanations¶

Understand how NLSQ works and why it’s designed the way it is. These guides explain the theory, architecture, and design decisions behind NLSQ.

Fundamentals¶

How Curve Fitting Works: How Curve Fitting Works explains the mathematical foundation of nonlinear least squares optimization - what it means to “fit” a model to data and how the algorithm finds optimal parameters.
Trust Region Reflective Algorithm: Trust Region Reflective Algorithm provides a deep dive into the TRF algorithm that NLSQ uses for optimization, including how it handles bounds and ensures convergence.
JAX and Automatic Differentiation: JAX and Automatic Differentiation explains how NLSQ uses JAX for GPU acceleration and automatic Jacobian computation, and why this is faster than finite differences.
Numerical Stability: Numerical Stability Guide covers the 4-layer defense strategy that prevents divergence and ensures robust optimization even with challenging data.
Streaming Optimization: Adaptive Hybrid Streaming Optimizer explains how NLSQ handles datasets too large to fit in memory using streaming optimization techniques.
GPU Architecture: GPU Architecture and Acceleration describes how NLSQ leverages GPU hardware for massive speedups and when GPU acceleration is most beneficial.