WuWan: High-Performance Layered Elastic Half-Space Solver

WuWan is a high-performance computational library designed for the forward and inverse analysis of pavement mechanics. It solves deflections in a 5-layer elastic half-space system with exceptional speed and accuracy.

Built with a modern C++ backend (relying on Boost and Eigen) and wrapped for Python, it leverages analytical gradients and custom linear algebra optimizations to achieve millisecond-level inversions.

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🚀 Key Features

• High-Performance Core: Originally a Cython project, now fully rewritten in C++ for maximum efficiency.
• Analytical Gradients: Implements analytical derivatives for Jacobian calculations, significantly outperforming finite difference methods in stability and speed.
• Advanced Back-Calculation:
  • Utilizes scipy.optimize combined with high-speed C++ gradient providers.
  • Solves inverse problems in tens of milliseconds.
• Robust Error Modeling: Supports noise injection for thickness, deflection, load, and sensor positioning to simulate real-world measurement uncertainties.

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🧠 Methodology

The core algorithm solves the Layered Elastic Theory (LET) equations using advanced numerical techniques:

1. Hankel Transform: The integral transform is converted into algebraic equations using high-precision Gauss-Legendre quadrature.
2. System Solving: Instead of using generic solvers, WuWan employs a custom implementation of LU decomposition. This is specifically optimized for the sparse, banded structure of the 5-layer system matrices, reducing memory overhead and computation time.
3. Gradient Computation: The Jacobian matrix is computed via analytical derivation of the stiffness matrix. This allows for precise sensitivity analysis without the computational overhead or truncation errors associated with numerical differentiation.

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📊 Performance Benchmarks

Benchmarks performed on a standard workstation (Single-threaded):

Operation	Batch Size	Computation Time	Note
Forward Calculation	10,000 calls (10 points/call)	~1.5 seconds	Pure deflection calculation
Forward + Gradient	10,000 calls	~3.5 seconds	Deflection + Jacobian w.r.t moduli
Inverse Analysis	Single Basin	~10 - 50 ms	Dependent on convergence criteria

Note: The solver is optimized to handle large-scale batch processing for sensitivity analysis and probabilistic inversion.

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🔮 Roadmap

• C++ Core Rewrite: Transformed from Cython to C++ with Eigen/Boost.
• Forward Calculation & Analytical Gradients: Implementation of high-speed forward modeling and derivative calculation.
• Deterministic Back-calculation: Fast inverse analysis for moduli estimation.
• Bayesian Uncertainty Analysis: Implementation of MCMC or variational inference for posterior distributions (In Progress).
• Global Sensitivity Analysis: Sobol indices or similar methods to quantify parameter influence (In Progress).
• Batch Error Simulation: Wrappers for large-scale Monte Carlo simulations with noise injection.

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🛠 Installation & Dependencies

Prerequisites

• C++ Compiler supporting C++14/17
• Boost Math Library
• Eigen3 Linear Algebra Library
• Python 3.x

Building from Source

git clone [https://github.com/lewiswan/WuWan.git](https://github.com/lewiswan/WuWan.git)
cd WuWan
pip install .