Tutorials

These tutorials will guide you through using diffstruc for automatic differentiation in Fortran.

The tutorials are organised to build your understanding progressively:

1. Basics - Get started with automatic differentiation using diffstruc

2. Forward Mode - Learn how to use forward-mode automatic differentiation

3. Reverse Mode - Learn how to use reverse-mode (backpropagation) automatic differentiation

4. Higher-Order Derivatives - Learn how to compute second and higher-order derivatives

5. Operations - Learn about the supported mathematical operations and how to define custom ones

6. Memory Management - Learn how to manage memory effectively when using diffstruc

Before starting these tutorials, make sure you have:

• Installed diffstruc (see Installation)

• A working Fortran compiler (gfortran >= 14.3.0 or ifx >= 2025.2.0)

• Basic understanding of Fortran programming

• Familiarity with calculus and derivatives

Basics of Automatic Differentiation:

• Automatic Differentiation using array_type
  • What is Automatic Differentiation?
  • The array_type
  • Worked Example
  • Multi-Dimensional Arrays
  • Key Concepts
  • Graph Visualisation
  • Common Issues

1st order Derivatives:

• Forward-Mode Differentiation
  • Basic Usage
  • Partial Derivatives
  • Directional Derivatives
  • Complex Functions
  • Iterative Use Cases
  • Summary
• Reverse-Mode Differentiation (Backpropagation)
  • Basic Usage
  • Partial Derivatives
  • Practical Application: Gradient Descent
  • Summary

Higher-Order Derivatives:

• Higher-Order Derivatives
  • Computing Second Derivatives
  • Partial Derivatives
  • Summary

Supported Operations and Custom Definitions:

• Supported Operations
  • Operation Summary Table
  • Custom Operations
  • Chaining Operations issues

Memory Management:

• Memory Management
  • Essential Cleanup Operations
  • The nullify_graph Procedure
  • The is_temporary Flag
  • Memory Leak Patterns
  • Efficient Memory Usage
  • Global Variables
  • Debugging Memory Issues