README.md

Educational resources in topology optimization

This repository is a collection of resouces that I find to be sufficiently educational in various areas of topology optimization and related fields. Feel free to recommend articles via issues or pull requests.

Constrained nonlinear optimization

• Some popular nonlinear programming algorithms

Automatic differentiation

• Automatic differentiation in machine learning: a survey
• Understanding automatic differentiation (in Julia)
• Overview of automatic differentiation
• Forward-Mode Automatic Differentiation (AD) via High Dimensional Algebras
• AbstractDifferentiation.jl: Backend-Agnostic Differentiable Programming in Julia
• Basic Parameter Estimation, Reverse-Mode AD, and Inverse Problems
• Understanding Automatic Differentiation Pitfalls
• Efficient and Modular Implicit Differentiation
• Notes on Adjoint Methods for 18.335
• Supercharging Programming through Compiler Technology

Neural ODEs

• On Neural Differential Equations
• Differentiable Programming and Neural Differential Equations

Neural networks for topology optimization

• On the use of Artificial Neural Networks in Topology Optimisation
• DNN-based Topology Optimisation: Spatial Invariance and Neural Tangent Kernel
• NTopo: Mesh-free Topology Optimization using Implicit Neural Representations
• TONR: An exploration for a novel way combining neural network with topology optimization
• TOuNN: Topology Optimization using Neural Networks
• Neural reparameterization improves structural optimization
• Topology Optimization via Frequency Tuning of Neural Design Representations
• Self-directed online machine learning for topology optimization
• Neural reparameterization improves structural optimization
• Machine learning for topology optimization: Physics-based learning through an independent training strategy

Linear algebra

• Essence of Linear Algebra
• Matrix Computations

Stress-constrained topology optimization

• On an alternative approach to stress constraints relaxation in topology optimization
• Damage approach: A new method for topology optimization with local stress constraints
• A unified aggregation and relaxation approach for stress-constrained topology optimization

Buckling-constrained topology optimization

• Structural stability and artificial buckling modes in topology optimization
• Layout optimization of pin-jointed truss structures with minimum frequency constraints

Reliability-based topology optimization

• A survey on approaches for reliability-based optimization
• Second-order reliability methods: a review and comparative study

Fluid mechanics

• Illustrated Experiments in Fluid Mechanics: The NCFMF Book of Film Notes
• Understanding Laminar and Turbulent Flow

Fluid flow topology optimization

• A detailed introduction to density-based topology optimisation of fluid flow problems with implementation in MATLAB