# Self-Directed Online Machine Learning for Topology Optimization

arXiv: https://arxiv.org/abs/2002.01927 · HTML: https://mlsanity.com/paper/2002.01927/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Feb 2020.

## Built on by (most cited first, 10 of 10)

- [Making Reconstruction-based Method Great Again for Video Anomaly Detection](https://mlsanity.com/paper/2301.12048/) (2023)
- [DADO -- Low-Cost Query Strategies for Deep Active Design Optimization](https://mlsanity.com/paper/2307.04536/) (2023)
- [3DID: Direct 3D Inverse Design for Aerodynamics with Physics-Aware Optimization](https://mlsanity.com/paper/2512.08987/) (2025)
- [Large Language Models as Optimization Controllers: Adaptive Continuation for SIMP Topology Optimization](https://mlsanity.com/paper/2603.25099/) (2026)
- [Harnessing AI for Inverse Partial Differential Equation Problems: Past, Present, and Prospects](https://mlsanity.com/paper/2605.16966/) (2026)
- [HPG-Diff: Hierarchical physics-guided diffusion with differentiable connectivity constraints for topology optimization](https://mlsanity.com/paper/2607.07233/) (2026)
- [Deep convolutional surrogates and degrees of freedom in thermal design](https://mlsanity.com/paper/2208.07482/) (2022)
- [A Meta-Generation framework for Industrial System Generation](https://mlsanity.com/paper/2306.05123/) (2023)
- [Censored Sampling for Topology Design: Guiding Diffusion with Human Preferences](https://mlsanity.com/paper/2508.01589/) (2025)
- [AutoSiMP: Autonomous Topology Optimization from Natural Language via LLM-Driven Problem Configuration and Adaptive Solver Control](https://mlsanity.com/paper/2603.27000/) (2026)

## Abstract (arXiv)

Topology optimization by optimally distributing materials in a given domain requires non-gradient optimizers to solve highly complicated problems. However, with hundreds of design variables or more involved, solving such problems would require millions of Finite Element Method (FEM) calculations whose computational cost is huge and impractical. Here we report Self-directed Online Learning Optimization (SOLO) which integrates Deep Neural Network (DNN) with FEM calculations. A DNN learns and substitutes the objective as a function of design variables. A small number of training data is generated dynamically based on the DNN's prediction of the optimum. The DNN adapts to the new training data and gives better prediction in the region of interest until convergence. The optimum predicted by the DNN is proved to converge to the true global optimum through iterations. Our algorithm was tested by four types of problems including compliance minimization, fluid-structure optimization, heat transfer enhancement and truss optimization. It reduced the computational time by 2 ~ 5 orders of magnitude compared with directly using heuristic methods, and outperformed all state-of-the-art algorithms tested in our experiments. This approach enables solving large multi-dimensional optimization problems.