Machine learning for topology optimization: Physics-based learning through an independent training strategy

Fernando V. Senhora, Heng Chi, Yuyu Zhang, Lucia Mirabella, Tsz Ling Elaine Tang, Glaucio H. Paulino

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


The high computational cost of topology optimization has prevented its widespread use as a generative design tool. To reduce this computational cost, we propose an artificial intelligence approach to drastically accelerate topology optimization without sacrificing its accuracy. The resulting AI-driven topology optimization can fully capture the underlying physics of the problem. As a result, the machine learning model, which consists of a convolutional neural network with residual links, is able to generalize what it learned from the training set to solve a wide variety of problems with different geometries, boundary conditions, mesh sizes, volume fractions and filter radius. We train the machine learning model separately from the topology optimization, which allows us to achieve a considerable speedup (up to 30 times faster than traditional topology optimization). Through several design examples, we demonstrate that the proposed AI-driven topology optimization framework is effective, scalable and efficient. The speedup enabled by the framework makes topology optimization a more attractive tool for engineers in search of lighter and stronger structures, with the potential to revolutionize the engineering design process. Although this work focuses on compliance minimization problems, the proposed framework can be generalized to other objective functions, constraints and physics.

Original languageEnglish (US)
Article number115116
JournalComputer Methods in Applied Mechanics and Engineering
StatePublished - Aug 1 2022
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • General Physics and Astronomy
  • Computer Science Applications


  • 3D convolutional neural network
  • Large-scale
  • Machine Learning
  • Physics-based machine learning
  • Topology optimization
  • Training Set


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