Physics-driven regularization of deep neural networks for enhanced engineering design and analysis

Mohammad Amin Nabian, Hadi Meidani

Research output: Contribution to journalArticlepeer-review


In this paper, we introduce a physics-driven regularization method for training of deep neural networks (DNNs) for use in engineering design and analysis problems. In particular, we focus on the prediction of a physical system, for which in addition to training data, partial or complete information on a set of governing laws is also available. These laws often appear in the form of differential equations, derived from first principles, empirically validated laws, or domain expertise, and are usually neglected in a data-driven prediction of engineering systems. We propose a training approach that utilizes the known governing laws and regularizes data-driven DNN models by penalizing divergence from those laws. The first two numerical examples are synthetic examples, where we show that in constructing a DNN model that best fits the measurements from a physical system, the use of our proposed regularization results in DNNs that are more interpretable with smaller generalization errors, compared with other common regularization methods. The last two examples concern metamodeling for a random Burgers’ system and for aerodynamic analysis of passenger vehicles, where we demonstrate that the proposed regularization provides superior generalization accuracy compared with other common alternatives.

Original languageEnglish (US)
Article number011006-1
JournalJournal of Computing and Information Science in Engineering
Issue number1
StatePublished - Feb 2020


  • Computational foundations for engineering optimization
  • Data-driven prediction
  • Deep neural networks
  • Design optimization
  • Machine learning for engineering applications
  • Metamodels
  • Physics-based simulations
  • Predictive modeling
  • Regularization

ASJC Scopus subject areas

  • Software
  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design
  • Industrial and Manufacturing Engineering


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