WIAS Preprint No. 2754, (2020)

Optimization with learning-informed differential equation constraints and its applications


  • Dong, Guozhi
    ORCID: 0000-0002-9674-6143
  • Hintermüller, Michael
    ORCID: 0000-0001-9471-2479
  • Papafitsoros, Kostas
    ORCID: 0000-0001-9691-4576

2010 Mathematics Subject Classification

  • 49M15 65J15 65J20 65K10 90C30 35J61 68T07


  • PDE constrained optimization, artificial neural network, semilinear PDEs, integrated physicsbased, imaging, learning-informed model, quantitative MRI, semi-smooth Newton SQP algorithm




Inspired by applications in optimal control of semilinear elliptic partial differential equations and physics-integrated imaging, differential equation constrained optimization problems with constituents that are only accessible through data-driven techniques are studied. A particular focus is on the analysis and on numerical methods for problems with machine-learned components. For a rather general context, an error analysis is provided, and particular properties resulting from artificial neural network based approximations are addressed. Moreover, for each of the two inspiring applications analytical details are presented and numerical results are provided.

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