Optimization with learning-informed differential equation constraints and its applications
This work addresses optimization challenges in fields like control and imaging by integrating data-driven techniques, but it appears incremental as it builds on existing methods with machine-learned approximations.
The paper tackles optimization problems with differential equation constraints that include machine-learned components, providing an error analysis and numerical methods for applications in optimal control and physics-integrated imaging, with numerical results presented.
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.