Multilevel Optimization for Inverse Problems

  • Weissmann, Simon (Heidelberg University)
  • Wilson, Ashia (MIT)
  • Zech, Jakob (Heidelberg University)

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Inverse problems occur in a variety of parameter identification tasks in engineering and the sciences. Such problems are challenging in practice, as they require repeated evaluation of computationally expensive forward models. I will discuss some recent work with collaborators which introduces a unifying framework of multilevel optimization that can be applied to a wide range of optimization-based solvers. Our framework provably reduces the computational cost associated with evaluating the expensive forward maps stemming from various physical models. To demonstrate the versatility of our analysis, I will discuss its implications for different methodologies including multilevel (accelerated, stochastic) gradient descent, a multilevel ensemble Kalman inversion and a multilevel Langevin sampler.