Information geometric regularization for computing sensitivities of flows with shocks

Florian Schäfer

arXiv:2608.09759v1 Primary: math.NA Secondary: math.OC

Abstract

Computing (adjoint) sensitivities of flows with shocks is a longstanding problem in computational fluid dynamics. The spurious sensitivities due to shock sensors and limiters frequently force practitioners to accept the errors incurred by "freezing" limiters and shock sensors. The recently proposed information geometric regularization (IGR) is an inviscid, PDE-based regularization of the compressible Euler equations that replaces shocks with smooth profiles without damping fine-scale structures. This work derives the forward and adjoint sensitivities for the IGR system with periodic boundary conditions and demonstrates their convergence, under grid refinement, to the sensitivities obtained by finite differences or automatic differentiation through the forward solve.

Disclosure

“manen for his contributions to preliminary work that derived the unidimensional forward sensitivity equation of IGR and Spencer Bryngelson for first making me aware of the challenges due to adjoint computations in flows with shocks. I used Claude Code for the following tasks: Checking mathematical derivations, nu- merical implementation, drafting a first version of section 4, running the numerical experiments, creating TikZ figures, and proofreading of the manuscript.”
PDF page 18

Classification: Drafting limited passages
Multiplier: 5
Verified: 2026-08-23T05:07:58.962143Z

Structural counts

Pages 21 pdf

Theorems 0 source

Lemmas 0 source

Propositions 0 source

Corollaries 0 source

Definitions 0 source

Displayed equations 55 source

Bibliography entries 206 source

Appendix pages 0 estimated

Count notes

Source counts use the expanded primary TeX file adjoints.tex.
Appendix pages include the first PDF page with an explicit Appendix heading through the final page.