Prediction of Shock Formation From Boundary Measurements

Helmuth Naumer, Farzad Kamalabadi

Research output: Chapter in Book/Report/Conference proceedingConference contribution


We propose a method for the Bayesian prediction of shocks in scalar partial differential equations (PDEs) representing conservation equations from noisy observations of the boundary conditions. By considering the implicit transformation from boundary conditions to shocks, we construct an arrival process interpretation of shocks as well as an associated arrival rate function. We then introduce a Monte Carlo method to approximate the arrival rate of shocks based on the probability of a sufficiently large range of values in an epsilon ball conditioned on noisy boundary measurements. We illustrate the method with simulations of Burgers' equation with initial conditions set by Brownian motion. Despite the non-smooth boundary, our proposed method constructs a sparse and readily interpretable probabilistic structure of shock arrival and propagation.

Original languageEnglish (US)
Title of host publicationProceedings of the 22nd IEEE Statistical Signal Processing Workshop, SSP 2023
PublisherIEEE Computer Society
Number of pages5
ISBN (Electronic)9781665452458
StatePublished - 2023
Event22nd IEEE Statistical Signal Processing Workshop, SSP 2023 - Hanoi, Viet Nam
Duration: Jul 2 2023Jul 5 2023

Publication series

NameIEEE Workshop on Statistical Signal Processing Proceedings


Conference22nd IEEE Statistical Signal Processing Workshop, SSP 2023
Country/TerritoryViet Nam


  • Arrival Processes
  • Forecasting
  • Inverse Problems
  • Non-linear PDEs

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Applied Mathematics
  • Signal Processing
  • Computer Science Applications


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