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Variable Order Multigrid Data Compression With MGARD�RAPIDS/FASTMath Partnership

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Scientific Achievement

Developed a unified framework for hierarchical compression of data defined on finite-element type grids that enables higher order compression and has lower computational cost.

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Significance and Impact

  • Algorithms such as MGARD only have a uniform order, e.g., order 1 for linear compression
  • We investigate how we can use multiple orders to exploit varying data regularity – smooth data is better predictable with higher order methods
  • Local formulation enables faster computations

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Technical Approach

Reformulated MGARD as a wavelet lifting scheme with different choices for predictors and projectors resulting in different variants of the compression algorithm

data

order 1 coefficients

order 2 coefficients

Improved compressibility: higher order predictors produce smaller coefficients with smaller entropy.

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Improved cost: local projections need less computations and scale better with order

PI: Scott Klasky (ORNL), ASCR PM: Kalyan Perumalla; ASCR Program: SciDAC RAPIDS2

Publication(s) for this work:

[1] V. Reshniak, E. Ferguson, Q. Gong, N. Vidal, S. Klasky, R. Archibald. Lifting MGARD: compression and refactoring of scientific data with variable-order polynomial predictors, submitted to Applied Mathematics for Modern Challenges 

[2] Presentation at SIAM IS24 “Compression and Analysis for Large-scale Scientific Data” 

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