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Efficient Value Distribution Estimation from INR

With the BER ImPACTS SciDAC5 Partnership program

Scientific Achievement

Probabilistic Affine Form (PAF) is a novel approach for estimating neural network based value distributions for scientific simulations. The distribution estimation can be used to query quantity of interest (QoI) in a scalar field for efficient data visualization operations such as iso-surface extraction.

Significance and Impact

With PAF, scientists can query the distributions of data in arbitraries spatial locations of the simulation domain with significantly (1000x) reduced storage overhead. The predicted value distribution can be useful for iso-surface extraction and other visualization tasks that require adaptive data query.

FIgure: The probabilistic affine form (PAF) can be applied to a spatial region and its obtain value distributions efficiently. Based on the value distribution, isosurfaces can be computed adaptively with a significantly reduced computation cost.

PI: Han-Wei Shen; Ohio State University

SciDAC Partnership: ImPACTS, Improving Projections of AMOC and Collapse Through Advanced Simulations

ASCR Program: SciDAC RAPIDS2

Publication(s) for this work: Haoyu Li and Han-Wei Shen, “Improving Efficiency of Iso-Surface Extraction on Implicit Neural Representations Using Uncertainty Propagation,” IEEE Transactions on Visualization and Computer Graphics (2024). doi: 10.1109/TVCG.2024.3365089.

Technical Approach

PAF uses an affine combination of uncertainty units to represent data in the simulation domain. These uncertainty units can be propagated through the neural network model so that the output distribution in the region can be estimated from the affine combinations.
We use a hierarchical subdivision approach to query data adaptively according to the regional value distribution for isosurface extraction.

LOCAL LAB POC:

TALKING POINTS:

We input a region to the implicit neural representation. This region is decomposed into an affine combination of the uncertainty units called probabilistic affine form (PAF).
The PAFs can be propagated through the neural networks following the rules shown in figure 2.
The output from the implicit neural representation is also an affine form representing the value distribution inside the region. The value distribution can be approximated with a Gaussian distribution.
Based on whether the iso-value is inside this output distribution or not, we can subdivide the space hierarchical and identify the cells containing the iso-surfaces.

METADATA:

Name of the associated awarded project:

PI name(s): Patrick McCormick (LANL), Alex Aiken (Stanford)

Name of the program manager: Kalyan Perumalla

Supporting technology supported by both ECP and ASCR research (Laura Biven)

BACKGROUND AND CONTEXT INFORMATION:

Implicit neural representation is a function mapping from coordinates to scalar values. They are composed of a serial of linear functions and nonlinear activation functions. PAFs can be exactly propagated through linear functions (exact bound of output is preserved). However, we need to perform approximations for nonlinear functions.