  Implicit Neural representations (INRs) are widely used for scientific data
reduction and visualization by modeling the function that maps a spatial
location to a data value. Without any prior knowledge about the spatial
distribution of values, we are forced to sample densely from INRs to perform
visualization tasks like iso-surface extraction which can be very
computationally expensive. Recently, range analysis has shown promising results
in improving the efficiency of geometric queries, such as ray casting and
hierarchical mesh extraction, on INRs for 3D geometries by using arithmetic
rules to bound the output range of the network within a spatial region.
However, the analysis bounds are often too conservative for complex scientific
data. In this paper, we present an improved technique for range analysis by
revisiting the arithmetic rules and analyzing the probability distribution of
the network output within a spatial region. We model this distribution
efficiently as a Gaussian distribution by applying the central limit theorem.
Excluding low probability values, we are able to tighten the output bounds,
resulting in a more accurate estimation of the value range, and hence more
accurate identification of iso-surface cells and more efficient iso-surface
extraction on INRs. Our approach demonstrates superior performance in terms of
the iso-surface extraction time on four datasets compared to the original range
analysis method and can also be generalized to other geometric query tasks.
