  Feature grid Scene Representation Networks (SRNs) have been applied to
scientific data as compact functional surrogates for analysis and
visualization. As SRNs are black-box lossy data representations, assessing the
prediction quality is critical for scientific visualization applications to
ensure that scientists can trust the information being visualized. Currently,
existing architectures do not support inference time reconstruction quality
assessment, as coordinate-level errors cannot be evaluated in the absence of
ground truth data. We propose a parameter-efficient multi-decoder SRN (MDSRN)
ensemble architecture consisting of a shared feature grid with multiple
lightweight multi-layer perceptron decoders. MDSRN can generate a set of
plausible predictions for a given input coordinate to compute the mean as the
prediction of the multi-decoder ensemble and the variance as a confidence
score. The coordinate-level variance can be rendered along with the data to
inform the reconstruction quality, or be integrated into uncertainty-aware
volume visualization algorithms. To prevent the misalignment between the
quantified variance and the prediction quality, we propose a novel variance
regularization loss for ensemble learning that promotes the Regularized
multi-decoder SRN (RMDSRN) to obtain a more reliable variance that correlates
closely to the true model error. We comprehensively evaluate the quality of
variance quantification and data reconstruction of Monte Carlo Dropout, Mean
Field Variational Inference, Deep Ensemble, and Predicting Variance compared to
the proposed MDSRN and RMDSRN across diverse scalar field datasets. We
demonstrate that RMDSRN attains the most accurate data reconstruction and
competitive variance-error correlation among uncertain SRNs under the same
neural network parameter budgets.
