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.

翻译：特征网格场景表示网络（SRNs）作为紧凑的函数代理，已应用于科学数据的分析与可视化。由于SRNs属于黑箱有损数据表示，评估其预测质量对于科学可视化应用至关重要，以确保科研人员能够信赖所呈现的信息。当前，现有架构无法支持推理阶段的重建质量评估，因为在缺乏真实数据的情况下无法计算坐标级误差。本文提出一种参数高效的多解码器SRN（MDSRN）集成架构，该架构包含共享特征网格与多个轻量级多层感知机解码器。MDSRN能够为给定输入坐标生成一组合理预测，通过计算均值作为多解码器集成的预测结果，并以方差作为置信度评分。坐标级方差可与数据一同渲染以反映重建质量，或集成至不确定性感知的体积可视化算法中。为防止量化方差与预测质量之间的失准，我们提出一种新颖的集成学习方差正则化损失函数，促使正则化多解码器SRN（RMDSRN）获得与真实模型误差紧密相关的更可靠方差估计。我们在多种标量场数据集上，系统评估了蒙特卡洛丢弃法、平均场变分推断、深度集成及预测方差方法在方差量化与数据重建方面的质量，并与提出的MDSRN和RMDSRN进行对比。实验表明，在相同神经网络参数量预算下，RMDSRN在不确定性SRNs中实现了最精确的数据重建与最具竞争力的方差-误差相关性。