Neural Fields for Interactive Visualization of Statistical Dependencies in 3D Simulation Ensembles

TL;DR

This work presents the first neural network that has learned to compactly represent and can efficiently reconstruct the statistical dependencies between the values of physical variables at different spatial locations in large 3D simulation ensembles by circumventing compute-intensive statistical estimators at runtime.

Abstract

We present the first neural network that has learned to compactly represent and can efficiently reconstruct the statistical dependencies between the values of physical variables at different spatial locations in large 3D simulation ensembles. Going beyond linear dependencies, we consider mutual information as a measure of non-linear dependence. We demonstrate learning and reconstruction with a large weather forecast ensemble comprising 1000 members, each storing multiple physical variables at a 250 x 352 x 20 simulation grid. By circumventing compute-intensive statistical estimators at runtime, we demonstrate significantly reduced memory and computation requirements for reconstructing the major dependence structures. This enables embedding the estimator into a GPU-accelerated direct volume renderer and interactively visualizing all mutual dependencies for a selected domain point.

Figures (7)

• Figure 1: NDF architecture. $\mathbf{p}_{\mu}$ and $\mathbf{p}_{\nu}$ are respectively the reference and query positions. $\mathop{\mathrm{Grid}}\nolimits_\mu$ and $\mathop{\mathrm{Grid}}\nolimits_\nu$, respectively, are the hash grids. Variable-specific encoders $\mathop{\mathrm{Enc}}\nolimits_\mu$ and $\mathop{\mathrm{Enc}}\nolimits_\nu$ are MLPs. Since the feature grids involve trainable parameters, each encoder is equipped with a separate grid. Merger indicates the multiplication of the encoder outputs.
• Figure 2: Point-to-point Pearson self-correlations $S_\mu$ for different variables $\mu$ (temperature tk and longitudinal component u of wind speed) and reference positions $\mathbf{p}_{\text{ref}}$. Figures show ground truth (left) and NDF reconstruction (right). The reference is shown in red.
• Figure 3: Point-to-point MI self-correlations $S_\mu$ for different variables $\mu$ (temperature tk and longitudinal component u of wind speed) and reference positions $\mathbf{p}_{\text{ref}}$. Figures show ground truth (left) and NDF reconstruction (right). The reference is shown in red.
• Figure 4: Impact of hash table size and MLP hyperparameters on NDFs' reconstruction quality. The horizontal axis displays various encoder and decoder configurations, including the number of layers and hidden channels. The vertical axis shows the log-2 hash table size $T$ from section \ref{['sec:network']}. The plot considers variable temperature (tk) and Pearson correlation, with similar behavior observed for other variables and similarity metrics.
• Figure 5: Accuracy comparison between NDFs with MLP encoder (complete) and pure grid model (without encoder) using Pearson self-correlation fields for variable temperature (tk).