APEBench: A Benchmark for Autoregressive Neural Emulators of PDEs

We introduce the Autoregressive PDE Emulator Benchmark (APEBench), a comprehensive benchmark suite to evaluate autoregressive neural emulators for solving partial differential equations. APEBench is based on JAX and provides a seamlessly integrated differentiable simulation framework employing efficient pseudo-spectral methods, enabling 46 distinct PDEs across 1D, 2D, and 3D. Facilitating systematic analysis and comparison of learned emulators, we propose a novel taxonomy for unrolled training and introduce a unique identifier for PDE dynamics that directly relates to the stability criteria of classical numerical methods. APEBench enables the evaluation of diverse neural architectures, and unlike existing benchmarks, its tight integration of the solver enables support for differentiable physics training and neural-hybrid emulators. Moreover, APEBench emphasizes rollout metrics to understand temporal generalization, providing insights into the long-term behavior of emulating PDE dynamics. In several experiments, we highlight the similarities between neural emulators and numerical simulators.

Postprocessing of Ensemble Weather Forecasts Using Permutation-invariant Neural Networks

Statistical postprocessing is used to translate ensembles of raw numerical weather forecasts into reliable probabilistic forecast distributions. In this study, we examine the use of permutation-invariant neural networks for this task. In contrast to previous approaches, which often operate on ensemble summary statistics and dismiss details of the ensemble distribution, we propose networks which treat forecast ensembles as a set of unordered member forecasts and learn link functions that are by design invariant to permutations of the member ordering. We evaluate the quality of the obtained forecast distributions in terms of calibration and sharpness, and compare the models against classical and neural network-based benchmark methods. In case studies addressing the postprocessing of surface temperature and wind gust forecasts, we demonstrate state-of-the-art prediction quality. To deepen the understanding of the learned inference process, we further propose a permutation-based importance analysis for ensemble-valued predictors, which highlights specific aspects of the ensemble forecast that are considered important by the trained postprocessing models. Our results suggest that most of the relevant information is contained in few ensemble-internal degrees of freedom, which may impact the design of future ensemble forecasting and postprocessing systems.

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

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.

Fast Neural Representations for Direct Volume Rendering

Despite the potential of neural scene representations to effectively compress 3D scalar fields at high reconstruction quality, the computational complexity of the training and data reconstruction step using scene representation networks limits their use in practical applications. In this paper, we analyze whether scene representation networks can be modified to reduce these limitations and whether these architectures can also be used for temporal reconstruction tasks. We propose a novel design of scene representation networks using GPU tensor cores to integrate the reconstruction seamlessly into on-chip raytracing kernels. Furthermore, we investigate the use of image-guided network training as an alternative to classical data-driven approaches, and we explore the potential strengths and weaknesses of this alternative regarding quality and speed. As an alternative to spatial super-resolution approaches for time-varying fields, we propose a solution that builds upon latent-space interpolation to enable random access reconstruction at arbitrary granularity. We summarize our findings in the form of an assessment of the strengths and limitations of scene representation networks for scientific visualization tasks and outline promising future research directions in this field.

Inverting the Feature Visualization Process for Feedforward Neural Networks

This work sheds light on the invertibility of feature visualization in neural networks. Since the input that is generated by feature visualization using activation maximization does, in general, not yield the feature objective it was optimized for, we investigate optimizing for the feature objective that yields this input. Given the objective function used in activation maximization that measures how closely a given input resembles the feature objective, we exploit that the gradient of this function w.r.t. inputs is---up to a scaling factor---linear in the objective. This observation is used to find the optimal feature objective via computing a closed form solution that minimizes the gradient. By means of Inverse Feature Visualization, we intend to provide an alternative view on a networks sensitivity to certain inputs that considers feature objectives rather than activations.

Learning Adaptive Sampling and Reconstruction for Volume Visualization

A central challenge in data visualization is to understand which data samples are required to generate an image of a data set in which the relevant information is encoded. In this work, we make a first step towards answering the question of whether an artificial neural network can predict where to sample the data with higher or lower density, by learning of correspondences between the data, the sampling patterns and the generated images. We introduce a novel neural rendering pipeline, which is trained end-to-end to generate a sparse adaptive sampling structure from a given low-resolution input image, and reconstructs a high-resolution image from the sparse set of samples. For the first time, to the best of our knowledge, we demonstrate that the selection of structures that are relevant for the final visual representation can be jointly learned together with the reconstruction of this representation from these structures. Therefore, we introduce differentiable sampling and reconstruction stages, which can leverage back-propagation based on supervised losses solely on the final image. We shed light on the adaptive sampling patterns generated by the network pipeline and analyze its use for volume visualization including isosurface and direct volume rendering.

Volumetric Isosurface Rendering with Deep Learning-Based Super-Resolution

Rendering an accurate image of an isosurface in a volumetric field typically requires large numbers of data samples. Reducing the number of required samples lies at the core of research in volume rendering. With the advent of deep learning networks, a number of architectures have been proposed recently to infer missing samples in multi-dimensional fields, for applications such as image super-resolution and scan completion. In this paper, we investigate the use of such architectures for learning the upscaling of a low-resolution sampling of an isosurface to a higher resolution, with high fidelity reconstruction of spatial detail and shading. We introduce a fully convolutional neural network, to learn a latent representation generating a smooth, edge-aware normal field and ambient occlusions from a low-resolution normal and depth field. By adding a frame-to-frame motion loss into the learning stage, the upscaling can consider temporal variations and achieves improved frame-to-frame coherence. We demonstrate the quality of the network for isosurfaces which were never seen during training, and discuss remote and in-situ visualization as well as focus+context visualization as potential applications