DDSL: Deep Differentiable Simplex Layer for Learning Geometric Signals

We present a Deep Differentiable Simplex Layer (DDSL) for neural networks for geometric deep learning. The DDSL is a differentiable layer compatible with deep neural networks for bridging simplex mesh-based geometry representations (point clouds, line mesh, triangular mesh, tetrahedral mesh) with raster images (e.g., 2D/3D grids). The DDSL uses Non-Uniform Fourier Transform (NUFT) to perform differentiable, efficient, anti-aliased rasterization of simplex-based signals. We present a complete theoretical framework for the process as well as an efficient backpropagation algorithm. Compared to previous differentiable renderers and rasterizers, the DDSL generalizes to arbitrary simplex degrees and dimensions. In particular, we explore its applications to 2D shapes and illustrate two applications of this method: (1) mesh editing and optimization guided by neural network outputs, and (2) using DDSL for a differentiable rasterization loss to facilitate end-to-end training of polygon generators. We are able to validate the effectiveness of gradient-based shape optimization with the example of airfoil optimization, and using the differentiable rasterization loss to facilitate end-to-end training, we surpass state of the art for polygonal image segmentation given ground-truth bounding boxes

MeshfreeFlowNet: A Physics-Constrained Deep Continuous Space-Time Super-Resolution Framework

We propose MeshfreeFlowNet, a novel deep learning-based super-resolution framework to generate continuous (grid-free) spatio-temporal solutions from the low-resolution inputs. While being computationally efficient, MeshfreeFlowNet accurately recovers the fine-scale quantities of interest. MeshfreeFlowNet allows for: (i) the output to be sampled at all spatio-temporal resolutions, (ii) a set of Partial Differential Equation (PDE) constraints to be imposed, and (iii) training on fixed-size inputs on arbitrarily sized spatio-temporal domains owing to its fully convolutional encoder. We empirically study the performance of MeshfreeFlowNet on the task of super-resolution of turbulent flows in the Rayleigh-Benard convection problem. Across a diverse set of evaluation metrics, we show that MeshfreeFlowNet significantly outperforms existing baselines. Furthermore, we provide a large scale implementation of MeshfreeFlowNet and show that it efficiently scales across large clusters, achieving 96.80% scaling efficiency on up to 128 GPUs and a training time of less than 4 minutes.Comment: Supplementary Video: https://youtu.be/mjqwPch9gDo. Accepted to SC2

OpenScene: 3D Scene Understanding with Open Vocabularies

Traditional 3D scene understanding approaches rely on labeled 3D datasets to train a model for a single task with supervision. We propose OpenScene, an alternative approach where a model predicts dense features for 3D scene points that are co-embedded with text and image pixels in CLIP feature space. This zero-shot approach enables task-agnostic training and open-vocabulary queries. For example, to perform SOTA zero-shot 3D semantic segmentation it first infers CLIP features for every 3D point and later classifies them based on similarities to embeddings of arbitrary class labels. More interestingly, it enables a suite of open-vocabulary scene understanding applications that have never been done before. For example, it allows a user to enter an arbitrary text query and then see a heat map indicating which parts of a scene match. Our approach is effective at identifying objects, materials, affordances, activities, and room types in complex 3D scenes, all using a single model trained without any labeled 3D data.Comment: CVPR 2023. Project page: https://pengsongyou.github.io/openscen