Machine learning approaches for solving partial differential equations require learning mappings between function spaces. While convolutional or graph neural networks are constrained to discretized functions, neural operators present a promising milestone toward mapping functions directly. Despite impressive results they still face challenges with respect to the domain geometry and typically rely on some form of discretization. In order to alleviate such limitations, we present CORAL, a new method that leverages coordinate-based networks for solving PDEs on general geometries. CORAL is designed to remove constraints on the input mesh, making it applicable to any spatial sampling and geometry. Its ability extends to diverse problem domains, including PDE solving, spatio-temporal forecasting, and geometry-aware inference. CORAL demonstrates robust performance across multiple resolutions and performs well in both convex and non-convex domains, surpassing or performing on par with state-of-the-art models.

Traditional cameras produce desirable vision results but struggle with motion blur in high-speed scenes due to long exposure windows. Existing frame-based deblurring algorithms face challenges in extracting useful motion cues from severely blurred images. Recently, an emerging bio-inspired vision sensor known as the spike camera has achieved an extremely high frame rate while preserving rich spatial details, owing to its novel sampling mechanism. However, typical binary spike streams are relatively low-resolution, degraded image signals devoid of color information, making them unfriendly to human vision. In this paper, we propose a novel approach that integrates the two modalities from two branches, leveraging spike streams as auxiliary visual cues for guiding deblurring in high-speed motion scenes. We propose the first spike-based motion deblurring model with bidirectional information complementarity. We introduce a content-aware motion magnitude attention module that utilizes learnable mask to extract relevant information from blurry images effectively, and we incorporate a transposed cross-attention fusion module to efficiently combine features from both spike data and blurry RGB images. Furthermore, we build two extensive synthesized datasets for training and validation purposes, encompassing high-temporal-resolution spikes, blurry images, and corresponding sharp images. The experimental results demonstrate that our method effectively recovers clear RGB images from highly blurry scenes and outperforms state-of-the-art deblurring algorithms in multiple settings.

We present Shape Non-rigid Kinematics (SNK), a novel zero-shot method for non-rigid shape matching that eliminates the need for extensive training or ground truth data. SNK operates on a single pair of shapes, and employs a reconstructionbased strategy using an encoder-decoder architecture, which deforms the source shape to closely match the target shape. During the process, an unsupervised functional map is predicted and converted into a point-to-point map, serving as a supervisory mechanism for the reconstruction. To aid in training, we have designed a new decoder architecture that generates smooth, realistic deformations. SNK demonstrates competitive results on traditional benchmarks, simplifying the shapematching process without compromising accuracy. Our code can be found online: https://github.com/pvnieo/SNK.