Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries

Partial Differential Equations (PDEs) underpin many scientific phenomena, yet traditional computational approaches often struggle with complex, nonlinear systems and irregular geometries. This paper introduces the \textbf{AMG} method, a \textbf{M}ulti-\textbf{G}raph neural operator approach designed for efficiently solving PDEs on \textbf{A}rbitrary geometries. AMG leverages advanced graph-based techniques and dynamic attention mechanisms within a novel GraphFormer architecture, enabling precise management of diverse spatial domains and complex data interdependencies. By constructing multi-scale graphs to handle variable feature frequencies and a physics graph to encapsulate inherent physical properties, AMG significantly outperforms previous methods, which are typically limited to uniform grids. We present a comprehensive evaluation of AMG across six benchmarks, demonstrating its consistent superiority over existing state-of-the-art models. Our findings highlight the transformative potential of tailored graph neural operators in surmounting the challenges faced by conventional PDE solvers. Our code and datasets are available on \url{https://github.com/lizhihao2022/AMG}.

Temporal As a Plugin: Unsupervised Video Denoising with Pre-Trained Image Denoisers

Recent advancements in deep learning have shown impressive results in image and video denoising, leveraging extensive pairs of noisy and noise-free data for supervision. However, the challenge of acquiring paired videos for dynamic scenes hampers the practical deployment of deep video denoising techniques. In contrast, this obstacle is less pronounced in image denoising, where paired data is more readily available. Thus, a well-trained image denoiser could serve as a reliable spatial prior for video denoising. In this paper, we propose a novel unsupervised video denoising framework, named ``Temporal As a Plugin'' (TAP), which integrates tunable temporal modules into a pre-trained image denoiser. By incorporating temporal modules, our method can harness temporal information across noisy frames, complementing its power of spatial denoising. Furthermore, we introduce a progressive fine-tuning strategy that refines each temporal module using the generated pseudo clean video frames, progressively enhancing the network's denoising performance. Compared to other unsupervised video denoising methods, our framework demonstrates superior performance on both sRGB and raw video denoising datasets.

SoccerNet 2024 Challenges Results

The SoccerNet 2024 challenges represent the fourth annual video understanding challenges organized by the SoccerNet team. These challenges aim to advance research across multiple themes in football, including broadcast video understanding, field understanding, and player understanding. This year, the challenges encompass four vision-based tasks. (1) Ball Action Spotting, focusing on precisely localizing when and which soccer actions related to the ball occur, (2) Dense Video Captioning, focusing on describing the broadcast with natural language and anchored timestamps, (3) Multi-View Foul Recognition, a novel task focusing on analyzing multiple viewpoints of a potential foul incident to classify whether a foul occurred and assess its severity, (4) Game State Reconstruction, another novel task focusing on reconstructing the game state from broadcast videos onto a 2D top-view map of the field. Detailed information about the tasks, challenges, and leaderboards can be found at https://www.soccer-net.org, with baselines and development kits available at https://github.com/SoccerNet.

EAGLE: Elevating Geometric Reasoning through LLM-empowered Visual Instruction Tuning

Multi-modal Large Language Models have recently experienced rapid developments and excel in various multi-modal tasks. However, they still struggle with mathematical geometric problem solving, which requires exceptional visual perception proficiency. Existing MLLMs mostly optimize the LLM backbone to acquire geometric reasoning capabilities, while rarely emphasizing improvements in visual comprehension. In this paper, we first investigate the visual perception performance of MLLMs when facing geometric diagrams. Our findings reveal that current MLLMs severely suffer from inaccurate geometric perception and hallucinations. To address these limitations, we propose EAGLE, a novel two-stage end-to-end visual enhancement MLLM framework designed to ElevAte Geometric reasoning through LLM-Empowered visual instruction tuning. Specifically, in the preliminary stage, we feed geometric image-caption pairs into our MLLM that contains a fully fine-tuning CLIP ViT and a frozen LLM, aiming to endow our model with basic geometric knowledge. In the subsequent advanced stage, we incorporate LoRA modules into the vision encoder and unfreeze the LLM backbone. This enables the model to leverage the inherent CoT rationales within question-answer pairs, guiding the MLLM to focus on nuanced visual cues and enhancing its overall perceptual capacity. Moreover, we optimize the cross-modal projector in both stages to foster adaptive visual-linguistic alignments. After the two-stage visual enhancement, we develop the geometry expert model EAGLE-7B. Extensive experiments on popular benchmarks demonstrate the effectiveness of our model. For example, on the GeoQA benchmark, EAGLE-7B not only surpasses the exemplary G-LLaVA 7B model by 2.9%, but also marginally outperforms the larger G-LLaVA 13B model. On the MathVista benchmark, EAGLE-7B achieves remarkable 3.8% improvements compared with the proprietary model GPT-4V.

Masked Angle-Aware Autoencoder for Remote Sensing Images

To overcome the inherent domain gap between remote sensing (RS) images and natural images, some self-supervised representation learning methods have made promising progress. However, they have overlooked the diverse angles present in RS objects. This paper proposes the Masked Angle-Aware Autoencoder (MA3E) to perceive and learn angles during pre-training. We design a \textit{scaling center crop} operation to create the rotated crop with random orientation on each original image, introducing the explicit angle variation. MA3E inputs this composite image while reconstruct the original image, aiming to effectively learn rotation-invariant representations by restoring the angle variation introduced on the rotated crop. To avoid biases caused by directly reconstructing the rotated crop, we propose an Optimal Transport (OT) loss that automatically assigns similar original image patches to each rotated crop patch for reconstruction. MA3E demonstrates more competitive performance than existing pre-training methods on seven different RS image datasets in three downstream tasks.

From Chaos to Clarity: 3DGS in the Dark

Novel view synthesis from raw images provides superior high dynamic range (HDR) information compared to reconstructions from low dynamic range RGB images. However, the inherent noise in unprocessed raw images compromises the accuracy of 3D scene representation. Our study reveals that 3D Gaussian Splatting (3DGS) is particularly susceptible to this noise, leading to numerous elongated Gaussian shapes that overfit the noise, thereby significantly degrading reconstruction quality and reducing inference speed, especially in scenarios with limited views. To address these issues, we introduce a novel self-supervised learning framework designed to reconstruct HDR 3DGS from a limited number of noisy raw images. This framework enhances 3DGS by integrating a noise extractor and employing a noise-robust reconstruction loss that leverages a noise distribution prior. Experimental results show that our method outperforms LDR/HDR 3DGS and previous state-of-the-art (SOTA) self-supervised and supervised pre-trained models in both reconstruction quality and inference speed on the RawNeRF dataset across a broad range of training views. Code can be found in \url{https://lizhihao6.github.io/Raw3DGS}.

M2NO: Multiresolution Operator Learning with Multiwavelet-based Algebraic Multigrid Method

Solving partial differential equations (PDEs) effectively necessitates a multi-scale approach, particularly critical in high-dimensional scenarios characterized by increasing grid points or resolution. Traditional methods often fail to capture the detailed features necessary for accurate modeling, presenting a significant challenge in scientific computing. In response, we introduce the Multiwavelet-based Algebraic Multigrid Neural Operator (M2NO), a novel deep learning framework that synergistically combines multiwavelet transformations and algebraic multigrid (AMG) techniques. By exploiting the inherent similarities between these two approaches, M2NO overcomes their individual limitations and enhances precision and flexibility across various PDE benchmarks. Employing Multiresolution Analysis (MRA) with high-pass and low-pass filters, the model executes hierarchical decomposition to accurately delineate both global trends and localized details within PDE solutions, supporting adaptive data representation at multiple scales. M2NO also automates node selection and adeptly manages complex boundary conditions through its multiwavelet-based operators. Extensive evaluations on a diverse array of PDE datasets with different boundary conditions confirm M2NO's superior performance. Furthermore, M2NO excels in handling high-resolution and super-resolution tasks, consistently outperforming competing models and demonstrating robust adaptability in complex computational scenarios.

ContextGS: Compact 3D Gaussian Splatting with Anchor Level Context Model

Recently, 3D Gaussian Splatting (3DGS) has become a promising framework for novel view synthesis, offering fast rendering speeds and high fidelity. However, the large number of Gaussians and their associated attributes require effective compression techniques. Existing methods primarily compress neural Gaussians individually and independently, i.e., coding all the neural Gaussians at the same time, with little design for their interactions and spatial dependence. Inspired by the effectiveness of the context model in image compression, we propose the first autoregressive model at the anchor level for 3DGS compression in this work. We divide anchors into different levels and the anchors that are not coded yet can be predicted based on the already coded ones in all the coarser levels, leading to more accurate modeling and higher coding efficiency. To further improve the efficiency of entropy coding, e.g., to code the coarsest level with no already coded anchors, we propose to introduce a low-dimensional quantized feature as the hyperprior for each anchor, which can be effectively compressed. Our work pioneers the context model in the anchor level for 3DGS representation, yielding an impressive size reduction of over 100 times compared to vanilla 3DGS and 15 times compared to the most recent state-of-the-art work Scaffold-GS, while achieving comparable or even higher rendering quality.

MagicDrive3D: Controllable 3D Generation for Any-View Rendering in Street Scenes

While controllable generative models for images and videos have achieved remarkable success, high-quality models for 3D scenes, particularly in unbounded scenarios like autonomous driving, remain underdeveloped due to high data acquisition costs. In this paper, we introduce MagicDrive3D, a novel pipeline for controllable 3D street scene generation that supports multi-condition control, including BEV maps, 3D objects, and text descriptions. Unlike previous methods that reconstruct before training the generative models, MagicDrive3D first trains a video generation model and then reconstructs from the generated data. This innovative approach enables easily controllable generation and static scene acquisition, resulting in high-quality scene reconstruction. To address the minor errors in generated content, we propose deformable Gaussian splatting with monocular depth initialization and appearance modeling to manage exposure discrepancies across viewpoints. Validated on the nuScenes dataset, MagicDrive3D generates diverse, high-quality 3D driving scenes that support any-view rendering and enhance downstream tasks like BEV segmentation. Our results demonstrate the framework's superior performance, showcasing its transformative potential for autonomous driving simulation and beyond.

MirrorGaussian: Reflecting 3D Gaussians for Reconstructing Mirror Reflections

3D Gaussian Splatting showcases notable advancements in photo-realistic and real-time novel view synthesis. However, it faces challenges in modeling mirror reflections, which exhibit substantial appearance variations from different viewpoints. To tackle this problem, we present MirrorGaussian, the first method for mirror scene reconstruction with real-time rendering based on 3D Gaussian Splatting. The key insight is grounded on the mirror symmetry between the real-world space and the virtual mirror space. We introduce an intuitive dual-rendering strategy that enables differentiable rasterization of both the real-world 3D Gaussians and the mirrored counterpart obtained by reflecting the former about the mirror plane. All 3D Gaussians are jointly optimized with the mirror plane in an end-to-end framework. MirrorGaussian achieves high-quality and real-time rendering in scenes with mirrors, empowering scene editing like adding new mirrors and objects. Comprehensive experiments on multiple datasets demonstrate that our approach significantly outperforms existing methods, achieving state-of-the-art results. Project page: https://mirror-gaussian.github.io/.