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Solving partial differential equations (PDEs) on fine spatio-temporal scales for high-fidelity solutions is critical for numerous scientific breakthroughs. Yet, this process can be prohibitively expensive, owing to the inherent complexities…

Numerical Analysis · Mathematics 2024-04-09 Yulong Lu , Wuzhe Xu

Deep learning has been extensively employed as a powerful function approximator for modeling physics-based problems described by partial differential equations (PDEs). Despite their popularity, standard deep learning models often demand…

Computational Engineering, Finance, and Science · Computer Science 2025-10-28 Jiachen Guo , Xiaoyu Xie , Chanwook Park , Hantao Zhang , Matthew Politis , Gino Domel , Thomas J. R. Hughes , Wing Kam Liu

Recent advancements in text-to-video (T2V) diffusion models have enabled high-fidelity and realistic video synthesis. However, current T2V models often struggle to generate physically plausible content due to their limited inherent ability…

Computer Vision and Pattern Recognition · Computer Science 2025-05-30 Xiangdong Zhang , Jiaqi Liao , Shaofeng Zhang , Fanqing Meng , Xiangpeng Wan , Junchi Yan , Yu Cheng

High-fidelity electron microscopy simulations required for quantitative crystal structure refinements face a fundamental challenge: while physical interactions are well-described theoretically, real-world experimental effects are…

Ptychographic imaging confronts inherent challenges in applying deep learning for phase retrieval from diffraction patterns. Conventional neural architectures, both convolutional neural networks and Transformer-based methods, are optimized…

In this paper, we present a method of embedding physics data manifolds with metric structure into lower dimensional spaces with simpler metrics, such as Euclidean and Hyperbolic spaces. We then demonstrate that it can be a powerful step in…

High Energy Physics - Phenomenology · Physics 2023-08-02 Sang Eon Park , Philip Harris , Bryan Ostdiek

The high-dimensional nature of the 4-D light field (LF) poses great challenges in achieving efficient and effective feature embedding, that severely impacts the performance of downstream tasks. To tackle this crucial issue, in contrast to…

Image and Video Processing · Electrical Eng. & Systems 2024-01-12 Xianqiang Lyu , Junhui Hou

Photons offer the potential to carry large amounts of information in their spectral, spatial, and polarisation degrees of freedom. While state-of-the-art classical communication systems routinely aim to maximize this information-carrying…

We introduce PDE-Transformer, an improved transformer-based architecture for surrogate modeling of physics simulations on regular grids. We combine recent architectural improvements of diffusion transformers with adjustments specific for…

Machine Learning · Computer Science 2025-06-02 Benjamin Holzschuh , Qiang Liu , Georg Kohl , Nils Thuerey

Unifying multimodal understanding, generation and reconstruction representation in a single tokenizer remains a key challenge in building unified models. Previous research predominantly attempts to address this in a dual encoder paradigm,…

Computer Vision and Pattern Recognition · Computer Science 2025-12-01 Sinan Du , Jiahao Guo , Bo Li , Shuhao Cui , Zhengzhuo Xu , Yifu Luo , Yongxian Wei , Kun Gai , Xinggang Wang , Kai Wu , Chun Yuan

Current image tokenization methods require a large number of tokens to capture the information contained within images. Although the amount of information varies across images, most image tokenizers only support fixed-length tokenization,…

Computer Vision and Pattern Recognition · Computer Science 2025-01-20 Keita Miwa , Kento Sasaki , Hidehisa Arai , Tsubasa Takahashi , Yu Yamaguchi

Dense prediction infers per-pixel values from a single image and is fundamental to 3D perception and robotics. Although real-world scenes exhibit strong structure, existing methods treat it as an independent pixel-wise prediction, often…

Computer Vision and Pattern Recognition · Computer Science 2026-02-02 Seung Hyun Lee , Sangwoo Mo , Stella X. Yu

Inferring parameters of high-dimensional partial differential equations (PDEs) poses significant computational and inferential challenges, primarily due to the curse of dimensionality and the inherent limitations of traditional numerical…

Computational Engineering, Finance, and Science · Computer Science 2025-09-18 Weihao Yan , Christoph Brune , Mengwu Guo

With the increases in computational power and advances in machine learning, data-driven learning-based methods have gained significant attention in solving PDEs. Physics-informed neural networks (PINNs) have recently emerged and succeeded…

Machine Learning · Computer Science 2023-02-07 Namgyu Kang , Byeonghyeon Lee , Youngjoon Hong , Seok-Bae Yun , Eunbyung Park

Gradient-based algorithms are crucial to modern computer-vision and graphics applications, enabling learning-based optimization and inverse problems. For example, photorealistic differentiable rendering pipelines for color images have been…

Computer Vision and Pattern Recognition · Computer Science 2021-08-10 Benjamin Planche , Rajat Vikram Singh

Partial differential equations (PDEs) are among the most universal and parsimonious descriptions of natural physical laws, capturing a rich variety of phenomenology and multi-scale physics in a compact and symbolic representation. This…

Machine Learning · Computer Science 2023-03-31 Steven L. Brunton , J. Nathan Kutz

Accurately modeling and forecasting complex systems governed by partial differential equations (PDEs) is crucial in various scientific and engineering domains. However, traditional numerical methods struggle in real-world scenarios due to…

Machine Learning · Computer Science 2025-05-06 Han Wan , Rui Zhang , Qi Wang , Yang Liu , Hao Sun

Learning-based simulators show great potential for simulating particle dynamics when 3D groundtruth is available, but per-particle correspondences are not always accessible. The development of neural rendering presents a new solution to…

Computer Vision and Pattern Recognition · Computer Science 2024-10-14 Jiaxu Wang , Jingkai Sun , Junhao He , Ziyi Zhang , Qiang Zhang , Mingyuan Sun , Renjing Xu

Capturing and labeling camera images in the real world is an expensive task, whereas synthesizing labeled images in a simulation environment is easy for collecting large-scale image data. However, learning from only synthetic images may not…

Computer Vision and Pattern Recognition · Computer Science 2018-07-06 Tadanobu Inoue , Subhajit Chaudhury , Giovanni De Magistris , Sakyasingha Dasgupta

The data-driven discovery of partial differential equations (PDEs) consistent with spatiotemporal data is experiencing a rebirth in machine learning research. Training deep neural networks to learn such data-driven partial differential…

Numerical Analysis · Mathematics 2020-11-10 Hassan Arbabi , Judith E. Bunder , Giovanni Samaey , Anthony J. Roberts , Ioannis G. Kevrekidis