English
Related papers

Related papers: Space-Time Continuous PDE Forecasting using Equiva…

200 papers

We present a novel physics-informed deep learning framework for solving steady-state incompressible flow on multiple sets of irregular geometries by incorporating two main elements: using a point-cloud based neural network to capture…

Fluid Dynamics · Physics 2022-10-28 Ali Kashefi , Tapan Mukerji

Although recent efforts have extended Neural Radiance Fields (NeRF) into LiDAR point cloud synthesis, the majority of existing works exhibit a strong dependence on precomputed poses. However, point cloud registration methods struggle to…

Computer Vision and Pattern Recognition · Computer Science 2024-07-09 Weiyi Xue , Zehan Zheng , Fan Lu , Haiyun Wei , Guang Chen , Changjun Jiang

Partial differential equations (PDEs) are widely used across the physical and computational sciences. Decades of research and engineering went into designing fast iterative solution methods. Existing solvers are general purpose, but may be…

Numerical Analysis · Mathematics 2024-09-23 Jun-Ting Hsieh , Shengjia Zhao , Stephan Eismann , Lucia Mirabella , Stefano Ermon

Neural Motion Planners (NMPs) have emerged as a promising tool for solving robot navigation tasks in complex environments. However, these methods often require expert data for learning, which limits their application to scenarios where data…

Robotics · Computer Science 2023-03-02 Ruiqi Ni , Ahmed H. Qureshi

Physics Informed Neural Networks is a numerical method which uses neural networks to approximate solutions of partial differential equations. It has received a lot of attention and is currently used in numerous physical and engineering…

Numerical Analysis · Mathematics 2025-07-10 Dimitrios Gazoulis , Ioannis Gkanis , Charalambos G. Makridakis

We aim to develop physics foundation models for science and engineering that provide real-time solutions to Partial Differential Equations (PDEs) which preserve structure and accuracy under adaptation to unseen geometries. To this end, we…

Machine Learning · Computer Science 2026-02-04 Benjamin D. Shaffer , Shawn Koohy , Brooks Kinch , M. Ani Hsieh , Nathaniel Trask

Neural operator surrogates for time-dependent partial differential equations (PDEs) conventionally employ autoregressive prediction schemes, which accumulate error over long rollouts and require uniform temporal discretization. We introduce…

Machine Learning · Computer Science 2025-12-08 Xianglong Hou , Xinquan Huang , Paris Perdikaris

The computational complexity of classical numerical methods for solving Partial Differential Equations (PDE) scales significantly as the resolution increases. As an important example, climate predictions require fine spatio-temporal…

Machine Learning · Computer Science 2022-10-12 Oussama Boussif , Dan Assouline , Loubna Benabbou , Yoshua Bengio

The numerical simulation and optimization of technical systems described by partial differential equations is expensive, especially in multi-query scenarios in which the underlying equations have to be solved for different parameters. A…

Numerical Analysis · Mathematics 2025-04-09 Franziska Griese , Fabian Hoppe , Alexander Rüttgers , Philipp Knechtges

This paper addresses the challenge of Neural Field (NeF) generalization, where models must efficiently adapt to new signals given only a few observations. To tackle this, we propose Geometric Neural Process Fields (G-NPF), a probabilistic…

Computer Vision and Pattern Recognition · Computer Science 2025-02-05 Wenzhe Yin , Zehao Xiao , Jiayi Shen , Yunlu Chen , Cees G. M. Snoek , Jan-Jakob Sonke , Efstratios Gavves

Accurately, efficiently, and stably computing complex fluid flows and their evolution near solid boundaries over long horizons remains challenging. Conventional numerical solvers require fine grids and small time steps to resolve near-wall…

Machine Learning · Computer Science 2026-03-18 Chenglin Li , Hang Xu , Jianting Chen , Yanfei Zhang

Multiphysics problems such as multicomponent diffusion, phase transformations in multiphase systems and alloy solidification involve numerical solution of a coupled system of nonlinear partial differential equations (PDEs). Numerical…

Materials Science · Physics 2022-11-24 Vir Karan , A. Maruthi Indresh , Saswata Bhattacharyya

Simulating spatiotemporal turbulence with high fidelity remains a cornerstone challenge in computational fluid dynamics (CFD) due to its intricate multiscale nature and prohibitive computational demands. Traditional approaches typically…

Fluid Dynamics · Physics 2024-07-01 Xiantao Fan , Deepak Akhare , Jian-Xun Wang

We introduce a novel grid-independent model for learning partial differential equations (PDEs) from noisy and partial observations on irregular spatiotemporal grids. We propose a space-time continuous latent neural PDE model with an…

Machine Learning · Computer Science 2023-10-27 Valerii Iakovlev , Markus Heinonen , Harri Lähdesmäki

Utilizing machine learning to address partial differential equations (PDEs) presents significant challenges due to the diversity of spatial domains and their corresponding state configurations, which complicates the task of encompassing all…

Machine Learning · Computer Science 2024-05-28 Masanobu Horie , Naoto Mitsume

To better conform to data geometry, recent deep generative modelling techniques adapt Euclidean constructions to non-Euclidean spaces. In this paper, we study normalizing flows on manifolds. Previous work has developed flow models for…

Machine Learning · Statistics 2020-06-19 Aaron Lou , Derek Lim , Isay Katsman , Leo Huang , Qingxuan Jiang , Ser-Nam Lim , Christopher De Sa

Neural ordinary differential equations describe how values change in time. This is the reason why they gained importance in modeling sequential data, especially when the observations are made at irregular intervals. In this paper we propose…

Machine Learning · Computer Science 2021-10-26 Marin Biloš , Johanna Sommer , Syama Sundar Rangapuram , Tim Januschowski , Stephan Günnemann

Computational cardiovascular flow modeling plays a crucial role in understanding blood flow dynamics. While 3D models provide acute details, they are computationally expensive, especially with fluid-structure interaction (FSI) simulations.…

Fluid Dynamics · Physics 2025-01-06 Hunor Csala , Arvind Mohan , Daniel Livescu , Amirhossein Arzani

Neural CDEs provide a natural way to process the temporal evolution of irregular time series. The number of function evaluations (NFE) is these systems' natural analog of depth (the number of layers in traditional neural networks). It is…

Machine Learning · Computer Science 2026-01-27 Ilya Kuleshov , Evgenia Romanenkova , Vladislav Zhuzhel , Galina Boeva , Evgeni Vorsin , Alexey Zaytsev

Partial differential equations (PDEs) govern nearly every physical process in science and engineering, yet solving them at scale remains prohibitively expensive. Generative AI has transformed language, vision, and protein science, but…

Machine Learning · Computer Science 2026-04-10 Yilong Dai , Shengyu Chen , Xiaowei Jia , Runlong Yu