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This paper introduces PDEformer, a neural solver for partial differential equations (PDEs) capable of simultaneously addressing various types of PDEs. We propose to represent the PDE in the form of a computational graph, facilitating the…

Numerical Analysis · Mathematics 2025-01-28 Zhanhong Ye , Xiang Huang , Leheng Chen , Hongsheng Liu , Zidong Wang , Bin Dong

Physics-informed neural networks (PINNs) have shown promising potential for solving partial differential equations (PDEs) using deep learning. However, PINNs face training difficulties for evolutionary PDEs, particularly for dynamical…

Neural and Evolutionary Computing · Computer Science 2023-12-25 Siqi Chen , Bin Shan , Ye Li

Large language models (LLMs) often face a bottleneck in inference speed due to their reliance on auto-regressive decoding. Recently, parallel decoding has shown significant promise in enhancing inference efficiency. However, we have…

Computation and Language · Computer Science 2024-10-18 Yuxuan Liu , Wenyuan Li , Laizhong Cui , Hailiang Yang

The field of meta-learning seeks to improve the ability of today's machine learning systems to adapt efficiently to small amounts of data. Typically this is accomplished by training a system with a parametrized update rule to improve a…

Machine Learning · Computer Science 2021-03-26 Lucas D. Lingle

This work presents a non-intrusive surrogate modeling scheme based on machine learning technology for predictive modeling of complex systems, described by parametrized time-dependent PDEs. For these problems, typical finite element…

Numerical Analysis · Mathematics 2021-04-26 Stefanos Nikolopoulos , Ioannis Kalogeris , Vissarion Papadopoulos

Making the right decision in traffic is a challenging task that is highly dependent on individual preferences as well as the surrounding environment. Therefore it is hard to model solely based on expert knowledge. In this work we use Deep…

Machine Learning · Computer Science 2020-02-04 Peter Wolf , Karl Kurzer , Tobias Wingert , Florian Kuhnt , J. Marius Zöllner

Neural networks are one tool for approximating non-linear differential equations used in scientific computing tasks such as surrogate modeling, real-time predictions, and optimal control. PDE foundation models utilize neural networks to…

Machine Learning · Computer Science 2025-02-11 Elisa Negrini , Yuxuan Liu , Liu Yang , Stanley J. Osher , Hayden Schaeffer

Invariance-based and generative methods have shown a conspicuous performance for 3D self-supervised representation learning (SSRL). However, the former relies on hand-crafted data augmentations that introduce bias not universally applicable…

Computer Vision and Pattern Recognition · Computer Science 2024-09-25 Naiwen Hu , Haozhe Cheng , Yifan Xie , Shiqi Li , Jihua Zhu

Large Language Models (LLMs) often struggle to maintain their original performance when faced with semantically coherent but task-irrelevant contextual information. Although prior studies have explored this issue using fixed-template or…

Computation and Language · Computer Science 2025-09-23 Yanbo Wang , Zixiang Xu , Yue Huang , Chujie Gao , Siyuan Wu , Jiayi Ye , Pin-Yu Chen , Xiuying Chen , Xiangliang Zhang

Fast and accurate solution of time-dependent partial differential equations (PDEs) is of key interest in many research fields including physics, engineering, and biology. Generally, implicit schemes are preferred over the explicit ones for…

Numerical Analysis · Mathematics 2019-11-28 Suprosanna Shit , Abinav Ravi Venkatakrishnan , Ivan Ezhov , Jana Lipkova , Marie Piraud , Bjoern Menze

Partial differential equations (PDEs) play a crucial role in studying a vast number of problems in science and engineering. Numerically solving nonlinear and/or high-dimensional PDEs is often a challenging task. Inspired by the traditional…

Numerical Analysis · Mathematics 2022-01-11 Yihao Hu , Tong Zhao , Shixin Xu , Zhiliang Xu , Lizhen Lin

Partial differential equations (PDEs) play a fundamental role in modeling and simulating problems across a wide range of disciplines. Recent advances in deep learning have shown the great potential of physics-informed neural networks…

Machine Learning · Computer Science 2022-01-31 Pu Ren , Chengping Rao , Yang Liu , Jianxun Wang , Hao Sun

Many important problems in science and engineering require solving the so-called parametric partial differential equations (PDEs), i.e., PDEs with different physical parameters, boundary conditions, shapes of computational domains, etc.…

Numerical Analysis · Mathematics 2024-02-06 Zhanhong Ye , Xiang Huang , Hongsheng Liu , Bin Dong

Building upon large language models (LLMs), recent large multimodal models (LMMs) unify cross-model understanding and generation into a single framework. However, LMMs still struggle to achieve accurate vision-language alignment, prone to…

Artificial Intelligence · Computer Science 2025-09-09 Jixiang Hong , Yiran Zhang , Guanzhong Wang , Yi Liu , Ji-Rong Wen , Rui Yan

Large foundation models have emerged in the last years and are pushing performance boundaries for a variety of tasks. Training or even finetuning such models demands vast datasets and computational resources, which are often scarce and…

Computer Vision and Pattern Recognition · Computer Science 2026-05-01 Leo Fillioux , Enzo Ferrante , Paul-Henry Cournède , Maria Vakalopoulou , Stergios Christodoulidis

Partial differential equations (PDEs) are often computationally challenging to solve, and in many settings many related PDEs must be be solved either at every timestep or for a variety of candidate boundary conditions, parameters, or…

Machine Learning · Computer Science 2022-11-04 Tian Qin , Alex Beatson , Deniz Oktay , Nick McGreivy , Ryan P. Adams

Deep surrogate models for parametric partial differential equations (PDEs) can deliver high-fidelity approximations but remain prohibitively data-hungry: training often requires thousands of fine-grid simulations, each incurring substantial…

Machine Learning · Computer Science 2026-03-03 Yang Meng , Ruoxi Jiang , Zhuokai Zhao , Chong Liu , Rebecca Willett , Yuxin Chen

Partial differential equations (PDEs) are instrumental for modeling dynamical systems in science and engineering. The advent of neural networks has initiated a significant shift in tackling these complexities though challenges in accuracy…

Machine Learning · Computer Science 2024-06-07 Zhuo Chen , Jacob McCarran , Esteban Vizcaino , Marin Soljačić , Di Luo

Recent progress in scientific machine learning (SciML) has opened up the possibility of training novel neural network architectures that solve complex partial differential equations (PDEs). Several (nearly data free) approaches have been…

We introduce a new class of spatially stochastic physics and data informed deep latent models for parametric partial differential equations (PDEs) which operate through scalable variational neural processes. We achieve this by assigning…

Machine Learning · Computer Science 2023-06-08 Arnaud Vadeboncoeur , Ieva Kazlauskaite , Yanni Papandreou , Fehmi Cirak , Mark Girolami , Ömer Deniz Akyildiz