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Neural operators (NO) are discretization invariant deep learning methods with functional output and can approximate any continuous operator. NO have demonstrated the superiority of solving partial differential equations (PDEs) over other…

Numerical Analysis · Mathematics 2024-02-02 Jianguo Huang , Yue Qiu

In the study of subsurface seismic imaging, solving the acoustic wave equation is a pivotal component in existing models. The advancement of deep learning enables solving partial differential equations, including wave equations, by applying…

Machine Learning · Computer Science 2023-03-10 Bian Li , Hanchen Wang , Shihang Feng , Xiu Yang , Youzuo Lin

We extend Regularised Diffusion-Shock (RDS) filtering from Euclidean space $\mathbb{R}_2$ [1] to position-orientation space $\mathbb{M}_2 \cong \mathbb{R}^2 \times S^1$. This has numerous advantages, e.g. making it possible to enhance and…

Differential Geometry · Mathematics 2026-03-20 Finn M. Sherry , Kristina Schaefer , Remco Duits

Time-dependent partial differential equations (PDEs) are ubiquitous in science and engineering. Recently, mostly due to the high computational cost of traditional solution techniques, deep neural network based surrogates have gained…

Machine Learning · Computer Science 2023-10-24 Phillip Lippe , Bastiaan S. Veeling , Paris Perdikaris , Richard E. Turner , Johannes Brandstetter

We develop a class of data-driven generative models that approximate the solution operator for parameter-dependent partial differential equations (PDE). We propose a novel probabilistic formulation of the operator learning problem based on…

Numerical Analysis · Mathematics 2026-04-21 Ting Wang , Petr Plechac , Jaroslaw Knap

Predicting the large-scale dynamics of three-dimensional (3D) turbulence is challenging for machine learning approaches. This paper introduces a transformer-based neural operator (TNO) to achieve precise and efficient predictions in the…

Fluid Dynamics · Physics 2024-06-07 Zhijie Li , Tianyuan Liu , Wenhui Peng , Zelong Yuan , Jianchun Wang

The solution of partial differential equations (PDEs) plays a central role in numerous applications in science and engineering, particularly those involving multiphase flow in porous media. Complex, nonlinear systems govern these problems…

Operator learning has emerged as a promising paradigm for developing efficient surrogate models to solve partial differential equations (PDEs). However, existing approaches often overlook the domain knowledge inherent in the underlying PDEs…

Machine Learning · Computer Science 2025-10-20 Ziqian Li , Kang Liu , Yongcun Song , Hangrui Yue , Enrique Zuazua

Machine learning has witnessed substantial growth, leading to the development of advanced artificial intelligence models crafted to address a wide range of real-world challenges spanning various domains, such as computer vision, natural…

Machine Learning · Computer Science 2023-10-31 Tapas Tripura , Souvik Chakraborty

Physics-informed neural networks (PINNs) and neural operators (NOs) for solving the problem of diffraction of Extreme Ultraviolet (EUV) electromagnetic waves from contemporary lithography masks are presented. A novel hybrid Waveguide Neural…

Machine Learning · Computer Science 2026-03-18 Vasiliy A. Es'kin , Egor V. Ivanov

Operator learning is a powerful paradigm for solving partial differential equations, with Fourier Neural Operators serving as a widely adopted foundation. However, FNOs face significant scalability challenges due to overparameterization and…

Machine Learning · Computer Science 2025-10-20 Albert Matveev , Sanmitra Ghosh , Aamal Hussain , James-Michael Leahy , Michalis Michaelides

Standard Latent Diffusion Models rely on a complex, three-part architecture consisting of a separate encoder, decoder, and diffusion network, which are trained in multiple stages. This modular design is computationally inefficient, leads to…

Computer Vision and Pattern Recognition · Computer Science 2025-11-19 Xiyuan Wang , Muhan Zhang

We integrate neural operators with diffusion models to address the spectral limitations of neural operators in surrogate modeling of turbulent flows. While neural operators offer computational efficiency, they exhibit deficiencies in…

Machine Learning · Computer Science 2025-02-14 Vivek Oommen , Aniruddha Bora , Zhen Zhang , George Em Karniadakis

This work introduces DiffuseLoco, a framework for training multi-skill diffusion-based policies for dynamic legged locomotion from offline datasets, enabling real-time control of diverse skills on robots in the real world. Offline learning…

In many mechanistic medical, biological, physical and engineered spatiotemporal dynamic models the numerical solution of partial differential equations (PDEs) can make simulations impractically slow. Biological models require the…

Soft Condensed Matter · Physics 2021-02-11 J. Quetzalcóatl Toledo-Marín , Geoffrey Fox , James P. Sluka , James A. Glazier

The diffusion model has recently emerged as a potent approach in computer vision, demonstrating remarkable performances in the field of generative artificial intelligence. Capable of producing high-quality synthetic images, diffusion models…

Image and Video Processing · Electrical Eng. & Systems 2025-05-14 Abdullah , Tao Huang , Ickjai Lee , Euijoon Ahn

Learning partial differential equations' (PDEs) solution operators is an essential problem in machine learning. However, there are several challenges for learning operators in practical applications like the irregular mesh, multiple input…

Machine Learning · Computer Science 2023-06-16 Zhongkai Hao , Zhengyi Wang , Hang Su , Chengyang Ying , Yinpeng Dong , Songming Liu , Ze Cheng , Jian Song , Jun Zhu

Diffusion models have emerged as powerful generative tools with applications in computer vision and scientific machine learning (SciML), where they have been used to solve large-scale probabilistic inverse problems. Traditionally, these…

In this work, we focus on the alignment problem of diffusion models with a continuous reward function, which represents specific objectives for downstream tasks, such as increasing darkness or improving the aesthetics of images. The central…

Machine Learning · Computer Science 2024-10-03 Zhiwei Tang , Jiangweizhi Peng , Jiasheng Tang , Mingyi Hong , Fan Wang , Tsung-Hui Chang

Recent advances in deep learning have inspired numerous works on data-driven solutions to partial differential equation (PDE) problems. These neural PDE solvers can often be much faster than their numerical counterparts; however, each…

Machine Learning · Computer Science 2025-02-06 Anthony Zhou , Zijie Li , Michael Schneier , John R Buchanan , Amir Barati Farimani