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Related papers: jNO: A JAX Library for Neural Operator and Foundat…

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This focused review explores a range of neural operator architectures for approximating solutions to parametric partial differential equations (PDEs), emphasizing high-level concepts and practical implementation strategies. The study covers…

Computational Engineering, Finance, and Science · Computer Science 2025-03-10 Prashant K. Jha

For linear partial differential equations with known fundamental solutions, this work introduces a novel operator learning framework that relies exclusively on domain boundary data, including solution values and normal derivatives, rather…

Machine Learning · Computer Science 2026-01-19 Haochen Wu , Heng Wu , Benzhuo Lu

This work introduces the Wavelet-Laplace Neural Operator (WLNO), a novel neural operator that fuses Haar wavelet multi-scale spatial decomposition with the Laplace-domain pole-residue formulation of the Laplace Neural Operator (LNO). While…

Machine Learning · Computer Science 2026-05-26 Muhammad Abid , Arth Sojitra , Omer San

Neural operators learn mappings from function-dependent inputs to solutions, providing an effective framework for solving partial differential equations (PDEs). For time-dependent PDEs, existing methods typically perform long-horizon…

Machine Learning · Computer Science 2026-05-29 Jiaquan Zhang , Caiyan Qin , Haoyu Bian , Libin Cai , Yi Lu , Chaoning Zhang , Wei Dong , Yuanfang Guo , Yang Yang , Hen Tao Shen

As artificial intelligence emerges as a transformative enabler for fusion energy commercialization, fast and accurate solvers become increasingly critical. In magnetic confinement nuclear fusion, rapid and accurate solution of the…

Multiscale problems are ubiquitous in physics. Numerical simulations of such problems by solving partial differential equations (PDEs) at high resolution are computationally too expensive for many-query scenarios, such as uncertainty…

Computational Physics · Physics 2026-02-03 Hamidreza Eivazi , Jendrik-Alexander Tröger , Stefan Wittek , Stefan Hartmann , Andreas Rausch

Inverse microstructure design plays a central role in materials discovery, yet remains challenging due to the complexity of structure-property linkages and the scarcity of labeled training data. We propose Design-GenNO, a physics-informed…

Mathematical Physics · Physics 2025-09-11 Yaohua Zang , Phaedon-Stelios Koutsourelakis

Neural networks are typically sensitive to small input perturbations, leading to unexpected or brittle behaviour. We present RobustNeuralNetworks.jl: a Julia package for neural network models that are constructed to naturally satisfy a set…

Machine Learning · Computer Science 2025-10-01 Nicholas H. Barbara , Max Revay , Ruigang Wang , Jing Cheng , Ian R. Manchester

Neural operators have emerged as promising surrogate models for solving partial differential equations (PDEs), but struggle to generalise beyond training distributions and are often constrained to a fixed temporal discretisation. This work…

Scenic is an open-source JAX library with a focus on Transformer-based models for computer vision research and beyond. The goal of this toolkit is to facilitate rapid experimentation, prototyping, and research of new vision architectures…

Computer Vision and Pattern Recognition · Computer Science 2021-10-25 Mostafa Dehghani , Alexey Gritsenko , Anurag Arnab , Matthias Minderer , Yi Tay

Neural operators have emerged as a powerful tool for solving partial differential equations (PDEs) and other complex scientific computing tasks. However, the performance of single operator block is often limited, thus often requiring…

Numerical Analysis · Mathematics 2025-07-18 Yichen Wang , Wenlian Lu

Foundation models, such as large language models, have demonstrated success in addressing various language and image processing tasks. In this work, we introduce a multi-modal foundation model for scientific problems, named PROSE-PDE. Our…

Machine Learning · Computer Science 2025-02-04 Jingmin Sun , Yuxuan Liu , Zecheng Zhang , Hayden Schaeffer

By learning the mappings between infinite function spaces using carefully designed neural networks, the operator learning methodology has exhibited significantly more efficiency than traditional methods in solving complex problems such as…

Numerical Analysis · Mathematics 2023-03-06 Ziyuan Liu , Haifeng Wang , Hong Zhang , Kaijuna Bao , Xu Qian , Songhe Song

This paper proposes a physics-informed neural operator (PINO) framework for solving inverse scattering problems, enabling rapid and accurate reconstructions under diverse measurement conditions. In the proposed approach, the dielectric…

Computational Physics · Physics 2026-03-27 Q. C. Dong , Zi-Xuan Su , Qing Huo Liu , Wen Chen , Zhizhang , Chen

Operator learning refers to the application of ideas from machine learning to approximate (typically nonlinear) operators mapping between Banach spaces of functions. Such operators often arise from physical models expressed in terms of…

Machine Learning · Computer Science 2024-02-27 Nikola B. Kovachki , Samuel Lanthaler , Andrew M. Stuart

Edge computing addresses the growing data demands of connected-device networks by placing computational resources closer to end users through decentralized infrastructures. This decentralization challenges traditional, fully centralized…

Artificial Intelligence · Computer Science 2026-03-03 Frederico Metelo , Alexandre Oliveira , Stevo Racković , Pedro Ákos Costa , Cláudia Soares

Neural operators have become an effective framework for learning mappings between function spaces, yet most existing architectures realize operators within a single representational domain, such as physical, spectral, or latent space. In…

Machine Learning · Computer Science 2026-05-14 Hanli Qiao , George Em Karniadakis , Muhammad Muniruzzaman

Scientific machine learning has enabled the extraction of physical insights and data-driven modeling of high-dimensional spatiotemporal data, yet achieving physically interpretable latent representations and computationally efficient…

Machine Learning · Computer Science 2026-05-04 Siva Viknesh , Amirhossein Arzani

We introduce the Laplace neural operator (LNO), which leverages the Laplace transform to decompose the input space. Unlike the Fourier Neural Operator (FNO), LNO can handle non-periodic signals, account for transient responses, and exhibit…

Machine Learning · Computer Science 2023-05-31 Qianying Cao , Somdatta Goswami , George Em Karniadakis

Normalizing flow is a class of deep generative models for efficient sampling and likelihood estimation, which achieves attractive performance, particularly in high dimensions. The flow is often implemented using a sequence of invertible…

Machine Learning · Statistics 2024-02-19 Chen Xu , Xiuyuan Cheng , Yao Xie