Latest Neural Operators (FNO, DeepONet) Research Papers

The newest Neural Operators (FNO, DeepONet) papers from across the field — arXiv, NeurIPS, CVPR, Nature, and more — refreshed daily and ranked by relevance. Distill AI tracks Neural Operators (FNO, DeepONet) so you don’t have to: get the standout work delivered to your inbox every morning, with 2-sentence summaries and the option to chat with any paper.

Recent papers

• OncoTraj: a public benchmark for longitudinal resistance prediction in EGFR-mutant non-small-cell lung cancer on osimertinib
  Abhijoy Sarkar, Aarchi Singh Thakur · arXiv · Jun 9, 2026

  Resistance to first-line osimertinib in EGFR-mutant non-small-cell lung cancer (NSCLC) is the canonical example of predictable clonal evolution under therapeutic pressure, yet no public benchmark exists for training or evaluating computatio…

• Topological Neural Operators
  Lennart Bastian, Samuel Leventhal, Mustafa Hajij, Tolga Birdal · arXiv · Jun 8, 2026

  We introduce Topological Neural Operators (TNOs), a principled framework for operator learning on cell complexes that lifts neural operators (NOs) from functions on points and/or edges to topological domains. TNOs represent data as features…

• Spectral Audit of In-Context Operator Networks
  Zhiwei Gao, Liu Yang, George Em Karniadakis · arXiv · Jun 1, 2026

  Existing evaluations of neural operators and in-context operator learning rely primarily on prediction error, but accurate output prediction does not guarantee the correct local dynamical structure. A model may match solutions while exhibit…

• Neural Operator-Based Surrogate Model for CFD:Helical Coil Steam Generator in Small Modular Reactor
  Minseo Lee, Seongmin Oh, Chaehyeon Song, Bumjin Cho et al. · arXiv · May 28, 2026

  Real-time thermal-hydraulic simulation is essential for digital twin (DT) technology that supports the safe and efficient operation of small modular reactors (SMRs). Computational fluid dynamics (CFD) provides high-fidelity flow analysis, b…

• Accelerating Bayesian inverse design in computational fluid dynamics using neural operators
  Bipin Tiwari, Omer San · arXiv · May 25, 2026

  Bayesian inverse design provides a principled framework for inferring aerodynamic geometries from sparse flow observations while quantifying uncertainty. However, its practical use in computational fluid dynamics (CFD) is severely limited b…

• Eradicating Negative Transfer in Multi-Physics Foundation Models via Sparse Mixture-of-Experts Routing
  Ellwil Sharma, Arastu Sharma · arXiv · May 14, 2026

  Scaling Scientific Machine Learning (SciML) toward universal foundation models is bottlenecked by negative transfer: the simultaneous co-training of disparate partial differential equation (PDE) regimes can induce gradient conflict, unstabl…

• Learning the Helmholtz equation operator with DeepONet for non-parametric 2D geometries
  Rodolphe Barlogis, Ferhat Tamssaouet, Quentin Falcoz, Stéphane Grieu · arXiv · May 1, 2026

  This paper deals with solving the 2D Helmholtz equation on non-parametric domains, leveraging a physics-informed neural operator network based on the DeepONet framework. We consider a 2D square domain with an inclusion of arbitrary boundary…

• Turning the TIDE: Cross-Architecture Distillation for Diffusion Large Language Models
  Gongbo Zhang, Wen Wang, Ye Tian, Li Yuan · arXiv · Apr 29, 2026

  Diffusion large language models (dLLMs) offer parallel decoding and bidirectional context, but state-of-the-art dLLMs require billions of parameters for competitive performance. While existing distillation methods for dLLMs reduce inference…

• Physics-Informed Shearlet Neural Operator (PI-ShearletNO) for parametric partial differential equations
  Fabio Pereira dos Santos, Júlio de Castro Vargas Fernandes, Adriano M A Cortes · AI&PDE Poster · Mar 1, 2026

  This paper introduces the Physics-Informed Shearlet Neural Operator (PI-ShearletNO), a framework for learning solution operators of parametric partial differential equations. The model combines neural operator learning with the geometric se…

• KANO: Kolmogorov-Arnold Neural Operator
  Jin Lee, Ziming Liu, Xinling Yu, Yixuan Wang et al. · ICLR 2026 Poster · Jan 26, 2026

  We introduce Kolmogorov–Arnold Neural Operator (KANO), a dual‑domain neural operator jointly parameterized by both spectral and spatial bases with intrinsic symbolic interpretability. We theoretically demonstrate that KANO overcomes the pur…

• Riesz Neural Operator for Solving Partial Differential Equations
  shouyiliu, Xiaokang Yang, Yuntian Chen · ICLR 2026 Poster · Jan 26, 2026

  Local non-stationarity is pivotal to solving partial differential equations (PDEs). However, in operator learning, the spatially local information inherent in the data is often overlooked. Even when explicitly modeled, it is usually collaps…

• Tucker-FNO: Tensor Tucker-Fourier Neural Operator and its Universal Approximation Theory
  Guancheng Zhou, Zelin Zeng, Yisi Luo, Qi Xie et al. · ICLR 2026 Poster · Jan 26, 2026

  Fourier neural operator (FNO) has demonstrated substantial potential in learning mappings between function spaces, such as numerical partial differential equations (PDEs). However, FNO may suffer from inefficiencies when applied to large-sc…

• Guided and Interpretable Neural Operator Design for Partial Differential Equation Learning
  Zeyuan Song, Zheyu Jiang · Submitted to ICLR 2026 · Sep 19, 2025

  Accurate numerical solutions of partial differential equations (PDEs) are crucial in numerous science and engineering applications. In this work, we introduce a novel neural PDE solver named AFDONet, which incorporates neural operator learn…

• PIVNO: Particle Image Velocimetry Neural Operator
  Jie Xu, Xuesong Zhang, Jing Jiang, Qinghua Cui · NeurIPS 2025 poster · Sep 18, 2025

  Particle Image Velocimetry (PIV) aims to infer underlying velocity fields from time-separated particle images, forming a PDE-constrained inverse problem governed by advection dynamics. Traditional cross-correlation methods and deep learning…

• Solving Partial Differential Equations via Radon Neural Operator
  Wenbin Lu, Yihan Chen, Junnan Xu, Wei Li et al. · NeurIPS 2025 poster · Sep 18, 2025

  Neural operator is considered a popular data-driven alternative to traditional partial differential equation (PDE) solvers. However, most current solutions, whether fulfilling computations in frequency, Laplacian, and wavelet domains, all d…

• POD-KAN-NO: a physically interpretable neural operator
  Yanyu Ke · AI4Math@ICML25 Poster · Jul 9, 2025

  POD-KAN-NO is a novel neural operator framework that combines the interpretability of modal decomposition with the expressive power of modern neural networks. By integrating Proper Orthogonal Decomposition (POD) with Kolmogorov–Arnold Netwo…

• QuanONet: Quantum Neural Operator with Application to Differential Equation
  Ruocheng Wang, Zhuo Xia, Ge Yan, Junchi Yan · ICML 2025 poster · May 1, 2025

  Differential equations are essential and popular in science and engineering. Learning-based methods including neural operators, have emerged as a promising paradigm. We explore its quantum counterpart, and propose QuanONet -- a quantum neur…

• Kernel Neural Operators (KNOs) for Scalable, Memory-efficient, Geometrically-flexible Operator Learning
  Matthew Lowery, John Turnage, Zachary Morrow, John Davis Jakeman et al. · ICLR 2025 Conference Withdrawn Submission · Sep 25, 2024

  This paper introduces the Kernel Neural Operator (KNO), a novel operator learning technique that uses deep kernel-based integral operators in conjunction with quadrature for function-space approximation of operators (maps from functions to …

• Alias-Free Mamba Neural Operator
  Jianwei Zheng, LiweiNo, Ni Xu, Junwei Zhu et al. · NeurIPS 2024 poster · Sep 25, 2024

  Benefiting from the booming deep learning techniques, neural operators (NO) are considered as an ideal alternative to break the traditions of solving Partial Differential Equations (PDE) with expensive cost. Yet with the remarkable progress…

• Mamba Neural Operator: Who Wins? Transformers vs. State-Space Models for PDEs
  Chun-Wun Cheng, Jiahao Huang, Yi Zhang, Guang Yang et al. · ICLR 2025 Conference Withdrawn Submission · Sep 25, 2024

  Partial differential equations (PDEs) are widely used to model complex physical systems, but solving them efficiently remains a significant challenge. Recently, Transformers have emerged as the preferred architecture for PDEs due to their a…

• Geometry-Informed Neural Operator for Large-Scale 3D PDEs
  Zongyi Li, Nikola Borislavov Kovachki, Chris Choy, Boyi Li et al. · NeurIPS 2023 poster · Sep 21, 2023

  We propose the geometry-informed neural operator (GINO), a highly efficient approach for learning the solution operator of large-scale partial differential equations with varying geometries. GINO uses a signed distance function (SDF) repres…

• Improved Operator Learning by Orthogonal Attention
  Zipeng Xiao, Zhongkai Hao, Bokai Lin, Zhijie Deng et al. · Submitted to ICLR 2024 · Sep 21, 2023

  Neural operators, as an efficient surrogate model for learning the solutions of PDEs, have received extensive attention in the field of scientific machine learning. Among them, attention-based neural operators have become one of the mainstr…

• Equivariant Graph Neural Operator for Modeling 3D Dynamics
  Minkai Xu, Jiaqi Han, Aaron Lou, Kamyar Azizzadenesheli et al. · Submitted to ICLR 2024 · Sep 20, 2023

  Modeling the complex three-dimensional (3D) dynamics of relational systems is an important problem in the natural sciences, with applications ranging from molecular simulations to particle mechanics. Machine learning methods have achieved g…