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

• Morphology-, noise-, and resolution-robust ultrasound elasticity imaging with Fourier neural operator.
  Heekyu Kim, H Lee, Minwoo Park, Seunghwa Ryu · PubMed · Aug 15, 2026

  Quasi-static strain elastography is a non-invasive technique for estimating tissue stiffness fields from displacement fields obtained by comparing ultrasound signals before and after compression. While recent deep learning approaches have e…

• Operator learning in nonlinear optics beyond perturbation theory
  Emmanuel Lorin, Adam Miles, Xu Yang, Kemal Yazlyyev · Physica Scripta · Jul 21, 2026

  Abstract This paper is focused on the computation of the nonperturbative nonlinear response of a gas to external intense electromagnetic fields. Ultimately, the long-term objective is to derive data-driven algorithms for the efficient compu…

• Transformer-based neural operators for 3D wind field prediction over complex mountainous terrain
  Yujia Zhang, Jiaxi Qi, Ruiyan Chen, Ying Liu et al. · Communications Physics · Jul 20, 2026
• Variationally correct operator learning: Reduced basis neural operator with a posteriori error estimation
  Yuan Qiu, Wolfgang Dahmen, Peng Chen · Computer Methods in Applied... · Jul 17, 2026
• Graph Neural Operator-Based Surrogate Modelling of Multi-Field CFD Results in Biomass Boiler
  Przemysław Motyl, Danuta Król, Sławomir Poskrobko · Energies · Jul 14, 2026

  Computational fluid dynamics provides detailed spatial distributions of physical fields in biomass boiler combustion, but the computational cost of each simulation limits its application in parametric studies and near-real-time workflows. T…

• A boundary integral-based neural operator for mesh deformation
  Zhengyu Wu, J J Liu, Wei Wang · Engineering With Computers · Jul 11, 2026
• Neural Operator-enabled Topology-informed Evolutionary Strategy for PDE-Constrained Optimization
  Xiangming Huang, Guannan Zhang, Lu Lu, Raphaël Pestourie · arXiv · Jul 8, 2026

  The inverse design of physical systems governed by partial differential equations is computationally demanding due to the high dimensionality and non-convexity of design spaces. Generative models for inverse design often lack robustness and…

• Kernel-based Operator Learning: Error Analysis, Budget Allocation, and a Physics-Informed Extension
  Rüdiger Kempf · arXiv · Jul 7, 2026

  We study kernel-based operator learning in a two-stage sampling framework, where an offline kernel regression operator learns a discretized representation of the target operator from input-output pairs and an online kernel reconstruction op…

• TriA Pipeline: A Large-Scale Automatic Audio Annotation Pipeline For Audio Classification In Specific Scenarios
  Hong Lyu, Mingru Yang, Qianhua He, Yanxiong Li et al. · arXiv · Jul 7, 2026

  There are some datasets of varying scales for audio classification (AC) applied to different tasks. However, annotated data is limited for most scenarios, such as domestic environments. To address this challenge, we propose an $\textbf{A}$u…

• From Theory to Application: A Practical Introduction to Neural Operators in Scientific Computing
  Prashant K. Jha · Mathematics · Jul 6, 2026

  This review examines neural operator architectures for learning solution operators of parametric partial differential equations (PDEs), with an emphasis on conceptual clarity and practical implementation. The work analyzes key models, inclu…

• GAIA: Geometry-Adaptive Operator Learning for Forward and Inverse Problems
  Meenakshi Krishnan, Pranav Pulijala, Ke Chen, Haizhao Yang et al. · arXiv · Jul 1, 2026

  Operator learning for partial differential equations (PDEs) on arbitrary geometries builds fast neural surrogates for large-scale simulation. Although recent geometry-adaptive neural operators have made substantial progress, they are mainly…

• Recovering Governing Equations from Solution Data: Identifiability Bounds for Linear and Nonlinear ODEs
  Yang Pan, Helmut Bölcskei · arXiv · Jun 25, 2026

  Learning governing equations from observed solution data is a fundamental challenge in scientific machine learning \cite{bruntonDiscoveringGoverningEquations2016,kovachkiNeuralOperatorLearning2023,longPDENetLearningPDEs2018,rudyDatadrivenDi…

• Real vs. Complex Spectral Bases for Neural Operators: The Role of Green's Function Alignment
  Jason Sulskis, Sathya Ravi · arXiv · Jun 23, 2026

  Fourier Neural Operators (FNO) learn solution operators of partial differential equations by parameterizing global convolutions in the complex Fourier domain. For real-valued PDE solutions, the complex FFT carries representational redundanc…

• Hedgementation = Hedgerow Segmentation: A Remote Sensing Benchmark
  Nathan Senyard, Salem Hamdani, Astrid Zhang, Derek Wang et al. · arXiv · Jun 22, 2026

  We propose Hedgementation: a new benchmark to evaluate machine learning models for hedgerow mapping from remote sensing data at country scale and 10m$^2$ spatial resolution. We combine and harmonize multiple remote sensing data products and…

• Scaling Linear Mode Connectivity and Merging to Billion Parameter Pretrained Transformers
  Tianyi Li, Zhiqiang Shen · arXiv · Jun 22, 2026

  Linear mode connectivity (LMC) provides a promising foundation for understanding and merging independently trained neural networks, but existing methods typically optimize the interpolation path from only one model endpoint, limiting their …

• Zero-shot generalization of transformer neural operators to larger domains
  Armand de Villeroché, Sibo Cheng, Vincent Le Guen, Marc Bocquet et al. · arXiv · Jun 12, 2026

  Transformer-based neural operators have shown remarkable performance for approximating solution operators of partial differential equations on complex geometries. However, existing approaches implicitly assume a fixed domain size, which lim…

• Claw-SWE-Bench: A Benchmark for Evaluating OpenClaw-style Agent Harnesses on Coding Tasks
  Mengyu Zheng, Kai Han, Boxun Li, Haiyang Xu et al. · arXiv · Jun 10, 2026

  General-purpose agents such as OpenClaw are increasingly used as autonomous tool users, but their coding ability is difficult to measure under SWE-bench: a generic agent does not by itself satisfy the clean Docker workspace, patch, and pred…

• Harness In-Context Operator Learning with Chain of Operators
  Minghui Yang, Ling Guo, Liu Yang · arXiv · Jun 10, 2026

  Neural operators approximate mappings between function spaces, but often generalize poorly to other operators and usually require fine-tuning or retraining. In-Context Operator Networks (ICON) addresses this issue by prompting the model wit…

• 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 Schur Complement Operators for Coarse-to-Fine Neural Operator Transfer
  Ansh Tiwari · AI4Physics · May 30, 2026

  Neural operators are advertised as discretization-flexible, but deploying them from a coarse grid to a finer one routinely loses accuracy that same-grid validation cannot predict. We show that this failure is structural rather than a traini…

• 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…

• Hyperbolic Neural Operator
  Jieyuan Pei, Zhuoxuan Li, Wei Li, Haobo Zhang et al. · ICML 2026 regular · Apr 30, 2026

  Neural operators have emerged as powerful surrogates for solving PDEs, significantly accelerating scientific computation. While transformer-based architectures offer unmatched flexibility for irregular domains, they suffer from a fundament…

• 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…

• Generalized Koopman Neural Operator for Data-Driven Modeling of Electric Railway Pantograph–Catenary Systems
  Hui Wang, Yang Song, Haonan Yang, Zhigang Liu · IEEE Transactions on Transportation Electrification · Dec 1, 2025

  In electric railways, the interaction performance of the pantograph–catenary systems (PCS) is crucial for maintaining a stable current supply. Establishing high-fidelity numerical models based on the finite-element method (FEM) is a common …