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

• Homebrewed SLMs: Autoregressive and Masked Diffusion Language Models Built at Home for Portuguese
  Pedro Carvalho Brom · arXiv · Oct 29, 2026

  Building a language model of one's own no longer requires a data centre. This tutorial trains one from scratch, tokenizer included, on one consumer GPU, and shows how to tell whether it is good for the tasks of a specialist domain. It propo…

• NEOPIC: A Neural Operator Framework for Particle-based Kinetic Plasma Simulations
  Sriramkrishnan Muralikrishnan, Chelsea Maria John, Jeffrey Kelling, Michael Bussmann et al. · arXiv · Oct 29, 2026

  We introduce NEOPIC, a framework for learning the field operator in particle-based methods applied to kinetic plasma simulations. Its key novelty is a neural operator that acts directly on the empirical measure of the particles, rather than…

• A Neuro-Physical Framework for Three-Dimensional Elastodynamic Wave Prediction in Mechanical Components
  Khaled Aldhufri · Zenodo (CERN European Organ... · Oct 25, 2026

  Predicting vibration-wave propagation in mechanical components requires solvingtransient, three-dimensional elastodynamic equations across complex geometries, material interfaces, and frequency-dependent damping. This paper proposes a resea…

• ZENO: Nonlinear filtering with Zakai Equation Neural Operators
  Aaditya Prasad, Steven W. Flavell, Brian DePasquale · arXiv · Oct 23, 2026

  State inference and parameter learning for nonlinear filters is a core computation for scientific machine learning with varied applications in engineering and neuroscience. The unnormalized filtering distribution is governed by the Zakai eq…

• Discontinuous Galerkin Finite Element Operator Network for Solving Non-Smooth PDEs
  Kapil Chawla, Youngjoon Hong, Jae Yong Lee, Sanghyun Lee · SIAM Journal on Scientific ... · Oct 23, 2026

  Abstract. We introduce the Discontinuous Galerkin Finite Element Operator Network (DG–FEONet), a data-free operator learning framework that combines the strengths of the discontinuous Galerkin (DG) method with neural networks to solve param…

• Planning under Noise with Neural Operators
  Michael Chen, Hong Chul Nam, Xi Deng, Anima Anandkumar · arXiv · Oct 20, 2026

  Planning under uncertain control execution noise requires reliable feedback policies across diverse environments. We introduce Planning Under Noise (PUN), a neural operator that learns noise-aware value fields for planning in unseen geometr…

• Kronecker Delta Rule for Long Context Linear Attention
  Anamaria-Roberta Hartl, Levente Zólyomi, Michael List, Günter Klambauer et al. · arXiv · Oct 19, 2026

  We propose KronLSTM, a linear attention architecture based on the Kronecker Delta Rule, a novel update rule for associative matrix memories. KronLSTM extends the xLSTM family with a memory-revision mechanism that corrects targeted associati…

• A neural operator framework for data-driven discovery of stability and receptivity in physical systems
  Chengyun Wang, Liwei Chen, Nils Thuerey · Proceedings of the National... · Oct 16, 2026

  Understanding how complex systems respond to perturbations, such as whether they will remain stable or what their most sensitive patterns are, is a fundamental challenge across science and engineering. Traditional stability and receptivity …

• Fourier Neural Operator-based surrogate modeling of offshore tsunami propagation and its application to rapid tsunami source inversion
  Masayoshi Someya, Takashi Furumura, Ryoichiro Agata · Earth Planets and Space · Oct 9, 2026
• Decoupling Exploration from Optimization in RLVR
  Saif Punjwani, Micah Goldblum · arXiv · Oct 7, 2026

  Modern language models undergo reinforcement learning with verifiable rewards (RLVR) on top of already-trained checkpoints. A key promise of RLVR is the discovery of new reasoning strategies. In principle, a model can sample novel ideas abs…

• Fourier neural operators with least-squares readout refit for learning random obstacle-to-solution maps
  Chenhui Zhu, Fang Wang · Nonlinear Analysis Real Wor... · Oct 6, 2026
• IdeaLens: Detecting AI Ideas in Long-form Writing
  Rishanth Rajendhran, Minjoon Choi, Jenna Russell, Ramya Namuduri et al. · arXiv · Oct 5, 2026

  While modern AI detectors identify who wrote the words, emerging policies on AI use increasingly hinge on a different question: who came up with the ideas? We introduce IdeaLens, a detector that identifies whether a document's ideas came fr…

• hyperbolix: Hyperbolic Deep Learning in JAX
  Timo Klein, Thomas Lang, Yllka Velaj, Sebastian Tschiatschek · arXiv · Sep 23, 2026

  We present hyperbolix, an open-source library for hyperbolic deep learning in JAX, built on Flax NNX. To our knowledge, it is the first comprehensive, general-purpose hyperbolic deep learning library in JAX. It includes six manifolds with a…

• Learning Physics from an Imperfect Ancestor
  S. Mohammad Mousavi, Teeratorn Kadeethum, Nikolaos Bouklas, Somdatta Goswami · arXiv · Sep 21, 2026

  Neural operators evaluate parametric partial differential equations cheaply but degrade sharply outside their training distribution. Physics-informed neural networks avoid dependence on labeled data, yet their optimization can be basin-frag…

• Enhancing Transformer Representations of Symbolic ODE Expressions
  Xiyue Fan, Adam Prugel-Bennett, Stuart E. Middleton · arXiv · Sep 21, 2026

  Existing approaches to solving differential equations, such as symbolic regression, physics informed neural networks, and neural operators, typically focus on numerical approximations or blind symbolic search via fitting to numerical data. …

• A neural operator for predicting vibration frequency response curves from limited data
  D. Bluedorn, A. Badawy, B. E. Saunders, D. Roettgen et al. · Computers & Structures · Sep 21, 2026

  In the design of engineered components, rigorous vibration testing is essential for performance validation and identification of resonant frequencies and amplitudes encountered during operation. Performing this evaluation numerically via ma…

• pCHA: Ultrametric categorical forecasting of chaos under extreme data shortage - equation-free, data-driven, strict out-of-sample, with blind-test protocol.
  Valentin Globa · Zenodo (CERN European Organ... · Sep 20, 2026

  pCHA is a method for long-horizon forecasting of chaotic trajectories when training data is scarce. It works with as few as 15 observed points, without any knowledge of the governing equations, and produces trajectories out to T = 50 Lyapun…

• pCHA: Ultrametric categorical forecasting of chaos under extreme data shortage - equation-free, data-driven, strict out-of-sample, with blind-test protocol.
  Valentin Globa · Zenodo (CERN European Organ... · Sep 20, 2026

  pCHA is a method for long-horizon forecasting of chaotic trajectories when training data is scarce. It works with as few as 15 observed points, without any knowledge of the governing equations, and produces trajectories out to T = 50 Lyapun…

• Continuous time evolution warning and optimal control decision of graduation requirement indicator points based on Fourier neural operators and differential games
  Fang Xia, GaoFeng Han, Xiaomei Ding, Huaibao Ding · International Journal of Ap... · Sep 16, 2026
• Predicting stress hotspots in crystal plasticity with Fourier neural operator surrogates
  Ajaikrishna Ramalingam, Niklas Fehlemann, Sebastian Münstermann · Computer Methods in Applied... · Sep 13, 2026
• LoRA-TSD: Tangent-Space Spectral Descent for LoRA via Muon-Style Updates
  Dmitrii Andriianov, Andrey Veprikov, Aleksandr Beznosikov · arXiv · Sep 2, 2026

  Low-rank adaptation (LoRA) is the standard way to fine-tune large models, yet when its two factors are trained independently, the update ignores the geometry of the low-rank weight change it induces. We introduce LoRA-TSD, an optimizer that…

• Learning Nonlinear Responses in PET Bottle Buckling With a Hybrid DeepONet–Transolver Framework
  Varun Kumar, Jing Bi, Cyril Ngo Ngoc, Victor Oancea et al. · International Journal for N... · Sep 2, 2026

  ABSTRACT Neural surrogates and operator networks for solving partial differential equation (PDE) problems have attracted significant research interest in recent years. However, most existing approaches are limited in their ability to genera…

• DVL-DeepONet: A physics-guided operator learning for resilient underwater navigation
  Arup Kumar Sahoo, Itzik Klein · Ocean Engineering · Aug 31, 2026
• 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…

• 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…

• Generalized Koopman Neural Operator for Data-Driven Modeling of Electric Railway Pantograph–Catenary Systems
  Hui Wang, Yang Song, Hao-Nan Yang, Zhi-Gang 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 …

• NOWS: Neural Operator Warm Starts for Accelerating Iterative Solvers
  M. Eshaghi, C. Anitescu, N. Valizadeh, Yi-Zheng Wang et al. · Computer Methods in Applied Mechanics and Engineering · Nov 4, 2025

  Partial differential equations (PDEs) underpin quantitative descriptions across the physical sciences and engineering, yet high-fidelity simulation remains a major computational bottleneck for many-query, real-time, and design tasks. Data-d…

• Propagation-adaptive 4K computer-generated holography using physics-constrained spatial and Fourier neural operator
  Ninghe Liu, Ke-Xuan Liu, Yi-Xin Yang, Yi-Fan Peng et al. · Nature Communications · Aug 20, 2025

  Computer-generated holography (CGH) offers a promising method to create true-to-life reconstructions of objects. While recent advances in deep learning-based CGH algorithms have significantly improved the tradeoff between algorithm runtime …

• Single‐Pass Wavefront Reconstruction via Depth Heterogeneity Self‐Supervised Neural Operator for Turbulence Correction
  Haoyu Zhang, Chaoxu Chen, Fujie Li, Jifan Cai et al. · Laser & Photonics Reviews · Jun 22, 2025

  Turbulence‐induced distortion remains a major bottleneck for high‐fidelity applications such as optical wireless communication and laser‐based remote sensing, as conventional adaptive optics systems struggle to meet the combined demands of …

• Mesh-Informed Neural Operator : A Transformer Generative Approach
  Yaozhong Shi, Zachary E. Ross, D. Asimaki, K. Azizzadenesheli · Trans. Mach. Learn. Res. · Jun 20, 2025

  Generative models in function spaces, situated at the intersection of generative modeling and operator learning, are attracting increasing attention due to their immense potential in diverse scientific and engineering applications. While fu…