Operator learning

Description from the archive archive 2025-07-28.

Benchmarks archive 2025-07-28

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Libraries

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Datasets archive 2025-07-28

1 dataset whose archive record lists this task, ordered by the archive's paper count.

Subtasks archive 2025-07-28

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Most implemented papers archive 2025-07-28

30 shown of 125 papers with code (347 tagged with this task in all), ordered by repositories listed in the archive, not by stars (the archive holds no stars, so PwC's “Social” and “Latest” sorts cannot be reproduced). Papers without a page here are shown as plain text.

• Physics-Informed Neural Operator for Learning Partial Differential Equations
  6 Nov 2021 6 repositories listed Syntology ran 1 of 8 samples · 7 unverified
  Specifically, in PINO, we combine coarse-resolution training data with PDE constraints imposed at a higher resolution.
• Convolutional Analysis Operator Learning: Acceleration and Convergence
  15 Feb 2018 5 repositories listed
  This paper proposes a new convolutional analysis operator learning (CAOL) framework that learns an analysis sparsifying regularizer with the convolution perspective, and develops a new convergent Block Proximal…
• Spherical Fourier Neural Operators: Learning Stable Dynamics on the Sphere
  6 Jun 2023 3 repositories listed Syntology ran 0 of 3 samples · 3 unverified
  Fourier Neural Operators (FNOs) have proven to be an efficient and effective method for resolution-independent operator learning in a broad variety of application areas across scientific machine learning.
• Convolutional Analysis Operator Learning: Dependence on Training Data
  21 Feb 2019 3 repositories listed
  Convolutional analysis operator learning (CAOL) enables the unsupervised training of (hierarchical) convolutional sparsifying operators or autoencoders from large datasets.
• Geometry aware inference of steady state PDEs using Equivariant Neural Fields representations
  24 Apr 2025 2 repositories listed Syntology ran 9 of 21 samples · 12 unverified · 21 pointer-only (licence)
  Recent advances in Neural Fields have enabled powerful, discretization-invariant methods for learning neural operators that approximate solutions of Partial Differential Equations (PDEs) on general geometries.
• In-Context Learning of Linear Systems: Generalization Theory and Applications to Operator Learning
  18 Sep 2024 2 repositories listed Syntology ran 8 of 11 samples · 3 unverified · 11 pointer-only (licence)
  For out-of-domain generalization, we find that the behavior of trained transformers under task distribution shifts depends crucially on the distribution of the tasks seen during training.
• Poseidon: Efficient Foundation Models for PDEs
  29 May 2024 2 repositories listed Syntology ran 3 of 3 samples · 0 unverified
  Moreover, Poseidon scales with respect to model and data size, both for pretraining and for downstream tasks.
• CViT: Continuous Vision Transformer for Operator Learning
  22 May 2024 2 repositories listed Syntology ran 5 of 5 samples · 0 unverified
  Here we introduce the Continuous Vision Transformer (CViT), a novel neural operator architecture that leverages advances in computer vision to address challenges in learning complex physical systems.
• Towards a Foundation Model for Partial Differential Equations: Multi-Operator Learning and Extrapolation
  18 Apr 2024 2 repositories listed
  More importantly, we provide three extrapolation studies to demonstrate that PROSE-PDE can generalize physical features through the robust training of multiple operators and that the proposed model can extrapolate to…
• Neural Operators with Localized Integral and Differential Kernels
  26 Feb 2024 2 repositories listed Syntology ran 6 of 10 samples · 4 unverified · 10 pointer-only (licence)
  In this work, we present a principled approach to operator learning that can capture local features under two frameworks by learning differential operators and integral operators with locally supported kernels.
• Neural Dynamical Operator: Continuous Spatial-Temporal Model with Gradient-Based and Derivative-Free Optimization Methods
  20 Nov 2023 2 repositories listed
  Data-driven modeling techniques have been explored in the spatial-temporal modeling of complex dynamical systems for many engineering applications.
• Learning to Predict Structural Vibrations
  9 Oct 2023 2 repositories listed Syntology ran 9 of 12 samples · 3 unverified · 12 pointer-only (licence)
  To quantify such trade-offs systematically and foster the development of methods, we present a benchmark on the task of predicting the vibration of harmonically excited plates.
• An enrichment approach for enhancing the expressivity of neural operators with applications to seismology
  7 Jun 2023 2 repositories listed
  The Eikonal equation plays a central role in seismic wave propagation and hypocenter localization, a crucial aspect of efficient earthquake early warning systems.
• In-Context Operator Learning with Data Prompts for Differential Equation Problems
  17 Apr 2023 2 repositories listed Syntology ran 3 of 4 samples · 1 unverified
  This paper introduces a new neural-network-based approach, namely In-Context Operator Networks (ICON), to simultaneously learn operators from the prompted data and apply it to new questions during the inference stage,…
• GNOT: A General Neural Operator Transformer for Operator Learning
  28 Feb 2023 2 repositories listed
  However, there are several challenges for learning operators in practical applications like the irregular mesh, multiple input functions, and complexity of the PDEs' solution.
• Convolutional Neural Operators for robust and accurate learning of PDEs
  2 Feb 2023 2 repositories listed Syntology ran 3 of 3 samples · 0 unverified
  Although very successfully used in conventional machine learning, convolution based neural network architectures -- believed to be inconsistent in function space -- have been largely ignored in the context of learning…
• Mesh-Informed Neural Operator : A Transformer Generative Approach
  20 Jun 2025 1 repository listed
  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…
• Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning
  12 Jun 2025 1 repository listed
  A key factor in deep learning's success has been the careful engineering of neural architectures through extensive empirical testing.
• Learning Where to Learn: Training Distribution Selection for Provable OOD Performance
  27 May 2025 1 repository listed
  Out-of-distribution (OOD) generalization remains a fundamental challenge in machine learning.
• Self-Supervised Evolution Operator Learning for High-Dimensional Dynamical Systems
  24 May 2025 1 repository listed Syntology ran 0 of 8 samples · 8 unverified
  We introduce an encoder-only approach to learn the evolution operators of large-scale non-linear dynamical systems, such as those describing complex natural phenomena.
• Geometry Aware Operator Transformer as an Efficient and Accurate Neural Surrogate for PDEs on Arbitrary Domains
  24 May 2025 1 repository listed
  The very challenging task of learning solution operators of PDEs on arbitrary domains accurately and efficiently is of vital importance to engineering and industrial simulations.
• Operator Learning for Schrödinger Equation: Unitarity, Error Bounds, and Time Generalization
  23 May 2025 1 repository listed
  We consider the problem of learning the evolution operator for the time-dependent Schr\"{o}dinger equation, where the Hamiltonian may vary with time.
• Neural Functional: Learning Function to Scalar Maps for Neural PDE Surrogates
  19 May 2025 1 repository listed Syntology ran 4 of 5 samples · 1 unverified · 5 pointer-only (licence)
  Many architectures for neural PDE surrogates have been proposed in recent years, largely based on neural networks or operator learning.
• DeepOHeat-v1: Efficient Operator Learning for Fast and Trustworthy Thermal Simulation and Optimization in 3D-IC Design
  4 Apr 2025 1 repository listed
  Third, we propose a confidence score to evaluate the trustworthiness of the predicted results, and further develop a hybrid optimization workflow that combines operator learning with finite difference (FD) using…
• A Physics-Informed Meta-Learning Framework for the Continuous Solution of Parametric PDEs on Arbitrary Geometries
  3 Apr 2025 1 repository listed
  In training and inference, a physics-informed loss function is minimized during the PDE encoding and decoding.
• EquiNO: A Physics-Informed Neural Operator for Multiscale Simulations
  27 Mar 2025 1 repository listed
  This limitation has motivated the application of data-driven surrogate models, where the microscale computations are substituted with a surrogate, usually acting as a black-box mapping between macroscale quantities.
• ON-Traffic: An Operator Learning Framework for Online Traffic Flow Estimation and Uncertainty Quantification from Lagrangian Sensors
  18 Mar 2025 1 repository listed
  Accurate traffic flow estimation and prediction are critical for the efficient management of transportation systems, particularly under increasing urbanization.
• Improve Representation for Imbalanced Regression through Geometric Constraints
  2 Mar 2025 1 repository listed
  In a geometric aspect, we uniquely focus on ensuring uniformity in the latent space for imbalanced regression through two key losses: enveloping and homogeneity.
• Cauchy Random Features for Operator Learning in Sobolev Space
  1 Mar 2025 1 repository listed
  Motivated by the recent kernel-based operator learning framework, we propose a random feature operator learning method with theoretical guarantees and error bounds.
• RIGNO: A Graph-based framework for robust and accurate operator learning for PDEs on arbitrary domains
  31 Jan 2025 1 repository listed
  Our model, termed RIGNO, is tested on a challenging suite of benchmarks, composed of various time-dependent and steady PDEs defined on a diverse set of domains.

Syntology lines on 12 of the papers shown; no Syntology record for the others (a paper without an arXiv id cannot be joined to the graph, and absence from the graph layer is not a recorded non-run). “Ran” means the sample executed on a synthesized fixture, not that the paper's result was reproduced. Read from the graph 2026-09-24.