{"url":"/task/operator-learning","name":"Operator learning","slug":"operator-learning","description_markdown":"Learn an operator between infinite dimensional Hilbert spaces or Banach spaces","categories":[{"name":"Miscellaneous","url":"/area/miscellaneous"}],"source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","slug_source":"archive_url"},"counts":{"papers_tagged":347,"papers_with_code":125,"benchmarks":0,"benchmark_tables_in_archive":0,"benchmark_tables_shown":0,"benchmark_tables_withheld_as_spam":0,"benchmark_definition":"a leaderboard table with at least one row; benchmark_tables_shown also counts the zero-row tables; benchmark_tables_in_archive adds the tables withheld as spam","datasets":1,"subtasks":0,"parent_tasks":0},"benchmarks":[],"datasets":[{"url":"/dataset/bubbleml","name":"BubbleML","full_name":"","num_papers_in_archive":1}],"subtasks":[],"parent_tasks":[],"papers":{"order":"repositories listed in the archive (desc), then date (desc); the archive holds no stars","population":"papers tagged with this task that list at least one repository in the archive","shown":30,"of":125,"tagged_in_all":347,"items":[{"url":"/paper/physics-informed-neural-operator-for-learning-1","title":"Physics-Informed Neural Operator for Learning Partial Differential Equations","date":"2021-11-06","arxiv_id":"2111.03794","repositories_listed":6,"syntology":{"n":8,"n_ran":1,"n_unverified":7,"n_pointer_only":0}},{"url":"/paper/convolutional-analysis-operator-learning-1","title":"Convolutional Analysis Operator Learning: Acceleration and Convergence","date":"2018-02-15","arxiv_id":"1802.05584","repositories_listed":5,"syntology":null},{"url":"/paper/spherical-fourier-neural-operators-learning","title":"Spherical Fourier Neural Operators: Learning Stable Dynamics on the Sphere","date":"2023-06-06","arxiv_id":"2306.03838","repositories_listed":3,"syntology":{"n":3,"n_ran":0,"n_unverified":3,"n_pointer_only":0}},{"url":"/paper/convolutional-analysis-operator-learning","title":"Convolutional Analysis Operator Learning: Dependence on Training Data","date":"2019-02-21","arxiv_id":"1902.08267","repositories_listed":3,"syntology":null},{"url":"/paper/geometry-aware-inference-of-steady-state-pdes","title":"Geometry aware inference of steady state PDEs using Equivariant Neural Fields representations","date":"2025-04-24","arxiv_id":"2504.18591","repositories_listed":2,"syntology":{"n":21,"n_ran":9,"n_unverified":12,"n_pointer_only":21}},{"url":"/paper/provable-in-context-learning-of-linear","title":"In-Context Learning of Linear Systems: Generalization Theory and Applications to Operator Learning","date":"2024-09-18","arxiv_id":"2409.12293","repositories_listed":2,"syntology":{"n":11,"n_ran":8,"n_unverified":3,"n_pointer_only":11}},{"url":"/paper/poseidon-efficient-foundation-models-for-pdes","title":"Poseidon: Efficient Foundation Models for PDEs","date":"2024-05-29","arxiv_id":"2405.19101","repositories_listed":2,"syntology":{"n":3,"n_ran":3,"n_unverified":0,"n_pointer_only":0}},{"url":"/paper/bridging-operator-learning-and-conditioned","title":"CViT: Continuous Vision Transformer for Operator Learning","date":"2024-05-22","arxiv_id":"2405.13998","repositories_listed":2,"syntology":{"n":5,"n_ran":5,"n_unverified":0,"n_pointer_only":0}},{"url":"/paper/towards-a-foundation-model-for-partial","title":"Towards a Foundation Model for Partial Differential Equations: Multi-Operator Learning and Extrapolation","date":"2024-04-18","arxiv_id":"2404.12355","repositories_listed":2,"syntology":null},{"url":"/paper/neural-operators-with-localized-integral-and","title":"Neural Operators with Localized Integral and Differential Kernels","date":"2024-02-26","arxiv_id":"2402.16845","repositories_listed":2,"syntology":{"n":10,"n_ran":6,"n_unverified":4,"n_pointer_only":10}},{"url":"/paper/operator-learning-for-continuous-spatial","title":"Neural Dynamical Operator: Continuous Spatial-Temporal Model with Gradient-Based and Derivative-Free Optimization Methods","date":"2023-11-20","arxiv_id":"2311.11798","repositories_listed":2,"syntology":null},{"url":"/paper/vibroacoustic-frequency-response-prediction","title":"Learning to Predict Structural Vibrations","date":"2023-10-09","arxiv_id":"2310.05469","repositories_listed":2,"syntology":{"n":12,"n_ran":9,"n_unverified":3,"n_pointer_only":12}},{"url":"/paper/a-novel-deeponet-model-for-learning-moving","title":"An enrichment approach for enhancing the expressivity of neural operators with applications to seismology","date":"2023-06-07","arxiv_id":"2306.04096","repositories_listed":2,"syntology":null},{"url":"/paper/in-context-operator-learning-for-differential","title":"In-Context Operator Learning with Data Prompts for Differential Equation Problems","date":"2023-04-17","arxiv_id":"2304.07993","repositories_listed":2,"syntology":{"n":4,"n_ran":3,"n_unverified":1,"n_pointer_only":0}},{"url":"/paper/gnot-a-general-neural-operator-transformer","title":"GNOT: A General Neural Operator Transformer for Operator Learning","date":"2023-02-28","arxiv_id":"2302.14376","repositories_listed":2,"syntology":null},{"url":"/paper/convolutional-neural-operators-for-robust-and-1","title":"Convolutional Neural Operators for robust and accurate learning of PDEs","date":"2023-02-02","arxiv_id":"2302.01178","repositories_listed":2,"syntology":{"n":3,"n_ran":3,"n_unverified":0,"n_pointer_only":0}},{"url":"/paper/mesh-informed-neural-operator-a-transformer","title":"Mesh-Informed Neural Operator : A Transformer Generative Approach","date":"2025-06-20","arxiv_id":"2506.16656","repositories_listed":1,"syntology":null},{"url":"/paper/2506-10973","title":"Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning","date":"2025-06-12","arxiv_id":"2506.10973","repositories_listed":1,"syntology":null},{"url":"/paper/learning-where-to-learn-training-distribution","title":"Learning Where to Learn: Training Distribution Selection for Provable OOD Performance","date":"2025-05-27","arxiv_id":"2505.21626","repositories_listed":1,"syntology":null},{"url":"/paper/self-supervised-evolution-operator-learning","title":"Self-Supervised Evolution Operator Learning for High-Dimensional Dynamical Systems","date":"2025-05-24","arxiv_id":"2505.18671","repositories_listed":1,"syntology":{"n":8,"n_ran":0,"n_unverified":8,"n_pointer_only":0}},{"url":"/paper/geometry-aware-operator-transformer-as-an","title":"Geometry Aware Operator Transformer as an Efficient and Accurate Neural Surrogate for PDEs on Arbitrary Domains","date":"2025-05-24","arxiv_id":"2505.18781","repositories_listed":1,"syntology":null},{"url":"/paper/operator-learning-for-schrodinger-equation","title":"Operator Learning for Schrödinger Equation: Unitarity, Error Bounds, and Time Generalization","date":"2025-05-23","arxiv_id":"2505.18288","repositories_listed":1,"syntology":null},{"url":"/paper/neural-functional-learning-function-to-scalar","title":"Neural Functional: Learning Function to Scalar Maps for Neural PDE Surrogates","date":"2025-05-19","arxiv_id":"2505.13275","repositories_listed":1,"syntology":{"n":5,"n_ran":4,"n_unverified":1,"n_pointer_only":5}},{"url":"/paper/deepoheat-v1-efficient-operator-learning-for","title":"DeepOHeat-v1: Efficient Operator Learning for Fast and Trustworthy Thermal Simulation and Optimization in 3D-IC Design","date":"2025-04-04","arxiv_id":"2504.03955","repositories_listed":1,"syntology":null},{"url":"/paper/a-physics-informed-meta-learning-framework","title":"A Physics-Informed Meta-Learning Framework for the Continuous Solution of Parametric PDEs on Arbitrary Geometries","date":"2025-04-03","arxiv_id":"2504.02459","repositories_listed":1,"syntology":null},{"url":"/paper/equino-a-physics-informed-neural-operator-for","title":"EquiNO: A Physics-Informed Neural Operator for Multiscale Simulations","date":"2025-03-27","arxiv_id":"2504.07976","repositories_listed":1,"syntology":null},{"url":"/paper/on-traffic-an-operator-learning-framework-for","title":"ON-Traffic: An Operator Learning Framework for Online Traffic Flow Estimation and Uncertainty Quantification from Lagrangian Sensors","date":"2025-03-18","arxiv_id":"2503.14053","repositories_listed":1,"syntology":null},{"url":"/paper/improve-representation-for-imbalanced","title":"Improve Representation for Imbalanced Regression through Geometric Constraints","date":"2025-03-02","arxiv_id":"2503.00876","repositories_listed":1,"syntology":null},{"url":"/paper/cauchy-random-features-for-operator-learning","title":"Cauchy Random Features for Operator Learning in Sobolev Space","date":"2025-03-01","arxiv_id":"2503.00300","repositories_listed":1,"syntology":null},{"url":"/paper/rigno-a-graph-based-framework-for-robust-and","title":"RIGNO: A Graph-based framework for robust and accurate operator learning for PDEs on arbitrary domains","date":"2025-01-31","arxiv_id":"2501.19205","repositories_listed":1,"syntology":null}],"syntology_records":12,"syntology_note":"a paper without a record is not a recorded non-run: it may lack an arXiv id or simply be absent from the graph layer"},"description_links":{"kept":0,"unwrapped_to_text":0,"bare_urls_linked":0,"relative_images_dropped":0,"rule":"internal links are kept only when the target slug exists in the catalog"},"syntology":{"read_at":"2026-09-24T18:15:14+00:00","claim":"Per-sample execution status on synthesized fixtures ('ran N of M samples'); not a correctness claim and not a ranking signal.","status_vocabulary":{"ran_honours":"ran, honoured the contract we drafted","ran_violates":"ran, violated the contract we drafted","ran_draft_wrong":"ran; our contract draft was wrong, not the code","ran_fixture":"ran; our fixture could not drive it","ran":"ran on a synthesized input","unverified":"unverified (harvested, no recorded run)"}},"not_shown":{"libraries":"the archive has no per-task library table","trend_sparklines":"the Trend column of the benchmarks table was a rendered image; it is not in the archive","social_and_latest_sorts":"stars and social signals are not in the archive"}}