Neural operators learn mappings between function spaces, but are typically developed with dense input-output training fields and fully observed inputs at inference. Many scientific problems require instead predicting solution fields from sparse, irregular, or partial observations under uncertainty.
arXiv:2608. 11831v1 Announce Type: new Abstract: Learning mappings between infinite-dimensional objects is a central challenge in scientific machine learning.
arXiv:2606. 14597v1 Announce Type: new Abstract: Transformer-based neural operators have shown remarkable performance for approximating solution operators of partial differential equations on complex geometries.
arXiv:2602. 11626v3 Announce Type: replace-cross Abstract: Learning solution operators on arbitrary geometries remains a central challenge in scientific machine learning, especially for many-query simulation, physics-informed learning, and evolving geometries requiring accurate, geometry-aware predictions at arbitrary spatial locations.
arXiv:2606. 17513v1 Announce Type: cross Abstract: Neural operators provide fast surrogates for PDEs but their deterministic predictions limit their use in tasks requiring uncertainty quantification (UQ), especially under geometric variability.
arXiv:2608. 13562v1 Announce Type: new Abstract: Modern operational systems face uncertainty even in routine conditions, where rare, bursty, and self-exciting events emerge from both exogenous covariates and endogenous event dynamics.
arXiv:2606. 17460v1 Announce Type: new Abstract: Neural operators are widely used as surrogate solution maps for partial differential equations (PDEs), but full-size models can be costly to store, deploy, and evaluate in many-query scientific workflows.
arXiv:2607. 23337v1 Announce Type: new Abstract: Neural operators provide data-driven mappings for modeling dynamical systems.
arXiv:2606. 01172v1 Announce Type: new Abstract: Modeling unknown latent functions from finite, irregularly sampled measurements is a recurring challenge across science and engineering.
arXiv:2503. 05598v2 Announce Type: replace-cross Abstract: 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.
arXiv:2607. 16725v1 Announce Type: cross Abstract: Conditional generative modeling remains a challenging problem in semi-supervised settings where labeled data is scarce but unlabeled samples are abundant.
arXiv:2605. 11287v2 Announce Type: replace-cross Abstract: A persistent paradox in time-series forecasting is that structurally simple MLP and linear models often outperform high-capacity Transformers.
Physics-informed neural operators (PINOs) aim to learn solution operators for partial differential equations by using the governing physics as supervision, rather than relying solely on paired input-output simulation data. By incorporating physical constraints into the training objective, PINOs combine the cross-instance generalization of neural operators with the data efficiency of physics-informed learning.