The paper introduces the Function‑Space Transformer (FST), a neural framework that learns from functions by using a spatially adaptive continuous latent representation. FST places features at anchors whose positions are predicted from input samples and refines these anchors through recursive function‑space interactions, allowing the representation to adapt to each input rather than relying on a fixed grid. Experiments on PDEBench (Burgers and Darcy flow) and ImageNet‑1K show that FST outperforms or matches state‑of‑the‑art baselines such as Perceiver IO and the Vision Transformer while using fewer parameters.
By Guorui Sang, Pedram Rooshenas
arXiv:2410. 10137v5 Announce Type: replace Abstract: We develop Riemannian approaches to variational autoencoders (VAEs) for PDE-type ambient data with regularizing geometric latent dynamics, which we refer to as VAE-DLM, or VAEs with dynamical latent manifolds.
By Andrew Gracyk
arXiv:2610.08475v1 Announce Type: new
Abstract: In many-query scenarios, data-driven surrogate models provide an efficient alternative to high-fidelity solvers for simulating physical systems governe...
By Stefano Maria Pizzamiglio, Stefano Pagani, Francesco Regazzoni
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.
By Wenqian Chen, Zhi-Feng Wei, Yucheng Fu, Michael Penwarden, Pratanu Roy, Panos Stinis
arXiv:2607. 01128v1 Announce Type: new Abstract: Operator learning for partial differential equations (PDEs) on arbitrary geometries builds fast neural surrogates for large-scale simulation.
By Meenakshi Krishnan, Pranav Pulijala, Ke Chen, Haizhao Yang, Ramani Duraiswami
The paper introduces GeoLAMP, a Geometry-aware Latent Autoregressive generative Model designed to solve multiphysics partial differential equations in highly irregular, micro‑scale tortuous geometries. GeoLAMP employs a dual‑encoder graph architecture to capture both global topology and fine‑scale geometry, transforms real‑space fields into compact latent representations, and uses a causal self‑attention transformer with flow matching for stable, scalable block‑wise autoregressive prediction. The model is evaluated on three benchmark datasets—reactive flow, heat convection, and elasticity—showing consistently low errors across the entire rollout horizon.
By Zi Wang, Minghui Xu, Tapan Mukerji
arXiv:2608.24049v1 Announce Type: new
Abstract: Neural operators provide efficient surrogates for spatiotemporal PDE systems, but purely data-driven formulations often accumulate substantial errors d...
By Jihao Zhang, Junyi Guo, Jian-Xun Wang
HiLNO is a hierarchical latent neural operator that builds a fine‑to‑coarse‑to‑fine latent space and incorporates multi‑scale supervision and anisotropic Gaussian attention to preserve spatial information in PDE solutions with multiscale structures. The hierarchy reduces information loss during compression, while multi‑scale supervision aligns intermediate predictions with downsampled targets, and anisotropic attention facilitates feature transfer across scales. Experiments on standard PDE benchmarks and a large‑scale automotive aerodynamics task show that HiLNO achieves competitive accuracy while cutting parameter count by 84.4% and FLOPs by 69.2% compared with LinearNO, and it generalizes effectively to unseen spatial resolutions.
By Zhicheng Hu, Jiacheng Li, Min Yang
arXiv:2509.06154v3 Announce Type: replace
Abstract: Developing accurate, data-efficient surrogate models is central to advancing AI for Science. Neural operators (NOs), which approximate mappings bet...
By Dibyajyoti Nayak, Somdatta Goswami
arXiv:2604. 07366v2 Announce Type: replace Abstract: Partial differential equations (PDEs) govern nearly every physical process in science and engineering, but solving them at scale remains prohibitively expensive.
By Yilong Dai, Shengyu Chen, Xiaowei Jia, Runlong Yu
arXiv:2605. 08832v3 Announce Type: replace Abstract: Neural surrogate models for computational fluid dynamics (CFD) are typically trained as forward operators that map explicit problem specifications, such as geometry and boundary conditions, to solution fields.
By Jonas Weidner, Yeray Martin-Ruisanchez, Daniel Rueckert, Benedikt Wiestler, Julian Suk
arXiv:2610.08075v1 Announce Type: new
Abstract: Conditional neural fields represent signals continuously, but their effectiveness depends on how the conditional latent representations are inferred fr...
By Rudolf L. M. van Herten, Soufiane Ben Haddou, Rachit Saluja, Johannes C. Paetzold