arXiv:2606. 03262v1 Announce Type: new Abstract: Neural operators learn mappings between infinite-dimensional function spaces and provide a data-driven surrogate modeling paradigm for parametric partial differential equations (PDEs).
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...
The paper presents a method for training single‑step neural surrogates that can handle wave‑scattering problems with tens of thousands of controllable variables. By dynamically generating training examples that highlight surrogate errors and using a replay dataset with normalization, the authors achieve a surrogate that accurately simulates two‑dimensional wave scattering for up to 41,772 variables and generalizes to over 3 million variables without retraining. The surrogate is applied to forward simulations and inverse design of freeform beam splitters and gradient‑index lenses, achieving speedups up to 26.5× compared to traditional FDTD methods.
arXiv:2609.38348v1 Announce Type: new Abstract: Many forms of data, including physical fields, geometric shapes, and visual signals, are naturally described by functions over continuous domains but a...
arXiv:2603. 04430v2 Announce Type: replace Abstract: We introduce Flowers, a neural architecture for learning PDE solution operators built entirely from multihead warps.
Can deep learning translate physical fields governed by fundamentally different equations? We address this question by introducing Cross-Physics Mapping (CPM), an operator-learning framework for mappi...
arXiv:2608. 09764v1 Announce Type: cross Abstract: Transformer-based neural operators have achieved substantial progress in solving Partial Differential Equations (PDEs) by projecting spatial observations into compact latent tokens and learning physical interactions in latent spaces.
The paper presents a method for training single‑step neural surrogates that can handle wave‑scattering inverse problems with tens of thousands of controllable variables. By dynamically generating training examples through gradient ascent and using a replay dataset with normalization, the authors achieve a surrogate that accurately models two‑dimensional wave scattering for up to 41,772 variables and can generalize to over 3 million variables without retraining. The surrogate demonstrates comparable or better performance than traditional FDTD simulations for large‑scale forward simulations and inverse design of photonic devices, achieving speedups up to 26.5×.
Euclidean Fourier Neural Operators (EFNOs) extend Fourier neural operators by making the spectral kernel a continuous function of physical wavevectors, thereby removing dependence on specific periodic domain shapes and sizes. This domain‑independent formulation allows EFNOs to learn operators that generalize across different grid resolutions and domain geometries. Experiments on a heat equation and a materials‑science task demonstrate that EFNOs can successfully transfer learned mappings to unseen grid sizes and crystal structures.
arXiv:2608. 06894v1 Announce Type: new Abstract: Neural operators have become a central tool for solving partial differential equations (PDEs), with spectral operators offering efficient global mixing across spatial locations.
The paper introduces Cross-Physics Mapping (CPM), an operator-learning framework that enables deep learning to translate physical fields governed by different equations. By aligning latent representations and applying a dimensionless scaling principle, CPM maps between heterogeneous domains such as diffusion and wave fields. Experiments with seven neural operator architectures show directional asymmetry: diffusion-to-wave mapping is harder, while wave-to-diffusion mapping is more stable, with neural operators outperforming conventional convolutional baselines.
arXiv:2606. 16900v1 Announce Type: new Abstract: Physical systems often exhibit heterogeneous mechanisms, where rapidly evolving dynamics coexist with persistent structures.
arXiv:2510. 25306v3 Announce Type: replace Abstract: Partial physical knowledge--governing structures known, constitutive relations or their combinations not--pervades spatiotemporal systems.