The paper introduces DANO, a domain‑decomposition attention neural operator that learns configuration‑dependent nonlocal interactions in heterogeneous systems governed by linear field equations using only field data. It demonstrates full‑field predictions for large‑scale optical metasurfaces, including transfer across domain sizes and inverse design, while validating the learned interactions through physics‑based interrogation. The work positions DANO as an AI‑for‑Science tool for discovering interactions and enabling scalable, customizable design of nonlocal multiscale systems such as virtual‑reality optics.
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:2603. 04430v2 Announce Type: replace Abstract: We introduce Flowers, a neural architecture for learning PDE solution operators built entirely from multihead warps.
arXiv:2510. 25306v3 Announce Type: replace Abstract: Partial physical knowledge--governing structures known, constitutive relations or their combinations not--pervades spatiotemporal systems.
The paper presents a data‑efficient pre‑training framework for neural surrogate models solving PDEs on unstructured 3D geometries. It introduces a geometry‑driven strategy for steady‑state problems that uses intrinsic shape descriptors, and a physics‑driven approach for transient problems that generates synthetic PDE data online. Experiments show faster convergence, higher data efficiency, and improved accuracy during fine‑tuning, especially in low‑data settings.
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:2609.07814v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) struggle on PDEs whose governing physics varies across the domain. We trace this to a structural property of s...
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: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...
arXiv:2606. 07712v1 Announce Type: cross Abstract: Progress in AI-driven crystal materials science has so far been carried by narrow architectures purpose-built for individual tasks -- graph neural networks for property prediction, diffusion and flow-matching models for crystal generation -- each excelling within its niche yet unable to act as a shared backbone across the full spectrum of materials problems.
arXiv:2606. 16900v1 Announce Type: new Abstract: Physical systems often exhibit heterogeneous mechanisms, where rapidly evolving dynamics coexist with persistent 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 SPARC, a reinforcement learning framework that generates crystalline materials while respecting symmetry constraints essential for meaningful physical properties. SPARC is applied to two tasks: optimizing uniaxial dielectric anisotropy, which requires specific crystal classes, and maximizing spectroscopic limited maximum efficiency, a scalar objective that lets the algorithm discover suitable crystallographic motifs. The results demonstrate that symmetry is a foundational requirement for producing robust, realizable functional materials.