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论文提出 L-SplineFNO，一种将 FNO 主干与稀疏可学习张量积 B 样条传输耦合的内存高效神经算子，用于在非结构化网格上近似 PDE 解算子，在六个三维工程基准上实现高精度并可扩展至 4600 万节点，还支持零样本超分辨率和基于 Bernstein 凸包与 Taylor 模型的严格预测界。
A University of Amsterdam paper proposes enriched holomorphic neural networks that are harmonic by construction, combining trainable singular functions derived from local geometry with boundary-only fitting to solve 2D and 3D Laplace problems. The enriched model outperforms all tested methods, with orders-of-magnitude gains where singularities are captured exactly.
该论文提出 Gen-PINNs，一种将生成对抗网络与物理信息神经网络结合的确定性残差-对抗框架，用于求解具有尖锐波前和刚性特征的偏微分方程，在 Burgers、Allen-Cahn 和 Kuramoto-Sivashinsky 方程上相较标准 PINNs 显著提升了精度和收敛性。
This paper introduces the Function-Space Transformer (FST), a framework that learns from functions over continuous domains by storing features at input-predicted anchor locations with recursive function-space refinement. FST outperforms Perceiver IO on PDEBench prediction, is competitive with Fourier Neural Operators, and beats ViT on ImageNet-1K with fewer parameters.
KernelOnet proposes an interpretable neural operator framework that explicitly incorporates kernel functions in place of trunk networks, offering data-driven, physics-informed, and hybrid kernel strategies for PDE solving with higher accuracy and fewer parameters than DeepONet.
The paper introduces the Transformer-Mamba for Flow Field (TM4FF) framework, a physics-constrained operator learning model that enhances accuracy and robustness in computational fluid dynamics simulations through innovations like Residual Wavelet Mamba and physics-informed loss.
PINNForge is an LLM-driven evolutionary framework for automating the design of Physics-Informed Neural Networks (PINNs) for solving partial differential equations (PDEs), achieving state-of-the-art performance through execution feedback.
This paper proposes using graph hypernetworks to explicitly represent relationships in PDEs for amortizing physics-informed neural networks, showing improved accuracy in solving coupled systems.
The paper proposes GeoLAMP, a geometry-aware latent autoregressive generative model for solving multiphysics partial differential equations in complex geometries, using a dual-encoder architecture and causal self-attention transformer with flow matching for stable and scalable predictions.
The paper presents the Frame Kernel Method, a novel multiscale operator learning approach for surrogate modeling of PDEs that uses kernel frame approximations and achieves higher accuracy than popular neural operators while enabling multiscale decomposition.
This paper introduces a physics-integrated operator learning framework using a feed-forward Gaussian splatting representation to directly incorporate PDE operators, reducing errors in long-horizon autoregressive predictions for spatiotemporal systems.
This paper presents AD-TLERT, a unified GPU-accelerated framework for time-lapse electrical resistivity tomography inversion based on automatic differentiation, enabling efficient and flexible hydrologic monitoring with significant speedup.
This arXiv paper introduces the Edge-Conditioned Spectral Operator (ESO), a spectral neural operator that uses local edge-wise variations to adapt global spectral mixing, improving performance on physics-sensitive PDE benchmarks.
This paper proposes FALM-PINN, an alternating Levenberg-Marquardt training framework for physics-informed neural networks that uses Fourier-enhanced features to address spectral bias and representation-coefficient coupling, achieving up to two orders of magnitude lower errors on high-frequency and nonlinear PDEs.
Introduces LLT, a transformer-based neural operator that combines linear global attention with local spatial mixing for PDE learning. It achieves competitive accuracy and faster training compared to baselines on multiple PDE problems.
AutoPDE is a code agent that explicitly represents solver strategies for partial differential equations, improving pass rate by 14.2% over baselines on the PDE Agent Bench.
Functional Attention is a novel attention mechanism that reinterprets attention as a functional correspondence between adaptive bases, replacing softmax affinities with structured linear operators inspired by geometric functional maps. The method achieves state-of-the-art performance on operator learning tasks including PDE solving and 3D segmentation while remaining resolution-invariant.
This paper investigates the generalization behavior of Fourier Neural Operators and Deep Operator Networks under distribution shifts in a variable-coefficient wave equation, revealing that FNO struggles with high-frequency inputs while DeepONet shows milder degradation.
This paper proposes a new architecture that augments Flux Neural Operators with recurrent Vision Transformers to solve conservation laws as a foundation model. It demonstrates robust generalization and long-time prediction capabilities across diverse conservative systems without explicit access to governing equations.