neural-operator

A single-authored arXiv paper proposes a data-free physics-informed neural operator for level-set interface advection, trained only on transport residuals and a geometric constraint without any reference solutions, outperforming supervised baselines in area conservation while quantifying the accuracy cost of refusing labels.

GeoWind2Plan 是一个面向城市低空无人机的几何-风场-规划框架，利用局部几何条件神经算子在约 3 秒内预测任务相关的 3D 城市风场（CFD 需约 8 小时），并据此优化能量高效的 3D 路径与速度剖面，相比无风感知规划可减少 4.5%–12.7% 的能耗。

This paper introduces Helix-FNO, a teacher-student architecture that couples a high-fidelity mechanistic model with a Fourier neural operator to learn solution operators for fast surrogate simulation in process engineering, enabling millisecond inference times.

This paper proposes a panoramic aerodynamic performance prediction framework for turbomachinery using a transformer-enhanced neural operator (TNO), which first predicts basic physical quantities like temperature and pressure before estimating key performance parameters, significantly reducing computational cost while maintaining accuracy.

The paper presents VIOT, a variational incompressible optimal transport operator that uses a Fourier Neural Operator to predict divergence-free velocity fields for efficient incompressible density transport, achieving orders of magnitude speedup over traditional optimization methods.

Introduces VATO, a vortex-force-aware transformer operator that improves predictions of unsteady separated aerodynamic flows by reducing errors in velocity, pressure, and vorticity through force-aware neural operator learning.

This paper presents a method to rank neural operator models during deployment using shared physics responses, achieving high accuracy without ground-truth reference solutions for scientific computing applications.

PIKFNO is a new interpretable neural operator framework that integrates physics-informed kernel functions from governing equations to enhance predictive accuracy and interpretability with limited training data.

This paper proposes the Transferable Latent Operator (TLO) for fluid dynamics, enabling zero-shot generalization from Eulerian field prediction to Lagrangian particle rollout without Lagrangian supervision.

Presents GeoIncNO, a geometry-aware incremental neural operator that improves long-horizon PDE prediction via residual latent increments and mean-fluctuation decoupled reconstruction, achieving better stability and spectral fidelity on 1D/2D/3D benchmarks.

This preprint proposes PI-HNO, a physics-informed hybrid neural operator for transient magnetization prediction in power magnetics, achieving low B-H energy consistency errors with only 4,777 trainable parameters per material model.

HypNO introduces a graph-based neural operator that uses physics-informed message passing on a space-time finite-volume cell graph to solve scalar hyperbolic conservation laws, accurately capturing shocks and discontinuities. The method is benchmarked on LWR and ARZ traffic-flow models.

Introduces DiffARFNO, a two-stage framework combining autoregressive Fourier-MIONet with a conditional DDIM corrector for long-horizon droplet evolution prediction in inkjet printing, achieving state-of-the-art performance on ANSYS Fluent datasets.

This paper presents an agentic AI scientific community of virtual labs that autonomously discover neural operator architectures for PDE problems. Using LLM planners, numerical workers, and reviewers under a citation-based economy, the system produces high-accuracy hybrid architectures, with results suggesting no universal winner among operator families.

PGD-NO is a neural operator that precomputes geometry decomposition to achieve linear memory scalability, enabling high-fidelity physics simulations on meshes exceeding 10 million nodes and overcoming the single-node memory bottleneck.

Proposes a hybrid least squares/gradient descent method for MIONets to accelerate training by using alternating least squares for the last layer parameters of multiple branch networks, leveraging Kronecker and Khatri-Rao products.

This paper introduces LiNO, a neural operator that uses a lifting-based multiresolution decomposition to learn solution operators for PDEs. It demonstrates strong performance on benchmarks including Darcy flow, Poisson equation, and Navier-Stokes, capturing both global dynamics and fine-scale structure.

This paper presents a geometry-conditioned Fourier Neural Operator (FNO) to learn the solution operator for the cubic nonlinear Schrödinger equation on periodic domains with varying aspect ratios. Numerical experiments show the model captures distinct Sobolev norm behaviors on rational and irrational tori, demonstrating geometry-aware neural operators for dispersive PDEs.

Introduces the ICML 2026 paper Functional Attention, which treats functions as first-class citizens and replaces softmax point-to-point similarity with structured linear operators. It addresses issues of discretization, resolution sensitivity, and high computational complexity in traditional Transformers when handling continuous functions. Achieves or surpasses SOTA in tasks like PDE solving and 3D segmentation, and exhibits strong OOD generalization.

This paper provides approximation and generalization error estimates for multi-input neural operators measured in Sobolev norms, analyzing how multiple input functions with different domains and regularities affect error bounds, applicable to PDE and scientific computing problems.