neural-operator

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.

SirenFNO leverages sinusoidal representation networks to learn full-frequency Fourier kernels, eliminating frequency truncation and achieving significant parameter reductions while improving accuracy on PDE benchmarks.

LFNO is a unified neural operator framework that integrates Laplace and Fourier transforms to decompose system dynamics into transient and steady-state components, significantly outperforming existing operators on ODE and PDE benchmarks.

This paper presents a comprehensive mathematical framework for sequential surrogate modeling of three-phase black-oil reservoir dynamics using Fourier Neural Operators (FNO) and physics-informed variants (PINO), applied to the Norne benchmark reservoir. Theoretical contributions include functional-analytic formulation, covariate shift analysis, physics-constrained spectral stability, and truncated backpropagation gradient analysis.

Introduces NEO, a neural framework that predicts low-frequency Laplace-Beltrami eigenspace from point clouds, achieving near-linear scaling and strong zero-shot generalization using a mass-aware neural operator and Rayleigh-Ritz refinement.

This paper introduces the Iterative Refinement Neural Operator (IRNO), which augments pretrained neural operators with a learned refinement module applied via fixed-point iteration to mitigate spectral bias. IRNO progressively corrects high-frequency errors, achieving up to 56% improvement on turbulent flow and showing stable extrapolation beyond the trained iteration count.

Introduces UFO, a cross-domain neural operator framework that adaptively learns operators across different representational domains, enabling discretization-decoupled predictions robust to distribution shifts.

This paper proposes a topology-preserving neural operator learning method using Hodge decomposition to separate topological and geometric components, improving accuracy and efficiency on geometric meshes.