Tag: Neural Operator

ScientificML

A high-performance PDE neural solver based on Manifold Function Encoder, featuring resolution-independent memory footprint and arbitrary PDE input support for large-scale physical simulations.

ScientificML

A benchmark dataset for PDE surrogate tasks within the ai4sci-tasks evaluation framework, containing training trajectories and evaluation splits for assessing neural operator and surrogate modeling performance.

Survey / Reading Material

A survey of data-driven and physics-informed neural operators, organizing the architecture landscape (DeepONet / FNO / GNO / PINO / Transformer-based / diffusion) along three axes: scalability, generalizability, and data sensitivity.

Tutorial / Reading Material

A practical focused review of neural operators covering DeepONet, FNO and PCANet with hands-on training strategies; benchmarked on Poisson and linear elasticity, and demonstrated as surrogates for Bayesian inversion - an engineering-ready primer.

Original Research Paper

ICML 2026 paper proposing APT, a geometry-/mesh-/physics-agnostic neural operator that fuses graph-based local feature extraction with global attention for long-range physical effects; achieves 4× saturation error reduction on 2D faulted CO2 storage vs prior SOTA, 19,873× speedup over GEOS and 6,800× over ECLIPSE.

Original Research Paper

ICLR 2026 paper proposing ATOM, a quasi-equivariant pretrained transformer neural operator that requires no explicit molecular graph and uses temporal attention for parallel decoding of multiple future states; curates TG80 (80 compounds, 2.5M fs trajectories) and demonstrates zero-shot generalization on MD17/RMD17/MD22.

Original Research Paper

Reframes Transolver's Physics-Attention as a special case of linear attention and proposes LinearNO (Linear Attention Neural Operator); achieves SOTA on six PDE benchmarks with 40.0% fewer parameters and 36.2% less compute, plus superior performance on AirfRANS and Shape-Net Car industrial datasets.

ScientificML

Proposes the Fractional Fourier Neural Operator (FrFNO) that embeds the analytic Mittag-Leffler propagator to address the computational challenge of memory-dependent time derivatives and nonlocal fractional Laplacians in fractional PDEs, enabling efficient surrogate modeling.

ScientificML

NeuIDO proposes a neural intrinsic dynamics operator that internalizes physical constraints into world models for predicting 3D object interaction trajectories, bridging the gap between physics-informed 4D generation and true world models.

CFD

Proposes p-FNM, a neural-operator framework using periodic Fourier mapping to predict unsteady pressure distributions and aeroelastic loads on turbine rotor blades, reducing high-fidelity CFD computational costs.

ScientificML

A 36M-parameter UNet-based PDE solver v2 by Los Alamos National Laboratory, designed for surrogate modeling of partial differential equations in scientific computing.

CFD/Fluid Dynamics

VIOT is a generative neural operator for incompressible density transport that predicts divergence-free velocity fields via feed-forward inference, replacing hour-scale optimization in adjoint fluid solvers and enabling rapid transport trajectory generation.

Geophysics

A continually learning neural-operator surrogate model replaces the traditional forward solver for efficient Bayesian inversion of three-dimensional time-domain airborne electromagnetic data, addressing prohibitive computational costs.

Electromagnetics

A physics-informed neural operator learns the map between function spaces in magnetohydrodynamic simulations, enabling efficient state inference for magnetic reconnection at any parameter and time step, significantly reducing computational cost at high Lundquist numbers.

Neural Operator

A neural operator model based on spherical Fourier transforms, designed for learning partial differential equations on spherical geometries.

ScientificML

Proposes the Kuramoto Neural Operator, introducing coupled oscillator dynamics into operator learning to overcome limitations of fixed-basis architectures for physical phenomena governed by local interactions.

Fourier Neural Operator / Beginner Tutorial

Systematic FNO from theory to code - for engineers and researchers wanting neural operators as PDE surrogates.

Neural Operator / Beginner Tutorial

Systematic DeepONet theory and DeepXDE implementation - for PINN developers handling multiphysics-parameter scenarios.

Framework Paper / Neural Operator

NVIDIA's PINN framework built on neural operators (FNO/DeepONet/AFNO) for end-to-end differentiable physics simulation, with multi-GPU training and deployment.

Annual Survey / Physics-Informed Learning

A systematic review of 2025-2026 progress in physics-informed ML - neural operators, diffusion for PDE solving, large benchmarks and industrial deployment.

ScientificML

Proposes a collaborative framework of AI virtual labs under a citation-based influence economy to automate neural operator architecture search and training evaluation.

CFD

Proposes an improved Fourier Neural Operator for modeling 2D Rayleigh-Bénard convection by predicting time increments, achieving a compact model (314k parameters, 7ms inference) while revealing accuracy limitations imposed by training data resolution.

Solver / Training Framework

NVIDIA's physics-ML training framework (formerly Modulus) with PINN, neural operators and physics-constrained training - commercial-friendly, industry-first choice.

CFD

Proposes a neural operator-based surrogate model for CFD-level transient thermal-hydraulic simulation of helical coil steam generators in SMRs, enabling real-time digital twin applications.

Thermal

Therm-FM adapts a pretrained PDE foundation model to steady-state and transient 3D-IC thermal simulation, reducing data-generation costs for cross-design reuse.

ScientificML

Proposes Adaptive Operator Transformation (AOT) to address structural diversity challenges in multi-PDE pre-training by adapting target solution operators rather than increasing model capacity, improving neural operator generalization across equations.

Neural Operator Library

Reference implementation library for FNO / DeepONet and other neural operators (MIT) - the de-facto standard for learning 'infinite-dimensional maps' as surrogates.

Neural Operator

A neural operator-based predictor model hosted on HuggingFace, designed for sampled measurement prediction tasks.

Foundational Paper

Presents a branch-trunk architecture realizing a deep learning version of the universal operator approximation theorem - the first systematic architecture for learning nonlinear operators and still a mainstream baseline.

Foundational Paper

Introduces neural operators with integral kernels parameterized in Fourier space, enabling resolution-invariant PDE solving - a foundational and highly cited work in physics AI.

Textbook / Systematic Course

A free online textbook from TU Munich covering physics + deep learning: differentiable physics, PINNs, neural operators and turbulence modeling, with runnable code.

PDE Foundation Model / Downstream Benchmark

ETH Zurich's PDE foundation model and downstream fine-tuning suite, using semigroup augmentation to mine abundant training pairs, covering 15 downstream PDE tasks.

ScientificML

Proposes a geometry-aware incremental neural operator to address error accumulation in long-horizon autoregressive PDE prediction, mitigating spectral inconsistency and unstable channel couplings.

Scientific Computing

NeuralOperator 2.0.0 major release introduces Codano model, improves documentation, and enhances usability for training Neural Operators in PyTorch.

Scientific Computing

A scientific computing model on HuggingFace that integrates Dynamic Mode Decomposition with Neural Operator for scientific data modeling and prediction tasks.

ScientificML

The Fractional Fourier Neural Operator (FrFNO) integrates the analytic Mittag-Leffler propagator into a Fourier-based neural operator to provide a resolution-robust surrogate for space-time fractional PDEs with memory-dependent derivatives.