Papers & Surveys

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.

CFD

Proposes PITT methodology combining symbolic equation tokenization with Fourier neural operator encoder to solve nonlinear hyperbolic balance laws for relativistic Schwarzschild-Burgers fluid flows with shock waves.

ScientificML

Proposes Graph Wavelet Compressed Sensing (GWCS) for offline compression of graph signals via sparse wavelet-domain representations, reducing data preparation costs for scientific machine learning training.

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.

ScientificML

PRONE introduces a Petrov-Galerkin regression framework Ψ(X)K≈Φ(Y) that unifies DMD, SINDy, Koopman regression, and sparse regression as variants of a single construction for data-driven dynamics learning.

ScientificML

Proposes an adaptive memory gating mechanism enabling neural operators to dynamically adjust memory weights based on observation conditions, improving adaptability in solving time-dependent PDEs.

Electromagnetics

Proposes a KAN-based single-parameterized surrogate model to accelerate drift kinetic equation solving for fast neoclassical toroidal viscosity torque calculation in tokamak plasma modeling.

CFD

Proposes a geometry-aware anisotropic boundary correction method using neural operators as an efficient alternative to traditional CFD solvers for aerodynamic simulation, improving physical modeling near solid boundaries.

ScientificML

Proposes a method to enforce hard physical constraints in generative models for semiconductor manufacturing by construction, ensuring that generated masks, layouts, and process recipes strictly comply with lithography, transport, reaction, and device-physics constraints.

ScientificML

GENERIC-FNO embeds the metriplectic degeneracy structure of nonequilibrium thermodynamics into Fourier neural operators, coupling reversible energy-conserving and irreversible entropy-producing dynamics via degeneracy conditions, extending structure-preserving neural operators beyond single conservation laws.

CFD

Proposes a physics-guided hybrid architecture combining UNet and FNO, integrating multi-modal Sentinel-1/2 remote sensing with shallow water equation constraints for end-to-end flood prediction.

Thermal Management

Proposes a validation-gated multi-agent governance framework enabling thermal-hydraulic surrogate models to adapt online during operating-regime shifts, preventing condition-locking issues in offline-pretrained models.

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.

CFD/Fluid Dynamics

A Transformer-based neural operator approach for 3D wind field prediction over complex mountainous terrain, addressing bottlenecks in traditional CFD methods that require expert-intensive mesh generation and computationally expensive iterative solvers.

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.

Frontier Paper

Proposes a physics-attention mechanism that projects meshes onto learnable physical-state tokens, improving efficiency and accuracy of PDE solving on large industrial geometries.

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.