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A novel AI model using a Fourier neural operator variant enables density functional theory to scale nearly linearly with system size, allowing efficient simulations of large quantum systems like a magnesium dislocation with 80k electrons on a single GPU.
The article highlights LLMs' lack of innate physical world understanding and introduces a Fourier Neural Operator-based framework that accelerates quantum dynamics prediction by 10^7 times, enabling efficient inverse design of quantum control protocols with improved success rates.
This paper introduces feature interaction modules based on factorization machines into physics-informed neural networks and neural operators (FM-PINN, FM-Operator, FM-DeepONet) to better capture spatio-temporal variable couplings for solving parameterized PDEs, showing accuracy gains particularly on shock-dominated equations.
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 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.
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.
Proposes the first application of split conformal prediction to neural operator-based physics simulation, providing distribution-free prediction intervals with finite-sample coverage guarantees and adaptive-width intervals using MC Dropout uncertainty.
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.
Fourier neural operators (FNOs) achieve extrapolation success in modeling periodically driven quantum systems, capturing temporal correlations in frequency space for physically faithful dynamics beyond training data.
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.