Related papers: Learning S-Matrix Phases with Neural Operators

Deep learning-based surrogate models have been widely applied in geological carbon storage (GCS) problems to accelerate the prediction of reservoir pressure and CO2 plume migration. Large amounts of data from physics-based numerical…

Interfacial dynamics underlie a wide range of phenomena, including phase transitions, microstructure coarsening, pattern formation, and thin-film growth, and are typically described by stiff, time-dependent nonlinear partial differential…

Magnetohydrodynamics (MHD) plays a pivotal role in describing the dynamics of plasma and conductive fluids, essential for understanding phenomena such as the structure and evolution of stars and galaxies, and in nuclear fusion for plasma…

Fourier neural operators (FNOs) are invariant with respect to the size of input images, and thus images with any size can be fed into FNO-based frameworks without any modification of network architectures, in contrast to traditional…

Self-training techniques have shown remarkable value across many deep learning models and tasks. However, such techniques remain largely unexplored when considered in the context of learning fast solvers for systems of partial differential…

Physics-Informed Neural Operators provide efficient, high-fidelity simulations for systems governed by partial differential equations (PDEs). However, most existing studies focus only on multi-scale, multi-physics systems within a single…

By learning the mappings between infinite function spaces using carefully designed neural networks, the operator learning methodology has exhibited significantly more efficiency than traditional methods in solving complex problems such as…

Recent advances in the theory of Neural Operators (NOs) have enabled fast and accurate computation of the solutions to complex systems described by partial differential equations (PDEs). Despite their great success, current NO-based…

Predicting plasma evolution within a Tokamak is crucial to building a sustainable fusion reactor. Whether in the simulation space or within the experimental domain, the capability to forecast the spatio-temporal evolution of plasma field…

Neural operators have shown great potential in solving a family of Partial Differential Equations (PDEs) by modeling the mappings between input and output functions. Fourier Neural Operator (FNO) implements global convolutions via…

We combine fast amplitude surrogates with neural importance sampling to accelerate NLO calculations. For virtual corrections, a learned ratio to the Born matrix element with calibrated uncertainties guarantees reliable precision across…

The physics-informed neural operator (PINO) is a machine learning paradigm that has demonstrated promising results for learning solutions to partial differential equations (PDEs). It leverages the Fourier Neural Operator to learn solution…

While Fourier-based neural operators are best suited to learning mappings between functions on periodic domains, several works have introduced techniques for incorporating non trivial boundary conditions. However, all previously introduced…

We propose the Inverse Neural Operator (INO), a two-stage framework for recovering hidden ODE parameters from sparse, partial observations. In Stage 1, a Conditional Fourier Neural Operator (C-FNO) with cross-attention learns a…

This paper presents a method for modeling transient fluid flow in subsurface reservoir systems based on the developed neural operator architecture (TFNO-opt). Reservoir systems are complex dynamic objects with distributed parameters…

The Fourier neural operator (FNO) framework is applied to the large eddy simulation (LES) of three-dimensional compressible Rayleigh-Taylor (RT) turbulence with miscible fluids at Atwood number $A_t=0.5$, stratification parameter $Sr=1.0$,…

Neural operators have emerged as a powerful, discretization-invariant framework for solving partial differential equations (PDEs). Although established approaches like the Deep Operator Network (DeepONet) have successfully achieved…

Neural operator learning directly constructs the mapping relationship from the equation parameter space to the solution space, enabling efficient direct inference in practical applications without the need for repeated solution of partial…

This short note proposes a model-driven conditional Fourier neural operator (MD-CFNO) for synthetic turbulence generation. Spectrum-consistent synthetic turbulence is essential for inflow boundary construction in computational fluid…

In this work, we introduce a new class of neural network operators designed to handle problems where memory effects and randomness play a central role. In this work, we introduce a new class of neural network operators designed to handle…