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One predominant challenge in additive manufacturing (AM) is to achieve specific material properties by manipulating manufacturing process parameters during the runtime. Such manipulation tends to increase the computational load imposed on…

Radiative heat transfer is a fundamental process in high energy density physics and inertial fusion. Accurately predicting the behavior of Marshak waves across a wide range of material properties and drive conditions is crucial for design…

Efficient and accurate time-domain simulation of electromagnetic fields in complex photonic devices is critical for designing broadband and ultrafast optical components, yet it is often limited by the high computational cost of conventional…

Data assimilation (DA) is crucial for enhancing solutions to partial differential equations (PDEs), such as those in numerical weather prediction, by optimizing initial conditions using observational data. Variational DA methods are widely…

Fourier Neural Operators (FNOs) have emerged as leading surrogates for solver operators for various functional problems, yet their stability, generalization and frequency behavior lack a principled explanation. We present a systematic…

Due to the strongly nonlinear behavior of ferromagnetic yokes, the numerical analysis of fast-ramping magnets is highly cumbersome and, therefore, in practice overly simplified by means of anhysteretic material descriptions and a posteriori…

Data driven materials discovery and optimization requires databases that are error free and experimentally verified. Performing material measurements are time-consuming and often restricted by the fact that material sample preparations are…

Fourier neural operators (FNOs) are a recently introduced neural network architecture for learning solution operators of partial differential equations (PDEs), which have been shown to perform significantly better than comparable deep…

Deep learning surrogate models have shown promise in solving partial differential equations (PDEs). Among them, the Fourier neural operator (FNO) achieves good accuracy, and is significantly faster compared to numerical solvers, on a…

Fourier neural operators (FNOs) can learn highly nonlinear mappings between function spaces, and have recently become a popular tool for learning responses of complex physical systems. However, to achieve good accuracy and efficiency, FNOs…

Operator learning is a variant of machine learning that is designed to approximate maps between function spaces from data. The Fourier Neural Operator (FNO) is one of the main model architectures used for operator learning. The FNO combines…

Background: Traumatic brain injury modeling requires integrating volumetric neuroimaging, demographic parameters, and acquisition metadata. Finite element solvers are too computationally expensive for clinical settings. Neural operators…

Time-periodic quantum systems exhibit a rich variety of far-from-equilibrium phenomena and serve as ideal platforms for quantum engineering and control. However, simulating their dynamics with conventional numerical methods remains…

We apply Fourier neural operators (FNOs), a state-of-the-art operator learning technique, to forecast the temporal evolution of experimentally measured velocity fields. FNOs are a recently developed machine learning method capable of…

Fourier Neural Operators (FNO) have emerged as promising solutions for efficiently solving partial differential equations (PDEs) by learning infinite-dimensional function mappings through frequency domain transformations. However, the…

The recent development of Neural Operator (NeurOp) learning for solutions to the elastic wave equation shows promising results and provides the basis for fast large-scale simulations for different seismological applications. In this paper,…

Fourier Neural Operators (FNOs) have demonstrated exceptional accuracy in mapping functional spaces by leveraging Fourier transforms to establish a connection with underlying physical principles. However, their opaque inner workings often…

This paper explores Neural Operators to predict turbulent flows, focusing on the Fourier Neural Operator (FNO) model. It aims to develop reduced-order/surrogate models for turbulent flow simulations using Machine Learning. Different model…

Partial differential equations (PDEs) govern a wide variety of dynamical processes in science and engineering, yet obtaining their numerical solutions often requires high-resolution discretizations and repeated evaluations of complex…

Magneto-static finite element (FE) simulations make numerical optimization of electrical machines very time-consuming and computationally intensive during the design stage. In this paper, we present the application of a hybrid data-and…