Related papers: Fourier Neural Operator Surrogate Model to Predict…

We present approximation theories and efficient training methods for derivative-informed Fourier neural operators (DIFNOs) with applications to PDE-constrained optimization. A DIFNO is an FNO trained by minimizing its prediction error…

The accurate and fast prediction of long-term dynamics of turbulence presents a significant challenge for both traditional numerical simulations and machine learning methods. In recent years, the emergence of neural operators has provided a…

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…

Numerical simulations of seismic wave propagation are crucial for investigating velocity structures and improving seismic hazard assessment. However, standard methods such as finite difference or finite element are computationally…

Flexible intelligent metasurfaces (FIMs) offer a new solution for wireless communications by introducing morphological degrees of freedom, dynamically morphing their three-dimensional shape to ensure multipath signals interfere…

Thermal management in 3D ICs is increasingly challenging due to higher power densities. Traditional PDE-solving-based methods, while accurate, are too slow for iterative design. Machine learning approaches like FNO provide faster…

Seismic events, among many other natural hazards, reduce due functionality and exacerbate vulnerability of in-service buildings. Accurate modeling and prediction of building's response subjected to earthquakes makes possible to evaluate…

The development of machine learning techniques enables us to construct surrogate models from data of direct numerical simulations, which has important implications for modeling complex physical systems. In this paper, based on the output…

Seismic wave forward and inverse modeling are fundamental tools for subsurface imaging and geological hazard assessment. Conventional grid-based numerical methods, such as finite-difference and finite-element approaches, often require dense…

Neural ordinary differential equations (NODEs), one of the most influential works of the differential equation-based deep learning, are to continuously generalize residual networks and opened a new field. They are currently utilized for…

We use physics-informed neural networks for solving the shallow-water equations for tsunami modeling. Physics-informed neural networks are an optimization based approach for solving differential equations that is completely meshless. This…

Objective: Real-time adaptive proton range verification systems based on produced neutrons require accurate information on their non-isotropic momentum distributions within short times, for which Monte Carlo (MC) methods are too…

Machine Learning surrogates for Computational Fluid Dynamics (CFD), particularly Graph Neural Networks (GNNs) and Transformers, have become a new important approach for accelerating physics simulations. However, we identify a critical…

Accurately forecasting the long-term evolution of turbulence represents a grand challenge in scientific computing and is crucial for applications ranging from climate modeling to aerospace engineering. Existing deep learning methods,…

Neural operators have shown great potential in surrogate modeling. However, training a well-performing neural operator typically requires a substantial amount of data, which can pose a major challenge in complex applications. In such…

Data-driven prediction of fluid flow and temperature distribution in marine and aerospace engineering has received extensive research and demonstrated its potential in real-time prediction recently. However, usually large amounts of…

In computational physics, a longstanding challenge lies in finding numerical solutions to partial differential equations (PDEs). Recently, research attention has increasingly focused on Neural Operator methods, which are notable for their…

We introduce the Fourier Learning Machine (FLM), a neural network (NN) architecture designed to represent a multidimensional nonharmonic Fourier series. The FLM uses a simple feedforward structure with cosine activation functions to learn…

Generative models in function spaces, situated at the intersection of generative modeling and operator learning, are attracting increasing attention due to their immense potential in diverse scientific and engineering applications. While…

This focused review explores a range of neural operator architectures for approximating solutions to parametric partial differential equations (PDEs), emphasizing high-level concepts and practical implementation strategies. The study covers…