Related papers: Enhancing Solutions for Complex PDEs: Introducing …

Solving partial differential equations is difficult. Recently proposed neural resolution-invariant models, despite their effectiveness and efficiency, usually require equispaced spatial points of data. However, sampling in spatial domain is…

This paper introduces a data-driven operator learning method for multiscale partial differential equations, with a particular emphasis on preserving high-frequency information. Drawing inspiration from the representation of multiscale…

Predicting the microstructural and morphological evolution of materials through phase-field modelling is computationally intensive, particularly for high-throughput parametric studies. While neural operators such as the Fourier neural…

We introduce the Laplace neural operator (LNO), which leverages the Laplace transform to decompose the input space. Unlike the Fourier Neural Operator (FNO), LNO can handle non-periodic signals, account for transient responses, and exhibit…

Attention mechanisms have emerged as transformative tools in core AI domains such as natural language processing and computer vision. Yet, their largely untapped potential for modeling intricate physical systems presents a compelling…

Neural operators have emerged as promising frameworks for learning mappings governed by partial differential equations (PDEs), serving as data-driven alternatives to traditional numerical methods. While methods such as the Fourier neural…

Solving cell problems in homogenization is hard, and available deep-learning frameworks fail to match the speed and generality of traditional computational frameworks. More to the point, it is generally unclear what to expect of…

We introduce DiffFNO, a novel diffusion framework for arbitrary-scale super-resolution strengthened by a Weighted Fourier Neural Operator (WFNO). Mode Rebalancing in WFNO effectively captures critical frequency components, significantly…

Eigenvalue problems for elliptic operators play an important role in science and engineering applications, where efficient and accurate numerical computation is essential. In this work, we propose a novel operator inference approach for…

Spectral methods are an important part of scientific computing's arsenal for solving partial differential equations (PDEs). However, their applicability and effectiveness depend crucially on the choice of basis functions used to expand the…

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…

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…

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…

This paper proposes a physics-informed neural operator (PINO) framework for solving inverse scattering problems, enabling rapid and accurate reconstructions under diverse measurement conditions. In the proposed approach, the dielectric…

Neural operator models for solving partial differential equations (PDEs) often rely on global mixing mechanisms-such as spectral convolutions or attention-which tend to oversmooth sharp local dynamics and introduce high computational cost.…

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…

Neural operators offer powerful approaches for solving parametric partial differential equations, but extending them to spherical domains remains challenging due to the need to preserve intrinsic geometry while avoiding distortions that…

We consider solving complex spatiotemporal dynamical systems governed by partial differential equations (PDEs) using frequency domain-based discrete learning approaches, such as Fourier neural operators. Despite their widespread use for…

Neural networks have emerged as promising tools for solving partial differential equations (PDEs), particularly through the application of neural operators. Training neural operators typically requires a large amount of training data to…

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…