相关论文: SpectraKAN: Conditioning Spectral Operators

In this paper, we present a spectral optimal control framework for Fokker-Planck equations based on the standard ground state transformation that maps the Fokker-Planck operator to a Schrodinger operator. Our primary objective is to…

Neural operators can learn nonlinear mappings between function spaces and offer a new simulation paradigm for real-time prediction of complex dynamics for realistic diverse applications as well as for system identification in science and…

In this work we propose a unified Fourier Spectral Transformer network that integrates the strengths of classical spectral methods and attention based neural architectures. By transforming the original PDEs into spectral ordinary…

Neural operators, which aim to approximate mappings between infinite-dimensional function spaces, have been widely applied in the simulation and prediction of physical systems. However, the limited representational capacity of network…

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…

Boundary conditions (BCs) are important groups of physics-enforced constraints that are necessary for solutions of Partial Differential Equations (PDEs) to satisfy at specific spatial locations. These constraints carry important physical…

Neural Operators that directly learn mappings between function spaces, such as Deep Operator Networks (DONs) and Fourier Neural Operators (FNOs), have received considerable attention. Despite the universal approximation guarantees for DONs…

Physics-informed neural operators have emerged as a powerful paradigm for solving parametric partial differential equations (PDEs), particularly in the aerospace field, enabling the learning of solution operators that generalize across…

Accurately modeling and forecasting complex systems governed by partial differential equations (PDEs) is crucial in various scientific and engineering domains. However, traditional numerical methods struggle in real-world scenarios due to…

In this paper, we propose a way to solve partial differential equations (PDEs) by combining machine learning techniques and the finite element method called Phi-FEM. For that, we use the Fourier Neural Operator (FNO), a learning mapping…

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…

Spiking Neural Networks (SNNs) draw inspiration from biological neurons to enable brain-like computation, demonstrating effectiveness in processing temporal information with energy efficiency and biological realism. Most existing SNNs are…

Operator learning has emerged as a promising paradigm for developing efficient surrogate models to solve partial differential equations (PDEs). However, existing approaches often overlook the domain knowledge inherent in the underlying PDEs…

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…

Rapidly developing machine learning methods has stimulated research interest in computationally reconstructing differential equations (DEs) from observational data which may provide additional insight into underlying causative mechanisms.…

Operator eigenvalue problems play a critical role in various scientific fields and engineering applications, yet numerical methods are hindered by the curse of dimensionality. Recent deep learning methods provide an efficient approach to…

In real-world applications with large state and action spaces, reinforcement learning (RL) typically employs function approximations to represent core components like the policies, value functions, and dynamics models. Although powerful…

Solving analytically intractable partial differential equations (PDEs) that involve at least one variable defined on an unbounded domain arises in numerous physical applications. Accurately solving unbounded domain PDEs requires efficient…

Untrained neural networks (UNNs) offer high-fidelity electromagnetic inverse scattering reconstruction but are computationally limited by high-dimensional spatial-domain optimization. We propose a Real-Time Physics-Driven Fourier-Spectral…

Neural operators have emerged as an efficient paradigm for solving PDEs, overcoming the limitations of traditional numerical methods and significantly improving computational efficiency. However, due to the diversity and complexity of PDE…