相关论文: Wiener Chaos Expansion based Neural Operator for S…
In this paper, we develop a new general approach to the existence and uniqueness theory of infinite dimensional stochastic equations of the form dX+A(t)Xdt = XdW in (0;T)xH, where A(t) is a nonlinear monotone and demicontinuous operator…
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…
Accurate modeling of spatiotemporal dynamics is crucial to understanding complex phenomena across science and engineering. However, this task faces a fundamental challenge when the governing equations are unknown and observational data are…
This work introduces the Wavelet-Laplace Neural Operator (WLNO), a novel neural operator that fuses Haar wavelet multi-scale spatial decomposition with the Laplace-domain pole-residue formulation of the Laplace Neural Operator (LNO). While…
Polynomial chaos expansion (PCE) is a classical and widely used surrogate modeling technique in physical simulation and uncertainty quantification. By taking a linear combination of a set of basis polynomials - orthonormal with respect to…
We study the dependence of mild solutions to linear stochastic evolution equations on Hilbert space driven by Wiener noise, with drift having linear part of the type $A+\varepsilon G$, on the parameter $\varepsilon$. In particular, we study…
Neural operators have been explored as surrogate models for simulating physical systems to overcome the limitations of traditional partial differential equation (PDE) solvers. However, most existing operator learning methods assume that the…
This article investigates the propagation of chaos property for weakly interacting mild solutions to semilinear stochastic partial differential equations whose coefficients might not satisfy Lipschitz conditions. Furthermore, we derive…
Machine learning has witnessed substantial growth, leading to the development of advanced artificial intelligence models crafted to address a wide range of real-world challenges spanning various domains, such as computer vision, natural…
Fractional Differential Equations (FDEs) are essential tools for modelling complex systems in science and engineering. They extend the traditional concepts of differentiation and integration to non-integer orders, enabling a more precise…
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…
Frequency response functions (FRFs) are important for assessing the behavior of stochastic linear dynamic systems. For large systems, their evaluations are time-consuming even for a single simulation. In such cases, uncertainty…
A non-intrusive reduced order model based on convolutional autoencoders (NIROM-CAEs) is proposed as a data-driven tool to build an efficient nonlinear reduced-order model for stochastic spatio-temporal large-scale physical problems. The…
The precise simulation of turbulent flows is of immense importance in a variety of scientific and engineering fields, including climate science, freshwater science, and the development of energy-efficient manufacturing processes. Within the…
The spin-diode effect is studied both experimentally and with our original semi-analytical method. The latter is based on an improved version of the Thiele equation approach (TEA) that we combine to micromagnetic simulation data to…
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…
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…
Partial differential equations (PDEs) underpin the modeling of many natural and engineered systems. It can be convenient to express such models as neural PDEs rather than using traditional numerical PDE solvers by replacing part or all of…
Recent advances in machine learning (ML) have opened new possibilities for solving partial differential equations (PDEs), yet robust performance in challenging regimes remains limited. In particular, singularly perturbed differential…
This study presents a novel unsupervised convolutional Neural Network (NN) architecture with nonlocal interactions for solving Partial Differential Equations (PDEs). The nonlocal Peridynamic Differential Operator (PDDO) is employed as a…