Related papers: NOFE - Neural Operator Function Embedding
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…
The direct computation of the third-order normal form for a geometrically nonlinear structure discretised with the finite element (FE) method, is detailed. The procedure allows to define a nonlinear mapping in order to derive accurate…
The classical development of neural networks has been primarily for mappings between a finite-dimensional Euclidean space and a set of classes, or between two finite-dimensional Euclidean spaces. The purpose of this work is to generalize…
Deep neural networks have emerged as powerful tools for learning operators defined over infinite-dimensional function spaces. However, existing theories frequently encounter difficulties related to dimensionality and limited…
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…
Existing neural operator architectures face challenges when solving multiphysics problems with coupled partial differential equations (PDEs) due to complex geometries, interactions between physical variables, and the limited amounts of…
The capacity to achieve out-of-distribution (OOD) generalization is a hallmark of human intelligence and yet remains out of reach for machines. This remarkable capability has been attributed to our abilities to make conceptual abstraction…
Time integration of stiff systems is a primary source of computational cost in combustion, hypersonics, and other reactive transport systems. This stiffness can introduce time scales significantly smaller than those associated with other…
Registration of point clouds related by rigid transformations is one of the fundamental problems in computer vision. However, a solution to the practical scenario of aligning sparsely and differently sampled observations in the presence of…
Solving partial differential equations (PDEs) on shapes underpins many shape analysis and engineering tasks; yet, prevailing PDE solvers operate on polygonal/triangle meshes while modern 3D assets increasingly live as neural…
We introduce a new multi-dimensional nonlinear embedding -- Piecewise Flat Embedding (PFE) -- for image segmentation. Based on the theory of sparse signal recovery, piecewise flat embedding with diverse channels attempts to recover a…
Neural ordinary differential equations (neural ODEs) have emerged as a novel network architecture that bridges dynamical systems and deep learning. However, the gradient obtained with the continuous adjoint method in the vanilla neural ODE…
Edge AI applications increasingly require ultra-low-power, low-latency inference. Neuromorphic computing based on event-driven spiking neural networks (SNNs) offers an attractive path, but practical deployment on resource-constrained…
Embedding is a useful technique to project a high-dimensional feature into a low-dimensional space, and it has many successful applications including link prediction, node classification and natural language processing. Current approaches…
Accurate null depth retrieval is critical in nulling interferometry. However, achieving accurate null depth calibration is challenging due to various noise sources, instrumental imperfections, and the complexity of real observational…
Graphs are ubiquitous due to their flexibility in representing social and technological systems as networks of interacting elements. Graph representation learning methods, such as node embeddings, are powerful approaches to map nodes into a…
Inverse problems for stiff parabolic partial differential equations (PDEs), such as the inverse heat conduction problem (IHCP), are severely ill-posed: the forward map rapidly damps high-frequency interior structure before it reaches the…
Real-world data usually have high dimensionality and it is important to mitigate the curse of dimensionality. High-dimensional data are usually in a coherent structure and make the data in relatively small true degrees of freedom. There are…
Solving parametric Partial Differential Equations (PDEs) for a broad range of parameters is a critical challenge in scientific computing. To this end, neural operators, which \textcolor{black}{predicts the PDE solution with variable PDE…
Network embedding aims to find a way to encode network by learning an embedding vector for each node in the network. The network often has property information which is highly informative with respect to the node's position and role in the…