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Learning solution operators of partial differential equations (PDEs) from data has emerged as a promising route to fast surrogate models in multi-query scientific workflows. However, for geometric PDEs whose inputs and outputs transform…

Many classical Computer Vision problems, such as essential matrix computation and pose estimation from 3D to 2D correspondences, can be tackled by solving a linear least-square problem, which can be done by finding the eigenvector…

Eigenvalue problems are fundamental to mathematics and science. We present a simple algorithm for determining eigenvalues and eigenfunctions of the Laplace--Beltrami operator on rather general curved surfaces. Our algorithm, which is based…

We propose a method for 3D shape reconstruction from unoriented point clouds. Our method consists of a novel SE(3)-equivariant coordinate-based network (TF-ONet), that parametrizes the occupancy field of the shape and respects the inherent…

Neural operators have emerged as fast surrogate solvers for parametric partial differential equations (PDEs). However, purely data-driven models often require extensive training data and can generalize poorly, especially in small-data…

Neural operators generalize neural networks to learn mappings between function spaces from data. They are commonly used to learn solution operators of parametric partial differential equations (PDEs) or propagators of time-dependent PDEs.…

Bootstrapping has been a primary tool for ensemble and uncertainty quantification in machine learning and statistics. However, due to its nature of multiple training and resampling, bootstrapping deep neural networks is computationally…

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…

Eigenoptions (EOs) have been recently introduced as a promising idea for generating a diverse set of options through the graph Laplacian, having been shown to allow efficient exploration. Despite its initial promising results, a couple of…

Detecting out-of-distribution (OOD) data is a critical challenge in machine learning due to model overconfidence, often without awareness of their epistemological limits. We hypothesize that ``neural collapse'', a phenomenon affecting…

Currently, prominent Transformer architectures applied on graphs and meshes for shape analysis tasks employ traditional attention layers that heavily utilize spectral features requiring costly eigenvalue decomposition-based methods. To…

AI for science (AI4Science) models often suffer from discretization: learned representations remain tied to the training grid, limiting transfer across resolutions, solvers and applications. We introduce Neural Proper Orthogonal…

Neural Operators (NOs) are a leading method for surrogate modeling of partial differential equations. Unlike traditional neural networks, which approximate individual functions, NOs learn the mappings between function spaces. While NOs have…

Implicit neural networks have been successfully used for surface reconstruction from point clouds. However, many of them face scalability issues as they encode the isosurface function of a whole object or scene into a single latent vector.…

Recently, learning multi-view neural surface reconstruction with the supervision of point clouds or depth maps has been a promising way. However, due to the underutilization of prior information, current methods still struggle with the…

The Laplace-Beltrami operator (LBO) emerges from studying manifolds equipped with a Riemannian metric. It is often called the Swiss army knife of geometry processing as it allows to capture intrinsic shape information and gives rise to heat…

By learning the mappings between infinite function spaces using carefully designed neural networks, the operator learning methodology has exhibited significantly more efficiency than traditional methods in solving complex problems such as…

Neural operators learn mappings from function-dependent inputs to solutions, providing an effective framework for solving partial differential equations (PDEs). For time-dependent PDEs, existing methods typically perform long-horizon…

Neural operators generalize classical neural networks to maps between infinite-dimensional spaces, e.g., function spaces. Prior works on neural operators proposed a series of novel methods to learn such maps and demonstrated unprecedented…

Neural operators (NOs) provide a new paradigm for efficiently solving partial differential equations (PDEs), but their training depends on costly high-fidelity data from numerical solvers, limiting applications in complex systems. We…