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Tag: riemannian

  • Riemannian Stochastic Interpolants for Amorphous Particle Systems

    Riemannian Stochastic Interpolants for Amorphous Particle Systems arXiv:2512.16607v1 Announce Type: new Abstract: Modern generative models hold great promise for accelerating diverse tasks involving the simulation of physical systems, but they must be adapted to the specific constraints of each domain. Significant progress has been made for biomolecules and crystalline materials. Here, we address amorphous materials…

  • Riemannian Principal Component Analysis

    Riemannian Principal Component Analysis arXiv:2506.00226v1 Announce Type: new Abstract: This paper proposes an innovative extension of Principal Component Analysis (PCA) that transcends the traditional assumption of data lying in Euclidean space, enabling its application to data on Riemannian manifolds. The primary challenge addressed is the lack of vector space operations on such manifolds. Fletcher et…

  • Riemannian Proximal Sampler for High-accuracy Sampling on Manifolds

    Riemannian Proximal Sampler for High-accuracy Sampling on Manifolds arXiv:2502.07265v1 Announce Type: new Abstract: We introduce the Riemannian Proximal Sampler, a method for sampling from densities defined on Riemannian manifolds. The performance of this sampler critically depends on two key oracles: the Manifold Brownian Increments (MBI) oracle and the Riemannian Heat-kernel (RHK) oracle. We establish high-accuracy…