Related papers: Rapid forward of gravity and tensor gravity data
A method of fast linear transform algorithm synthesis for an arbitrary tensor, matrix, or vector is proposed. The method is based on factorization of a tensor and using the factors for building computational structures performing fast…
Gravity inversion allows us to constrain the interior mass distribution of a planetary body using the observed shape, rotation, and gravity. Traditionally, techniques developed for gravity inversion can be divided into Monte Carlo methods,…
Sequence modeling has important applications in natural language processing and computer vision. Recently, the transformer-based models have shown strong performance on various sequence modeling tasks, which rely on attention to capture…
Fast Fourier transform (FFT) based methods have turned out to be an effective computational approach for numerical homogenisation. In particular, Fourier-Galerkin methods are computational methods for partial differential equations that are…
Machine Learning surrogates for Computational Fluid Dynamics (CFD), particularly Graph Neural Networks (GNNs) and Transformers, have become a new important approach for accelerating physics simulations. However, we identify a critical…
A fast algorithm for solving the under-determined 3-D linear gravity inverse problem based on the randomized singular value decomposition (RSVD) is developed. The algorithm combines an iteratively reweighted approach for $L_1$-norm…
In calculating integral or discrete transforms, use has been made of fast algorithms for multiplying vectors by matrices whose elements are specified as values of special (Chebyshev, Legendre, Laguerre, etc.) functions. The currently…
We introduce and demonstrate the power of a method to speed up current iterative techniques for N-body modified gravity simulations. Our method is based on the observation that the accuracy of the final result is not compromised if the…
This work proposes a time-efficient Natural Gradient Descent method, called TENGraD, with linear convergence guarantees. Computing the inverse of the neural network's Fisher information matrix is expensive in NGD because the Fisher matrix…
Embedding graphs in continous spaces is a key factor in designing and developing algorithms for automatic information extraction to be applied in diverse tasks (e.g., learning, inferring, predicting). The reliability of graph embeddings…
In this manuscript, we propose matrix- and tensor-oriented methods for the numerical solution of the multidimensional evolutionary space-fractional complex Ginzburg--Landau equation. After a suitable spatial semidiscretization, the…
We revisit the shift-and-invert Arnoldi method proposed in [S. Lee, H. Pang, and H. Sun. {\it Shift-invert Arnoldi approximation to the Toeplitz matrix exponential}, SIAM J. Sci. Comput., 32: 774--792, 2010] for numerical approximation to…
Iso-surface extraction from an implicit field is a fundamental process in various applications of computer vision and graphics. When dealing with geometric shapes with complicated geometric details, many existing algorithms suffer from high…
We propose an efficient algorithm for the evaluation of the potential and its gradient of gravitational/electrostatic $N$-body systems, which we call particle mesh multipole method (PMMM or PM$^3$). PMMM can be understood both as an…
We introduce a fast algorithm for computing sparse Fourier transforms supported on smooth curves or surfaces. This problem appear naturally in several important problems in wave scattering and reflection seismology. The main observation is…
Robots reason about the environment through dedicated representations. Popular choices for dense representations exploit Truncated Signed Distance Functions (TSDF) and Octree data structures. However, TSDF provides a projective or…
Different numerical approaches for the stray-field calculation in the context of micromagnetic simulations are investigated. We compare finite difference based fast Fourier transform methods, tensor grid methods and the finite-element…
We consider a dynamical triangulation model of euclidean quantum gravity where the topology is not fixed. This model is equivalent to a tensor generalization of the matrix model of two dimensional quantum gravity. A set of moves is given…
Solving the so-called geodesic endpoint problem, i.e., finding a geodesic that connects two given points on a manifold, is at the basis of virtually all data processing operations, including averaging, clustering, interpolation and…
Nontrivial isometric embeddings for flat metrics (i.e., those which are not just planes in the ambient space) can serve as useful tools in the description of gravity in the embedding gravity approach. Such embeddings can additionally be…