Covariance-based smoothed particle hydrodynamics. A machine-learning application to simulating disc fragmentation

• URL: http://arxiv.org/abs/2106.08870v1
• Date: Wed, 16 Jun 2021 15:44:49 GMT
• Title: Covariance-based smoothed particle hydrodynamics. A machine-learning application to simulating disc fragmentation
• Authors: Eraldo Pereira Marinho
• Abstract summary: The smoothing PCA is computed to have their eigenvalues proportional to the covariance's principal components. As an application, it was performed the simulation of collapse and fragmentation of a non-magnetic, rotating gaseous sphere.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: A PCA-based, machine learning version of the SPH method is proposed. In the present scheme, the smoothing tensor is computed to have their eigenvalues proportional to the covariance's principal components, using a modified octree data structure, which allows the fast estimation of the anisotropic self-regulating kNN. Each SPH particle is the center of such an optimal kNN cluster, i.e., the one whose covariance tensor allows the find of the kNN cluster itself according to the Mahalanobis metric. Such machine learning constitutes a fixed point problem. The definitive (self-regulating) kNN cluster defines the smoothing volume, or properly saying, the smoothing ellipsoid, required to perform the anisotropic interpolation. Thus, the smoothing kernel has an ellipsoidal profile, which changes how the kernel gradients are computed. As an application, it was performed the simulation of collapse and fragmentation of a non-magnetic, rotating gaseous sphere. An interesting outcome was the formation of protostars in the disc fragmentation, shown to be much more persistent and much more abundant in the anisotropic simulation than in the isotropic case.

Related papers

• Transient anisotropic kernel for probabilistic learning on manifolds [0.0]
  We propose a new ISDE projection vector basis built from a transient anisotropic kernel. The construction ensures that for times near the initial time, the DMAPS basis coincides with the transient basis. This new vector basis better represents statistical dependencies in the learned probability measure for any dimension.
  arXiv  Detail & Related papers  (2024-07-31T08:38:39Z)
• Gradient-Based Feature Learning under Structured Data [57.76552698981579]
  In the anisotropic setting, the commonly used spherical gradient dynamics may fail to recover the true direction. We show that appropriate weight normalization that is reminiscent of batch normalization can alleviate this issue. In particular, under the spiked model with a suitably large spike, the sample complexity of gradient-based training can be made independent of the information exponent.
  arXiv  Detail & Related papers  (2023-09-07T16:55:50Z)
• Capturing dynamical correlations using implicit neural representations [85.66456606776552]
  We develop an artificial intelligence framework which combines a neural network trained to mimic simulated data from a model Hamiltonian with automatic differentiation to recover unknown parameters from experimental data. In doing so, we illustrate the ability to build and train a differentiable model only once, which then can be applied in real-time to multi-dimensional scattering data.
  arXiv  Detail & Related papers  (2023-04-08T07:55:36Z)
• Learning Discretized Neural Networks under Ricci Flow [51.36292559262042]
  We study Discretized Neural Networks (DNNs) composed of low-precision weights and activations. DNNs suffer from either infinite or zero gradients due to the non-differentiable discrete function during training.
  arXiv  Detail & Related papers  (2023-02-07T10:51:53Z)
• Entropic trust region for densest crystallographic symmetry group packings [0.8399688944263843]
  Molecular crystal structure prediction seeks the most stable periodic structure given the chemical composition of a molecule and pressure-temperature conditions. Modern CSP solvers use global optimization methods to search for structures with minimal free energy within a complex energy landscape induced by intermolecular potentials. We propose a class of periodic packings restricted to crystallographic symmetry groups (CSG) and design a search method for the densest CSG packings in an information-geometric framework.
  arXiv  Detail & Related papers  (2022-02-24T08:39:07Z)
• Linearization and Identification of Multiple-Attractors Dynamical System through Laplacian Eigenmaps [8.161497377142584]
  We propose a Graph-based spectral clustering method that takes advantage of a velocity-augmented kernel to connect data-points belonging to the same dynamics. We prove that there always exist a set of 2-dimensional embedding spaces in which the sub-dynamics are linear, and n-dimensional embedding where they are quasi-linear. We learn a diffeomorphism from the Laplacian embedding space to the original space and show that the Laplacian embedding leads to good reconstruction accuracy and a faster training time.
  arXiv  Detail & Related papers  (2022-02-18T12:43:25Z)
• Spectral clustering under degree heterogeneity: a case for the random walk Laplacian [83.79286663107845]
  This paper shows that graph spectral embedding using the random walk Laplacian produces vector representations which are completely corrected for node degree. In the special case of a degree-corrected block model, the embedding concentrates about K distinct points, representing communities.
  arXiv  Detail & Related papers  (2021-05-03T16:36:27Z)
• Fast Gravitational Approach for Rigid Point Set Registration with Ordinary Differential Equations [79.71184760864507]
  This article introduces a new physics-based method for rigid point set alignment called Fast Gravitational Approach (FGA) In FGA, the source and target point sets are interpreted as rigid particle swarms with masses interacting in a globally multiply-linked manner while moving in a simulated gravitational force field. We show that the new method class has characteristics not found in previous alignment methods.
  arXiv  Detail & Related papers  (2020-09-28T15:05:39Z)
• Multipole Graph Neural Operator for Parametric Partial Differential Equations [57.90284928158383]
  One of the main challenges in using deep learning-based methods for simulating physical systems is formulating physics-based data. We propose a novel multi-level graph neural network framework that captures interaction at all ranges with only linear complexity. Experiments confirm our multi-graph network learns discretization-invariant solution operators to PDEs and can be evaluated in linear time.
  arXiv  Detail & Related papers  (2020-06-16T21:56:22Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.