Scalable Graph Networks for Particle Simulations
- URL: http://arxiv.org/abs/2010.06948v3
- Date: Sat, 20 Mar 2021 18:52:34 GMT
- Title: Scalable Graph Networks for Particle Simulations
- Authors: Karolis Martinkus, Aurelien Lucchi, Nathana\"el Perraudin
- Abstract summary: We introduce an approach that transforms a fully-connected interaction graph into a hierarchical one.
Using our approach, we are able to train models on much larger particle counts, even on a single GPU.
Our approach retains high accuracy and efficiency even on large-scale gravitational N-body simulations.
- Score: 1.933681537640272
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Learning system dynamics directly from observations is a promising direction
in machine learning due to its potential to significantly enhance our ability
to understand physical systems. However, the dynamics of many real-world
systems are challenging to learn due to the presence of nonlinear potentials
and a number of interactions that scales quadratically with the number of
particles $N$, as in the case of the N-body problem. In this work, we introduce
an approach that transforms a fully-connected interaction graph into a
hierarchical one which reduces the number of edges to $O(N)$. This results in
linear time and space complexity while the pre-computation of the hierarchical
graph requires $O(N\log (N))$ time and $O(N)$ space. Using our approach, we are
able to train models on much larger particle counts, even on a single GPU. We
evaluate how the phase space position accuracy and energy conservation depend
on the number of simulated particles. Our approach retains high accuracy and
efficiency even on large-scale gravitational N-body simulations which are
impossible to run on a single machine if a fully-connected graph is used.
Similar results are also observed when simulating Coulomb interactions.
Furthermore, we make several important observations regarding the performance
of this new hierarchical model, including: i) its accuracy tends to improve
with the number of particles in the simulation and ii) its generalisation to
unseen particle counts is also much better than for models that use all
$O(N^2)$ interactions.
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