Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Constructing coarse-scale bifurcation diagrams from spatio-temporal
  observations of microscopic simulations: A parsimonious machine learning
  approach   We address a three-tier data-driven approach to solve the inverse problem in
complex systems modelling from spatio-temporal data produced by microscopic
simulators using machine learning. In the first step, we exploit manifold
learning and in particular parsimonious Diffusion Maps using leave-one-out
cross-validation (LOOCV) to both identify the intrinsic dimension of the
manifold where the emergent dynamics evolve and for feature selection over the
parametric space. In the second step, based on the selected features, we learn
the right-hand-side of the effective partial differential equations (PDEs)
using two machine learning schemes, namely shallow Feedforward Neural Networks
(FNNs) with two hidden layers and single-layer Random Projection
Networks(RPNNs) which basis functions are constructed using an appropriate
random sampling approach. Finally, based on the learned black-box PDE model, we
construct the corresponding bifurcation diagram, thus exploiting the numerical
bifurcation analysis toolkit. For our illustrations, we implemented the
proposed method to construct the one-parameter bifurcation diagram of the 1D
FitzHugh-Nagumo PDEs from data generated by $D1Q3$ Lattice Boltzmann
simulations. The proposed method was quite effective in terms of numerical
accuracy regarding the construction of the coarse-scale bifurcation diagram.
Furthermore, the proposed RPNN scheme was $\sim$ 20 to 30 times less costly
regarding the training phase than the traditional shallow FNNs, thus arising as
a promising alternative to deep learning for solving the inverse problem for
high-dimensional PDEs.

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The categories of this paper are: gr-qc
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
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The categories of this paper are: nlin
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The categories of this paper are: cmp-lg
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The categories of this paper are: eess
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The categories of this paper are: hep-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom