Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: NeuralPDE: Automating Physics-Informed Neural Networks (PINNs) with
  Error Approximations   Physics-informed neural networks (PINNs) are an increasingly powerful way to
solve partial differential equations, generate digital twins, and create neural
surrogates of physical models. In this manuscript we detail the inner workings
of NeuralPDE.jl and show how a formulation structured around numerical
quadrature gives rise to new loss functions which allow for adaptivity towards
bounded error tolerances. We describe the various ways one can use the tool,
detailing mathematical techniques like using extended loss functions for
parameter estimation and operator discovery, to help potential users adopt
these PINN-based techniques into their workflow. We showcase how NeuralPDE uses
a purely symbolic formulation so that all of the underlying training code is
generated from an abstract formulation, and show how to make use of GPUs and
solve systems of PDEs. Afterwards we give a detailed performance analysis which
showcases the trade-off between training techniques on a large set of PDEs. We
end by focusing on a complex multiphysics example, the Doyle-Fuller-Newman
(DFN) Model, and showcase how this PDE can be formulated and solved with
NeuralPDE. Together this manuscript is meant to be a detailed and approachable
technical report to help potential users of the technique quickly get a sense
of the real-world performance trade-offs and use cases of the PINN techniques.

13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys