Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Physics-Informed Machine Learning with Conditional Karhunen-Lo\`eve
  Expansions   We present a new physics-informed machine learning approach for the inversion
of PDE models with heterogeneous parameters. In our approach, the
space-dependent partially-observed parameters and states are approximated via
Karhunen-Lo\`eve expansions (KLEs). Each of these KLEs is then conditioned on
their corresponding measurements, resulting in low-dimensional models of the
parameters and states that resolve observed data. Finally, the coefficients of
the KLEs are estimated by minimizing the norm of the residual of the PDE model
evaluated at a finite set of points in the computational domain, ensuring that
the reconstructed parameters and states are consistent with both the
observations and the PDE model to an arbitrary level of accuracy.
  In our approach, KLEs are constructed using the eigendecomposition of
covariance models of spatial variability. For the model parameters, we employ a
parameterized covariance model calibrated on parameter observations; for the
model states, the covariance is estimated from a number of forward simulations
of the PDE model corresponding to realizations of the parameters drawn from
their KLE. We apply the proposed approach to identifying heterogeneous
log-diffusion coefficients in diffusion equations from spatially sparse
measurements of the log-diffusion coefficient and the solution of the diffusion
equation. We find that the proposed approach compares favorably against
state-of-the-art point estimates such as maximum a posteriori estimation and
physics-informed neural networks.

20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
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The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: cmp-lg
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: q-bio
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The categories of this paper are: hep-lat
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The categories of this paper are: funct-an