Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Physics Constrained Learning for Data-driven Inverse Modeling from
  Sparse Observations   Deep neural networks (DNN) have been used to model nonlinear relations
between physical quantities. Those DNNs are embedded in physical systems
described by partial differential equations (PDE) and trained by minimizing a
loss function that measures the discrepancy between predictions and
observations in some chosen norm. This loss function often includes the PDE
constraints as a penalty term when only sparse observations are available. As a
result, the PDE is only satisfied approximately by the solution. However, the
penalty term typically slows down the convergence of the optimizer for stiff
problems. We present a new approach that trains the embedded DNNs while
numerically satisfying the PDE constraints. We develop an algorithm that
enables differentiating both explicit and implicit numerical solvers in
reverse-mode automatic differentiation. This allows the gradients of the DNNs
and the PDE solvers to be computed in a unified framework. We demonstrate that
our approach enjoys faster convergence and better stability in relatively stiff
problems compared to the penalty method. Our approach allows for the potential
to solve and accelerate a wide range of data-driven inverse modeling, where the
physical constraints are described by PDEs and need to be satisfied accurately.

8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ