  Physics-informed neural networks (PiNNs) recently emerged as a powerful
solver for a large class of partial differential equations under various
initial and boundary conditions. In this paper, we propose trapz-PiNNs,
physics-informed neural networks incorporated with a modified trapezoidal rule
recently developed for accurately evaluating fractional laplacian and solve the
space-fractional Fokker-Planck equations in 2D and 3D. We describe the modified
trapezoidal rule in detail and verify the second-order accuracy. We demonstrate
trapz-PiNNs have high expressive power through predicting solution with low
$\mathcal{L}^2$ relative error on a variety of numerical examples. We also use
local metrics such as pointwise absolute and relative errors to analyze where
could be further improved. We present an effective method for improving
performance of trapz-PiNN on local metrics, provided that physical observations
of high-fidelity simulation of the true solution are available. Besides the
usual advantages of the deep learning solvers such as adaptivity and
mesh-independence, the trapz-PiNN is able to solve PDEs with fractional
laplacian with arbitrary $\alpha\in (0,2)$ and specializes on rectangular
domain. It also has potential to be generalized into higher dimensions.
