Derivation of the probability density evolution provides invaluable insight
into the behavior of many stochastic systems and their performance. However,
for most real-time applica-tions, numerical determination of the probability
density evolution is a formidable task. The latter is due to the required
temporal and spatial discretization schemes that render most computational
solutions prohibitive and impractical. In this respect, the development of an
efficient computational surrogate model is of paramount importance. Recent
studies on the physics-constrained networks show that a suitable surrogate can
be achieved by encoding the physical insight into a deep neural network. To
this aim, the present work introduces DeepPDEM which utilizes the concept of
physics-informed networks to solve the evolution of the probability density via
proposing a deep learning method. DeepPDEM learns the General Density Evolution
Equation (GDEE) of stochastic structures. This approach paves the way for a
mesh-free learning method that can solve the density evolution problem with-out
prior simulation data. Moreover, it can also serve as an efficient surrogate
for the solu-tion at any other spatiotemporal points within optimization
schemes or real-time applica-tions. To demonstrate the potential applicability
of the proposed framework, two network architectures with different activation
functions as well as two optimizers are investigated. Numerical implementation
on three different problems verifies the accuracy and efficacy of the proposed
method