  Data-driven forward-inverse problems for the variable coefficients Hirota
(VCH) equation are discussed in this paper. The main idea is to use the
improved physics-informed neural networks (IPINN) algorithm with neuron-wise
locally adaptive activation function, slope recovery term and parameter
regularization to recover the data-driven solitons and high-order soliton of
the VCH equation with initial-boundary conditions, as well as the data-driven
parameters discovery for VCH equation with unknown parameters under noise of
different intensity. Numerical results are shown to demonstrate two facts: (i)
data-driven soliton solutions of the VCH equation are successfully learned by
adjusting the network layers, neurons, the original training data,
spatiotemporal regions and other parameters of the IPINN algorithm; (ii) the
prediction parameter can be trained stably and accurately by introducing a
parameter regularization strategy with an appropriate weight coefficients into
the IPINN algorithm. The results achieved in this work verify the effectiveness
of the IPINN algorithm in solving the forward-inverse problems of the variable
coefficients equation.
