  The complex and computationally expensive nature of landscape evolution
models pose significant challenges in the inference and optimisation of unknown
parameters. Bayesian inference provides a methodology for estimation and
uncertainty quantification of unknown model parameters. In our previous work,
we developed parallel tempering Bayeslands as a framework for parameter
estimation and uncertainty quantification for the Badlands landscape evolution
model. Parallel tempering Bayeslands features high-performance computing with
dozens of processing cores running in parallel to enhance computational
efficiency. Although we use parallel computing, the procedure remains
computationally challenging since thousands of samples need to be drawn and
evaluated. \textcolor{black}{In large-scale landscape and basin evolution
problems, a single model evaluation can take from several minutes to hours, and
in some instances, even days. Surrogate-assisted optimisation has been used for
several computationally expensive engineering problems which motivate its use
in optimisation and inference of complex geoscientific models.} The use of
surrogate models can speed up parallel tempering Bayeslands by developing
computationally inexpensive models to mimic expensive ones. In this paper, we
apply surrogate-assisted parallel tempering where that surrogate mimics a
landscape evolution model by estimating the likelihood function from the model.
\textcolor{black}{We employ a neural network-based surrogate model that learns
from the history of samples generated. } The entire framework is developed in a
parallel computing infrastructure to take advantage of parallelism. The results
show that the proposed methodology is effective in lowering the overall
computational cost significantly while retaining the quality of solutions.
