  The typical multi-task learning methods for spatio-temporal data prediction
involve low-rank tensor computation. However, such a method have relatively
weak performance when the task number is small, and we cannot integrate it into
non-linear models. In this paper, we propose a two-step suboptimal unitary
method (SUM) to combine a meta-learning strategy into multi-task models. In the
first step, it searches for a global pattern by optimising the general
parameters with gradient descents under constraints, which is a geological
regularizer to enable model learning with less training data. In the second
step, we derive an optimised model on each specific task from the global
pattern with only a few local training data. Compared with traditional
multi-task learning methods, SUM shows advantages of generalisation ability on
distant tasks. It can be applied on any multi-task models with the gradient
descent as its optimiser regardless if the prediction function is linear or
not. Moreover, we can harness the model to enable traditional prediction model
to make coKriging. The experiments on public datasets have suggested that our
framework, when combined with current multi-task models, has a conspicuously
better prediction result when the task number is small compared to low-rank
tensor learning, and our model has a quite satisfying outcome when adjusting
the current prediction models for coKriging.
