  Continuous-time dynamics models, such as neural ordinary differential
equations, have enabled the modeling of underlying dynamics in time-series data
and accurate forecasting. However, parameterization of dynamics using a neural
network makes it difficult for humans to identify causal structures in the
data. In consequence, this opaqueness hinders the use of these models in the
domains where capturing causal relationships carries the same importance as
accurate predictions, e.g., tsunami forecasting. In this paper, we address this
challenge by proposing a mechanism for mining causal structures from
continuous-time models. We train models to capture the causal structure by
enforcing sparsity in the weights of the input layers of the dynamics models.
We first verify the effectiveness of our method in the scenario where the exact
causal-structures of time-series are known as a priori. We next apply our
method to a real-world problem, namely tsunami forecasting, where the exact
causal-structures are difficult to characterize. Experimental results show that
the proposed method is effective in learning physically-consistent causal
relationships while achieving high forecasting accuracy.
