# Mining Causality from Continuous-time Dynamics Models: An Application to Tsunami Forecasting

arXiv: https://arxiv.org/abs/2210.04958 · HTML: https://mlsanity.com/paper/2210.04958/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 39 references that are in the map.
- First posted on arXiv 10 Oct 2022.

## Builds on (most cited first, 14 of 14)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [Weight Normalization: A Simple Reparameterization to Accelerate Training of Deep Neural Networks](https://mlsanity.com/paper/1602.07868/) (2016)
- [Augmented Neural ODEs](https://mlsanity.com/paper/1904.01681/) (2019)
- [Machine learning structure preserving brackets for forecasting irreversible processes](https://mlsanity.com/paper/2106.12619/) (2021)
- [Parameterized Neural Ordinary Differential Equations: Applications to Computational Physics Problems](https://mlsanity.com/paper/2010.14685/) (2020)
- [Structure-preserving Sparse Identification of Nonlinear Dynamics for Data-driven Modeling](https://mlsanity.com/paper/2109.05364/) (2021)
- [Neural Laplace: Learning diverse classes of differential equations in the Laplace domain](https://mlsanity.com/paper/2206.04843/) (2022)
- [Climate Modeling with Neural Diffusion Equations](https://mlsanity.com/paper/2111.06011/) (2021)
- [Towards Understanding Normalization in Neural ODEs](https://mlsanity.com/paper/2004.09222/) (2020)
- [Predicting Evacuation Decisions using Representations of Individuals' Pre-Disaster Web Search Behavior](https://mlsanity.com/paper/1906.07770/) (2019)

## Built on by (most cited first, 1 of 1)

- [Time and State Dependent Neural Delay Differential Equations](https://mlsanity.com/paper/2306.14545/) (2023)

## Abstract (arXiv)

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.