Cheap and Deterministic Inference for Deep State-Space Models of Interacting Dynamical Systems

Published: 01 Mar 2023, Last Modified: 01 Mar 2023Accepted by TMLREveryoneRevisionsBibTeX
Abstract: Graph neural networks are often used to model interacting dynamical systems since they gracefully scale to systems with a varying and high number of agents. While there has been much progress made for deterministic interacting systems, modeling is much more challenging for stochastic systems in which one is interested in obtaining a predictive distribution over future trajectories. Existing methods are either computationally slow since they rely on Monte Carlo sampling or make simplifying assumptions such that the predictive distribution is unimodal. In this work, we present a deep state-space model which employs graph neural networks in order to model the underlying interacting dynamical system. The predictive distribution is multimodal and has the form of a Gaussian mixture model, where the moments of the Gaussian components can be computed via deterministic moment matching rules. Our moment matching scheme can be exploited for sample-free inference leading to more efficient and stable training compared to Monte Carlo alternatives. Furthermore, we propose structured approximations to the covariance matrices of the Gaussian components in order to scale up to systems with many agents. We benchmark our novel framework on two challenging autonomous driving datasets. Both confirm the benefits of our method compared to state-of-the-art methods. We further demonstrate the usefulness of our individual contributions in a carefully designed ablation study and provide a detailed empirical runtime analysis of our proposed covariance approximations.
License: Creative Commons Attribution 4.0 International (CC BY 4.0)
Submission Length: Long submission (more than 12 pages of main content)
Changes Since Last Submission: 1st Edit: - Added a background section and reorganized Sec. 4 - Added a Theorem that shows that our method is exact for locally linear dynamics - Added a toy experiment with known ground truth dynamics - New algorithm for parameter inference - Added several citations to support our claims - Adjusted overly broad claims - Ouput moments of ReLU activation - New experiment on Out-Of-Domain testing - More experimental details - Detailed description of evaluation procedure 2nd Edit: - Changed RMSE calculation for multi-modal predictors - More details on the RMSE calculation
Assigned Action Editor: ~Arnaud_Doucet2
Submission Number: 344