Identifying Causal Structure in Dynamical Systems
- URL: http://arxiv.org/abs/2006.03906v2
- Date: Mon, 18 Jul 2022 06:29:31 GMT
- Title: Identifying Causal Structure in Dynamical Systems
- Authors: Dominik Baumann, Friedrich Solowjow, Karl H. Johansson, and Sebastian
Trimpe
- Abstract summary: We propose a method that identifies the causal structure of control systems.
Experiments on a robot arm demonstrate reliable causal identification from real-world data.
- Score: 6.451261098085498
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Mathematical models are fundamental building blocks in the design of
dynamical control systems. As control systems are becoming increasingly complex
and networked, approaches for obtaining such models based on first principles
reach their limits. Data-driven methods provide an alternative. However,
without structural knowledge, these methods are prone to finding spurious
correlations in the training data, which can hamper generalization capabilities
of the obtained models. This can significantly lower control and prediction
performance when the system is exposed to unknown situations. A preceding
causal identification can prevent this pitfall. In this paper, we propose a
method that identifies the causal structure of control systems. We design
experiments based on the concept of controllability, which provides a
systematic way to compute input trajectories that steer the system to specific
regions in its state space. We then analyze the resulting data leveraging
powerful techniques from causal inference and extend them to control systems.
Further, we derive conditions that guarantee the discovery of the true causal
structure of the system. Experiments on a robot arm demonstrate reliable causal
identification from real-world data and enhanced generalization capabilities.
Related papers
- Unified Causality Analysis Based on the Degrees of Freedom [1.2289361708127877]
This paper presents a unified method capable of identifying fundamental causal relationships between pairs of systems.
By analyzing the degrees of freedom in the system, our approach provides a more comprehensive understanding of both causal influence and hidden confounders.
This unified framework is validated through theoretical models and simulations, demonstrating its robustness and potential for broader application.
arXiv Detail & Related papers (2024-10-25T10:57:35Z) - Multi-modal Causal Structure Learning and Root Cause Analysis [67.67578590390907]
We propose Mulan, a unified multi-modal causal structure learning method for root cause localization.
We leverage a log-tailored language model to facilitate log representation learning, converting log sequences into time-series data.
We also introduce a novel key performance indicator-aware attention mechanism for assessing modality reliability and co-learning a final causal graph.
arXiv Detail & Related papers (2024-02-04T05:50:38Z) - Physics-Informed Kernel Embeddings: Integrating Prior System Knowledge
with Data-Driven Control [22.549914935697366]
We present a method to incorporate priori knowledge into data-driven control algorithms using kernel embeddings.
Our proposed approach incorporates prior knowledge of the system dynamics as a bias term in the kernel learning problem.
We demonstrate the improved sample efficiency and out-of-sample generalization of our approach over a purely data-driven baseline.
arXiv Detail & Related papers (2023-01-09T18:35:32Z) - Leveraging the structure of dynamical systems for data-driven modeling [111.45324708884813]
We consider the impact of the training set and its structure on the quality of the long-term prediction.
We show how an informed design of the training set, based on invariants of the system and the structure of the underlying attractor, significantly improves the resulting models.
arXiv Detail & Related papers (2021-12-15T20:09:20Z) - Sparsity in Partially Controllable Linear Systems [56.142264865866636]
We study partially controllable linear dynamical systems specified by an underlying sparsity pattern.
Our results characterize those state variables which are irrelevant for optimal control.
arXiv Detail & Related papers (2021-10-12T16:41:47Z) - Supervised DKRC with Images for Offline System Identification [77.34726150561087]
Modern dynamical systems are becoming increasingly non-linear and complex.
There is a need for a framework to model these systems in a compact and comprehensive representation for prediction and control.
Our approach learns these basis functions using a supervised learning approach.
arXiv Detail & Related papers (2021-09-06T04:39:06Z) - Beyond Predictions in Neural ODEs: Identification and Interventions [4.257168718582631]
Given large amounts of observational data about a system, can we uncover the rules that govern its evolution?
We show that combining simple regularization schemes with flexible neural ODEs can robustly recover the dynamics and causal structures from time-series data.
We conclude by showing that we can also make accurate predictions under interventions on variables or the system itself.
arXiv Detail & Related papers (2021-06-23T14:35:38Z) - Model-Based Deep Learning [155.063817656602]
Signal processing, communications, and control have traditionally relied on classical statistical modeling techniques.
Deep neural networks (DNNs) use generic architectures which learn to operate from data, and demonstrate excellent performance.
We are interested in hybrid techniques that combine principled mathematical models with data-driven systems to benefit from the advantages of both approaches.
arXiv Detail & Related papers (2020-12-15T16:29:49Z) - Knowledge-Based Learning of Nonlinear Dynamics and Chaos [3.673994921516517]
We present a universal learning framework for extracting predictive models from nonlinear systems based on observations.
Our framework can readily incorporate first principle knowledge because it naturally models nonlinear systems as continuous-time systems.
arXiv Detail & Related papers (2020-10-07T13:50:13Z) - How Training Data Impacts Performance in Learning-based Control [67.7875109298865]
This paper derives an analytical relationship between the density of the training data and the control performance.
We formulate a quality measure for the data set, which we refer to as $rho$-gap.
We show how the $rho$-gap can be applied to a feedback linearizing control law.
arXiv Detail & Related papers (2020-05-25T12:13:49Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.