Related papers: NeuroKoopman Dynamic Causal Discovery
Recent advances have established the identifiability of a directed acyclic graph (DAG) under additive noise models (ANMs), spurring the development of various causal discovery methods. However, most existing methods make restrictive model…
Granger Causality (GC) offers an elegant statistical framework to study the association between multivariate time series data. Vector autoregressive models (VAR) are simple and easy to fit, but have limited application because of their…
Causal discovery amounts to learning a directed acyclic graph (DAG) that encodes a causal model. This model selection problem can be challenging due to its large combinatorial search space, particularly when dealing with non-parametric…
Causal discovery for dynamical systems poses a major challenge in fields where active interventions are infeasible. Most methods used to investigate these systems and their associated benchmarks are tailored to deterministic,…
This paper explores a simple question: can we model the internal transformations of a neural network using dynamical systems theory? We introduce Koopman autoencoders to capture how neural representations evolve through network layers,…
Nonlinear differential equations are encountered as models of fluid flow, spiking neurons, and many other systems of interest in the real world. Common features of these systems are that their behaviors are difficult to describe exactly and…
This paper presents the results of identification of vehicle dynamics using the Koopman operator. The basic idea is to transform the state space of a nonlinear system (a car in our case) to a higher-dimensional space, using so-called basis…
Continuous monitoring of the spatio-temporal dynamic behavior of critical infrastructure networks, such as the power systems, is a challenging but important task. In particular, accurate and timely prediction of the (electro-mechanical)…
Granger causality is well established within the neurosciences for inference of directed functional connectivity from neurophysiological data. These data usually consist of time series which subsample a continuous-time biophysiological…
In contemporary scientific research, understanding the distinction between correlation and causation is crucial. While correlation is a widely used analytical standard, it does not inherently imply causation. This paper addresses the…
Causal discovery from time series is a fundamental task in machine learning. However, its widespread adoption is hindered by a reliance on untestable causal assumptions and by the lack of robustness-oriented evaluation in existing…
Causal discovery is a data-driven paradigm for analyzing complex systems, while physics-based models, such as ordinary differential equations (ODEs), provide mechanistic structure for real-world dynamical processes. Integrating these…
Granger causality and variants of this concept allow the study of complex dynamical systems as networks constructed from multivariate time series. In this work, a large number of Granger causality measures used to form causality networks…
Time-dependent structural reliability analysis of nonlinear dynamical systems is non-trivial; subsequently, scope of most of the structural reliability analysis methods is limited to time-independent reliability analysis only. In this work,…
Dynamic Mode Decomposition (DMD) is a technique to approximate generally non-linear dynamical systems using linear techniques, which are better understood and easier to analyze. Koopman theory extends DMD by transforming the original system…
We study nonlinear dynamics of the Earth's tropical climate system. For that, we apply a recently developed technique for feature extraction and mode decomposition of spatiotemporal data generated by ergodic dynamical systems. The method…
Causality in time series can be challenging to determine, especially in the presence of non-linear dependencies. Granger causality helps analyze potential relationships between variables, thereby offering a method to determine whether one…
Discovering causal relationships from time series data is significant in fields such as finance, climate science, and neuroscience. However, contemporary techniques rely on the simplifying assumption that data originates from the same…
Latent world models allow agents to reason about complex environments with high-dimensional observations. However, adapting to new environments and effectively leveraging previous knowledge remain significant challenges. We present…
Dynamic mode decomposition (DMD) is a data-driven technique used for capturing the dynamics of complex systems. DMD has been connected to spectral analysis of the Koopman operator, and essentially extracts spatial-temporal modes of the…