Related papers: Deep Koopman operator framework for causal discove…

Causal inference revealing causal dependencies between variables from empirical data has found applications in multiple sub-fields of scientific research. A quantum perspective of correlations holds the promise of overcoming the limitation…

Causal discovery studies the problem of mining causal relationships between variables from data, which is of primary interest in science. During the past decades, significant amount of progresses have been made toward this fundamental data…

It is commonplace to encounter heterogeneous or nonstationary data, of which the underlying generating process changes across domains or over time. Such a distribution shift feature presents both challenges and opportunities for causal…

The class of problems in causal inference which seeks to isolate causal correlations solely from observational data even without interventions has come to the forefront of machine learning, neuroscience and social sciences. As new large…

The Granger framework is useful for discovering causal relations in time-varying signals. However, most Granger causality (GC) methods are developed for densely sampled timeseries data. A substantially different setting, particularly common…

In this paper, we propose linear operator theoretic framework involving Koopman operator for the data-driven identification of power system dynamics. We explicitly account for noise in the time series measurement data and propose robust…

A comprehensive understanding of causality is critical for navigating and operating within today's complex real-world systems. The absence of realistic causal models with known data generating processes complicates fair benchmarking. In…

Deep learning is widely used to predict complex dynamical systems in many scientific and engineering areas. However, the black-box nature of these deep learning models presents significant challenges for carrying out simultaneous data…

Causal discovery estimates the underlying physical process that generates the observed data: does X cause Y or does Y cause X? Current methodologies use structural conditions to turn the causal query into a statistical query, when only…

Dynamic causal discovery in wireless networks is essential due to evolving interference, fading, and mobility, which complicate traditional static causal models. This paper addresses causal inference challenges in dynamic fading wireless…

This PhD thesis contains several contributions to the field of statistical causal modeling. Statistical causal models are statistical models embedded with causal assumptions that allow for the inference and reasoning about the behavior of…

Discovering causal relations from observational time series without making the stationary assumption is a significant challenge. In practice, this challenge is common in many areas, such as retail sales, transportation systems, and medical…

The study of the Two-Body and Circular Restricted Three-Body Problems in the field of aerospace engineering and sciences is deeply important because they help describe the motion of both celestial and artificial satellites. With the growing…

Multi-layer perceptrons (MLP's) have been extensively utilized in discovering Deep Koopman operators for linearizing nonlinear dynamics. With the emergence of Kolmogorov-Arnold Networks (KANs) as a more efficient and accurate alternative to…

In this paper, we explore the embedding of nonlinear dynamical systems into linear ordinary differential equations (ODEs) via the Carleman linearization method. Under dissipative conditions, numerous previous works have established rigorous…

Koopman analysis of a general dynamics system provides a linear Koopman operator and an embedded eigenfunction space, enabling the application of standard techniques from linear analysis. However, in practice, deriving exact operators and…

Analyzing the inner mechanisms of deep neural networks is a fundamental task in machine learning. Existing work provides limited analysis or it depends on local theories, such as fixed-point analysis. In contrast, we propose to analyze…

In many real-world applications where the system dynamics has an underlying interdependency among its variables (such as power grid, economics, neuroscience, omics networks, environmental ecosystems, and others), one is often interested in…

In this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace. The Koopman operator is an infinite-dimensional linear operator that evolves…

Transfer operators offer linear representations and global, physically meaningful features of nonlinear dynamical systems. Discovering transfer operators, such as the Koopman operator, require careful crafted dictionaries of observables,…