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Abstract This paper explores the Glauber dynamics of spin systems with asymmetric coupling, a scenario that inherently violates detailed balance, leading to non-equilibrium steady states. By focusing on weighted and heterogeneous networks, we extend the applicability of Glauber models to capture complex real-world interactions, such as those seen in multilayer and hierarchical systems. Under specific assumptions on the coupling matrix, we demonstrate the tractability of these dynamics in the limit as the number of spins approaches infinity. Our results highlight the influence of network topology on dynamic behavior and provide a framework for analyzing stochastic processes in diverse applications, from statistical mechanics to data-driven modeling in applied sciences. The approach also uncovers potential for leveraging non-equilibrium dynamics in machine learning and network analysis.
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A Review of Data‐Driven Discovery for Dynamic Systems
Summary Many real‐world scientific processes are governed by complex non‐linear dynamic systems that can be represented by differential equations. Recently, there has been an increased interest in learning, or discovering, the forms of the equations driving these complex non‐linear dynamic systems using data‐driven approaches. In this paper, we review the current literature on data‐driven discovery for dynamic systems. We provide a categorisation to the different approaches for data‐driven discovery and a unified mathematical framework to show the relationship between the approaches. Importantly, we discuss the role of statistics in the data‐driven discovery field, describe a possible approach by which the problem can be cast in a statistical framework and provide avenues for future work.
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- Award ID(s):
- 1853096
- PAR ID:
- 10473084
- Publisher / Repository:
- Wiley-Blackwell
- Date Published:
- Journal Name:
- International Statistical Review
- Volume:
- 91
- Issue:
- 3
- ISSN:
- 0306-7734
- Format(s):
- Medium: X Size: p. 464-492
- Size(s):
- p. 464-492
- Sponsoring Org:
- National Science Foundation
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