Anomaly Detection in Complex Dynamical Systems: A Systematic Framework Using Embedding Theory and Physics-Inspired Consistency

• URL: http://arxiv.org/abs/2502.19307v1
• Date: Wed, 26 Feb 2025 17:06:13 GMT
• Title: Anomaly Detection in Complex Dynamical Systems: A Systematic Framework Using Embedding Theory and Physics-Inspired Consistency
• Authors: Michael Somma, Thomas Gallien, Branka Stojanovic,
• Abstract summary: Anomaly detection in complex dynamical systems is essential for ensuring reliability, safety, and efficiency in industrial and cyber-physical infrastructures.<n>We propose a system-theoretic approach to anomaly detection, grounded in classical embedding theory and physics-inspired consistency principles.<n>Our findings support the hypothesis that anomalies disrupt stable system dynamics, providing a robust, interpretable signal for anomaly detection.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Anomaly detection in complex dynamical systems is essential for ensuring reliability, safety, and efficiency in industrial and cyber-physical infrastructures. Predictive maintenance helps prevent costly failures, while cybersecurity monitoring has become critical as digitized systems face growing threats. Many of these systems exhibit oscillatory behaviors and bounded motion, requiring anomaly detection methods that capture structured temporal dependencies while adhering to physical consistency principles. In this work, we propose a system-theoretic approach to anomaly detection, grounded in classical embedding theory and physics-inspired consistency principles. We build upon the Fractal Whitney Embedding Prevalence Theorem, extending traditional embedding techniques to complex system dynamics. Additionally, we introduce state-derivative pairs as an embedding strategy to capture system evolution. To enforce temporal coherence, we develop a Temporal Differential Consistency Autoencoder (TDC-AE), incorporating a TDC-Loss that aligns the approximated derivatives of latent variables with their dynamic representations. We evaluate our method on the C-MAPSS dataset, a benchmark for turbofan aeroengine degradation. TDC-AE outperforms LSTMs and Transformers while achieving a 200x reduction in MAC operations, making it particularly suited for lightweight edge computing. Our findings support the hypothesis that anomalies disrupt stable system dynamics, providing a robust, interpretable signal for anomaly detection.

Related papers

• Hybrid Temporal Differential Consistency Autoencoder for Efficient and Sustainable Anomaly Detection in Cyber-Physical Systems [0.0]
  Cyberattacks on critical infrastructure, particularly water distribution systems, have increased due to rapid digitalization. This study addresses key challenges in anomaly detection by leveraging time correlations in sensor data. We propose a hybrid autoencoder-based approach, referred to as hybrid TDC-AE, which extends TDC by incorporating both deterministic nodes and conventional statistical nodes.
  arXiv  Detail & Related papers  (2025-04-08T09:22:44Z)
• Efficient Transformed Gaussian Process State-Space Models for Non-Stationary High-Dimensional Dynamical Systems [49.819436680336786]
  We propose an efficient transformed Gaussian process state-space model (ETGPSSM) for scalable and flexible modeling of high-dimensional, non-stationary dynamical systems. Specifically, our ETGPSSM integrates a single shared GP with input-dependent normalizing flows, yielding an expressive implicit process prior that captures complex, non-stationary transition dynamics. Our ETGPSSM outperforms existing GPSSMs and neural network-based SSMs in terms of computational efficiency and accuracy.
  arXiv  Detail & Related papers  (2025-03-24T03:19:45Z)
• Physics-Informed Regularization for Domain-Agnostic Dynamical System Modeling [41.82469276824927]
  We present a framework that achieves high-precision modeling for a wide range of dynamical systems. It helps preserve energies for conservative systems while serving as a strong inductive bias for non-conservative, reversible systems. By integrating the TRS loss within neural ordinary differential equation models, the proposed model TREAT demonstrates superior performance on diverse physical systems.
  arXiv  Detail & Related papers  (2024-10-08T21:04:01Z)
• Learning Physics From Video: Unsupervised Physical Parameter Estimation for Continuous Dynamical Systems [49.11170948406405]
  State-of-the-art in automatic parameter estimation from video is addressed by training supervised deep networks on large datasets. We propose a method to estimate the physical parameters of any known, continuous governing equation from single videos.
  arXiv  Detail & Related papers  (2024-10-02T09:44:54Z)
• A Hierarchical Framework with Spatio-Temporal Consistency Learning for Emergence Detection in Complex Adaptive Systems [41.055298739292695]
  Emergence, a global property of complex adaptive systems, is prevalent in real-world dynamic systems, e.g., network-level traffic congestions. This paper proposes a hierarchical framework with CAS-temporal consistency to solve these two problems by learning the system representation and agent representations. Our method achieves more detection than traditional methods and deep learning methods on three datasets with well-known yet hard-to-detect emergent behaviors.
  arXiv  Detail & Related papers  (2024-01-18T08:55:05Z)
• Investigating Robustness in Cyber-Physical Systems: Specification-Centric Analysis in the face of System Deviations [8.8690305802668]
  A critical attribute of cyber-physical systems (CPS) is robustness, denoting its capacity to operate safely. This paper proposes a novel specification-based robustness, which characterizes the effectiveness of a controller in meeting a specified system requirement. We present an innovative two-layer simulation-based analysis framework designed to identify subtle robustness violations.
  arXiv  Detail & Related papers  (2023-11-13T16:44:43Z)
• TANGO: Time-Reversal Latent GraphODE for Multi-Agent Dynamical Systems [43.39754726042369]
  We propose a simple-yet-effective self-supervised regularization term as a soft constraint that aligns the forward and backward trajectories predicted by a continuous graph neural network-based ordinary differential equation (GraphODE) It effectively imposes time-reversal symmetry to enable more accurate model predictions across a wider range of dynamical systems under classical mechanics. Experimental results on a variety of physical systems demonstrate the effectiveness of our proposed method.
  arXiv  Detail & Related papers  (2023-10-10T08:52:16Z)
• DyEdgeGAT: Dynamic Edge via Graph Attention for Early Fault Detection in IIoT Systems [12.641578474466646]
  DyEdgeGAT is a novel approach for early-stage fault detection in IIoT systems. It incorporates operating condition contexts into node dynamics modeling, enhancing its accuracy and robustness. We rigorously evaluated DyEdgeGAT using both a synthetic dataset and a real-world industrial-scale flow facility benchmark.
  arXiv  Detail & Related papers  (2023-07-07T12:22:16Z)
• AttNS: Attention-Inspired Numerical Solving For Limited Data Scenarios [51.94807626839365]
  We propose the attention-inspired numerical solver (AttNS) to solve differential equations due to limited data.<n>AttNS is inspired by the effectiveness of attention modules in Residual Neural Networks (ResNet) in enhancing model generalization and robustness.
  arXiv  Detail & Related papers  (2023-02-05T01:39:21Z)
• Physics-Inspired Temporal Learning of Quadrotor Dynamics for Accurate Model Predictive Trajectory Tracking [76.27433308688592]
  Accurately modeling quadrotor's system dynamics is critical for guaranteeing agile, safe, and stable navigation. We present a novel Physics-Inspired Temporal Convolutional Network (PI-TCN) approach to learning quadrotor's system dynamics purely from robot experience. Our approach combines the expressive power of sparse temporal convolutions and dense feed-forward connections to make accurate system predictions.
  arXiv  Detail & Related papers  (2022-06-07T13:51:35Z)
• DySMHO: Data-Driven Discovery of Governing Equations for Dynamical Systems via Moving Horizon Optimization [77.34726150561087]
  We introduce Discovery of Dynamical Systems via Moving Horizon Optimization (DySMHO), a scalable machine learning framework. DySMHO sequentially learns the underlying governing equations from a large dictionary of basis functions. Canonical nonlinear dynamical system examples are used to demonstrate that DySMHO can accurately recover the governing laws.
  arXiv  Detail & Related papers  (2021-07-30T20:35:03Z)
• Stochastically forced ensemble dynamic mode decomposition for forecasting and analysis of near-periodic systems [65.44033635330604]
  We introduce a novel load forecasting method in which observed dynamics are modeled as a forced linear system. We show that its use of intrinsic linear dynamics offers a number of desirable properties in terms of interpretability and parsimony. Results are presented for a test case using load data from an electrical grid.
  arXiv  Detail & Related papers  (2020-10-08T20:25:52Z)
• Limited-angle tomographic reconstruction of dense layered objects by dynamical machine learning [68.9515120904028]
  Limited-angle tomography of strongly scattering quasi-transparent objects is a challenging, highly ill-posed problem. Regularizing priors are necessary to reduce artifacts by improving the condition of such problems. We devised a recurrent neural network (RNN) architecture with a novel split-convolutional gated recurrent unit (SC-GRU) as the building block.
  arXiv  Detail & Related papers  (2020-07-21T11:48:22Z)

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.