Probabilistic Performance-Pattern Decomposition (PPPD): analysis framework and applications to stochastic mechanical systems

• URL: http://arxiv.org/abs/2003.02205v1
• Date: Wed, 4 Mar 2020 17:18:43 GMT
• Title: Probabilistic Performance-Pattern Decomposition (PPPD): analysis framework and applications to stochastic mechanical systems
• Authors: Ziqi Wang, Marco Broccardo, Junho Song
• Abstract summary: The paper proposes a framework to obtain structuralized characterizations on behaviors of systems. The framework is named Probabilistic Performance-Pattern Decomposition (PPPD)
• Score: 8.975760915194765
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Since the early 1900s, numerous research efforts have been devoted to developing quantitative solutions to stochastic mechanical systems. In general, the problem is perceived as solved when a complete or partial probabilistic description on the quantity of interest (QoI) is determined. However, in the presence of complex system behavior, there is a critical need to go beyond mere probabilistic descriptions. In fact, to gain a full understanding of the system, it is crucial to extract physical characterizations from the probabilistic structure of the QoI, especially when the QoI solution is obtained in a data-driven fashion. Motivated by this perspective, the paper proposes a framework to obtain structuralized characterizations on behaviors of stochastic systems. The framework is named Probabilistic Performance-Pattern Decomposition (PPPD). PPPD analysis aims to decompose complex response behaviors, conditional to a prescribed performance state, into meaningful patterns in the space of system responses, and to investigate how the patterns are triggered in the space of basic random variables. To illustrate the application of PPPD, the paper studies three numerical examples: 1) an illustrative example with hypothetical stochastic processes input and output; 2) a stochastic Lorenz system with periodic as well as chaotic behaviors; and 3) a simplified shear-building model subjected to a stochastic ground motion excitation.

Related papers

• Logistic-beta processes for dependent random probabilities with beta marginals [58.91121576998588]
  We propose a novel process called the logistic-beta process, whose logistic transformation yields a process with common beta marginals. It can model dependence on both discrete and continuous domains, such as space or time, and has a flexible dependence structure through correlation kernels. We illustrate the benefits through nonparametric binary regression and conditional density estimation examples, both in simulation studies and in a pregnancy outcome application.
  arXiv  Detail & Related papers  (2024-02-10T21:41:32Z)
• Predictive complexity of quantum subsystems [0.0]
  We define predictive states and predictive complexity for quantum systems composed of distinct subsystems. Predictions are formed by equivalence classes of state vectors in the exterior Hilbert space. It can also serve as a local order parameter that can distinguish long and short range entanglement.
  arXiv  Detail & Related papers  (2023-09-26T18:58:56Z)
• An information field theory approach to Bayesian state and parameter estimation in dynamical systems [0.0]
  This paper develops a scalable Bayesian approach to state and parameter estimation suitable for continuous-time, deterministic dynamical systems. We construct a physics-informed prior probability measure on the function space of system responses so that functions that satisfy the physics are more likely.
  arXiv  Detail & Related papers  (2023-06-03T16:36:43Z)
• On the Benefits of Leveraging Structural Information in Planning Over the Learned Model [3.3512508970931236]
  We investigate the benefits of leveraging structural information about the system in terms of reducing sample complexity. Our analysis shows that there can be a significant saving in sample complexity by leveraging structural information about the model.
  arXiv  Detail & Related papers  (2023-03-15T18:18:01Z)
• Measure-Theoretic Probability of Complex Co-occurrence and E-Integral [15.263586201516159]
  The behavior of a class of natural integrals called E-integrals is investigated based on the defined conditional probability of co-occurrence. The paper offers a novel measure-theoretic framework where E-integral as a basic measure-theoretic concept can be the starting point.
  arXiv  Detail & Related papers  (2022-10-18T14:52:23Z)
• PAC Reinforcement Learning for Predictive State Representations [60.00237613646686]
  We study online Reinforcement Learning (RL) in partially observable dynamical systems. We focus on the Predictive State Representations (PSRs) model, which is an expressive model that captures other well-known models. We develop a novel model-based algorithm for PSRs that can learn a near optimal policy in sample complexity scalingly.
  arXiv  Detail & Related papers  (2022-07-12T17:57:17Z)
• Capturing Actionable Dynamics with Structured Latent Ordinary Differential Equations [68.62843292346813]
  We propose a structured latent ODE model that captures system input variations within its latent representation. Building on a static variable specification, our model learns factors of variation for each input to the system, thus separating the effects of the system inputs in the latent space.
  arXiv  Detail & Related papers  (2022-02-25T20:00:56Z)
• Probabilistic modeling of discrete structural response with application to composite plate penetration models [0.0]
  This paper deals with the development of a computational framework for generation of probabilistic penetration response of S-2 glass/SC-15 epoxy composite plates under ballistic impact. An adaptive domain-based decomposition and classification method, combined with sparse grid sampling, is used to develop an efficient classification surrogate modeling algorithm for such discrete outputs.
  arXiv  Detail & Related papers  (2020-11-23T22:45:09Z)
• Stein Variational Model Predictive Control [130.60527864489168]
  Decision making under uncertainty is critical to real-world, autonomous systems. Model Predictive Control (MPC) methods have demonstrated favorable performance in practice, but remain limited when dealing with complex distributions. We show that this framework leads to successful planning in challenging, non optimal control problems.
  arXiv  Detail & Related papers  (2020-11-15T22:36:59Z)
• 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)
• Multiplicative noise and heavy tails in stochastic optimization [62.993432503309485]
  empirical optimization is central to modern machine learning, but its role in its success is still unclear. We show that it commonly arises in parameters of discrete multiplicative noise due to variance. A detailed analysis is conducted in which we describe on key factors, including recent step size, and data, all exhibit similar results on state-of-the-art neural network models.
  arXiv  Detail & Related papers  (2020-06-11T09:58:01Z)

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.