Multiscale Simulations of Complex Systems by Learning their Effective Dynamics

• URL: http://arxiv.org/abs/2006.13431v3
• Date: Tue, 19 Oct 2021 17:05:03 GMT
• Title: Multiscale Simulations of Complex Systems by Learning their Effective Dynamics
• Authors: Pantelis R. Vlachas, Georgios Arampatzis, Caroline Uhler, Petros Koumoutsakos
• Abstract summary: We present a systematic framework that bridges large scale simulations and reduced order models to Learn the Effective Dynamics. LED provides a novel potent modality for the accurate prediction of complex systems. LED is applicable to systems ranging from chemistry to fluid mechanics and reduces computational effort by up to two orders of magnitude.
• Score: 10.52078600986485
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Predictive simulations of complex systems are essential for applications ranging from weather forecasting to drug design. The veracity of these predictions hinges on their capacity to capture the effective system dynamics. Massively parallel simulations predict the system dynamics by resolving all spatiotemporal scales, often at a cost that prevents experimentation while their findings may not allow for generalisation. On the other hand reduced order models are fast but limited by the frequently adopted linearization of the system dynamics and/or the utilization of heuristic closures. Here we present a novel systematic framework that bridges large scale simulations and reduced order models to Learn the Effective Dynamics (LED) of diverse complex systems. The framework forms algorithmic alloys between non-linear machine learning algorithms and the Equation-Free approach for modeling complex systems. LED deploys autoencoders to formulate a mapping between fine and coarse-grained representations and evolves the latent space dynamics using recurrent neural networks. The algorithm is validated on benchmark problems and we find that it outperforms state of the art reduced order models in terms of predictability and large scale simulations in terms of cost. LED is applicable to systems ranging from chemistry to fluid mechanics and reduces the computational effort by up to two orders of magnitude while maintaining the prediction accuracy of the full system dynamics. We argue that LED provides a novel potent modality for the accurate prediction of complex systems.

Related papers

• Stochastic Online Optimization for Cyber-Physical and Robotic Systems [9.392372266209103]
  We propose a novel online framework for solving programming problems in the context of cyber-physical and robotic systems. Our problem formulation constraints model the evolution of a cyber-physical system, which has, in general, a continuous state and action space space is nonlinear. We show that even rough estimates of the dynamics can significantly improve the convergence of our algorithms.
  arXiv  Detail & Related papers  (2024-04-08T09:08:59Z)
• Generative Learning for Forecasting the Dynamics of Complex Systems [5.393540462038596]
  We introduce generative models for accelerating simulations of complex systems through learning and evolving their effective dynamics. The results demonstrate that generative learning offers new frontiers for the accurate forecasting of the statistical properties of complex systems at a reduced computational cost.
  arXiv  Detail & Related papers  (2024-02-27T02:44:40Z)
• AI-Lorenz: A physics-data-driven framework for black-box and gray-box identification of chaotic systems with symbolic regression [2.07180164747172]
  We develop a framework that learns mathematical expressions modeling complex dynamical behaviors. We train a small neural network to learn the dynamics of a system, its rate of change in time, and missing model terms. This, in turn, enables us to predict the future evolution of the dynamical behavior.
  arXiv  Detail & Related papers  (2023-12-21T18:58:41Z)
• Interpretable learning of effective dynamics for multiscale systems [5.754251195342313]
  We propose a novel framework of Interpretable Learning Effective Dynamics (iLED) iLED offers comparable accuracy to state-of-theart recurrent neural network-based approaches. Our results show that the iLED framework can generate accurate predictions and obtain interpretable dynamics.
  arXiv  Detail & Related papers  (2023-09-11T20:29:38Z)
• Adaptive learning of effective dynamics: Adaptive real-time, online modeling for complex systems [2.6144444305800234]
  We propose a novel framework that bridges large scale simulations and reduced order models to extract and forecast adaptively effective dynamics. AdaLED employs an autoencoder to identify reduced-order representations of the system dynamics and an ensemble of probabilistic recurrent neural networks (RNNs) as the latent time-steppertemporal. The framework alternates between the computational solver and the surrogate, accelerating learned dynamics while leaving yet-to-be-learned dynamics regimes to the original solver.
  arXiv  Detail & Related papers  (2023-04-04T12:05:51Z)
• 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)
• 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)
• Leveraging the structure of dynamical systems for data-driven modeling [111.45324708884813]
  We consider the impact of the training set and its structure on the quality of the long-term prediction. We show how an informed design of the training set, based on invariants of the system and the structure of the underlying attractor, significantly improves the resulting models.
  arXiv  Detail & Related papers  (2021-12-15T20:09:20Z)
• Constructing Neural Network-Based Models for Simulating Dynamical Systems [59.0861954179401]
  Data-driven modeling is an alternative paradigm that seeks to learn an approximation of the dynamics of a system using observations of the true system. This paper provides a survey of the different ways to construct models of dynamical systems using neural networks. In addition to the basic overview, we review the related literature and outline the most significant challenges from numerical simulations that this modeling paradigm must overcome.
  arXiv  Detail & Related papers  (2021-11-02T10:51:42Z)
• 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)
• Using Data Assimilation to Train a Hybrid Forecast System that Combines Machine-Learning and Knowledge-Based Components [52.77024349608834]
  We consider the problem of data-assisted forecasting of chaotic dynamical systems when the available data is noisy partial measurements. We show that by using partial measurements of the state of the dynamical system, we can train a machine learning model to improve predictions made by an imperfect knowledge-based model.
  arXiv  Detail & Related papers  (2021-02-15T19:56:48Z)

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.