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Physics Guided Recurrent Neural Networks For Modeling Dynamical Systems: Application to Monitoring Water Temperature And Quality In Lakes
In this paper, we introduce a novel framework for combining scientific k...
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Time-series machine-learning error models for approximate solutions to parameterized dynamical systems
This work proposes a machine-learning framework for modeling the error i...
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Modeling of Missing Dynamical Systems: Deriving Parametric Models using a Nonparametric Framework
In this paper, we consider modeling missing dynamics with a non-Markovia...
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Using recurrent neural networks for nonlinear component computation in advection-dominated reduced-order models
Rapid simulations of advection-dominated problems are vital for multiple...
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What you need to know to train recurrent neural networks to make Flip Flops memories and more
Training neural networks to perform different tasks is relevant across v...
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Learning Nonlinear Dynamics and Chaos: A Universal Framework for Knowledge-Based System Identification and Prediction
We present a universal framework for learning the behavior of dynamical ...
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Using machine-learning modelling to understand macroscopic dynamics in a system of coupled maps
Machine learning techniques not only offer efficient tools for modelling...
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Machine Learning for Prediction with Missing Dynamics
This article presents a general framework for recovering missing dynamical systems using available data and machine learning techniques. The proposed framework reformulates the prediction problem as a supervised learning problem to approximate a map that takes the memories of the resolved and identifiable unresolved variables to the missing components in the resolved dynamics. We demonstrate the effectiveness of the proposed framework with a theoretical guarantee of a path-wise convergence of the resolved variables up to finite time and numerical tests on prototypical models in various scientific domains. These include the 57-mode barotropic stress models with multiscale interactions that mimic the blocked and unblocked patterns observed in the atmosphere, the nonlinear Schrödinger equation which found many applications in physics such as optics and Bose-Einstein-Condense, the Kuramoto-Sivashinsky equation which spatiotemporal chaotic pattern formation models trapped ion mode in plasma and phase dynamics in reaction-diffusion systems. While many machine learning techniques can be used to validate the proposed framework, we found that recurrent neural networks outperform kernel regression methods in terms of recovering the trajectory of the resolved components and the equilibrium one-point and two-point statistics. This superb performance suggests that recurrent neural networks are an effective tool for recovering the missing dynamics that involves approximation of high-dimensional functions.
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