A data-driven phase and isostable reduced modeling framework for oscillatory dynamical systems

2020 ◽  
Vol 30 (1) ◽  
pp. 013121 ◽  
Author(s):  
Dan Wilson
Keyword(s):  
Dynamical Systems ◽  
Data Driven ◽  
Modeling Framework ◽  
Reduced Modeling

Uncertainty Quantification in Metallic Additive Manufacturing Through Data-Driven Modelling Based on Multi-Scale Multi-Physics Models and Limited Experiment Data

2020 ◽  
Author(s):  
Zhuo Wang ◽  
Chen Jiang ◽  
Mark F. Horstemeyer ◽  
Zhen Hu ◽  
Lei Chen
Keyword(s):  
Temperature Field ◽  
Additive Manufacturing ◽  
Uncertainty Quantification ◽  
Surrogate Modeling ◽  
Data Driven ◽  
Modeling Framework ◽  
High Quality ◽  
Experimental Calibration ◽  
Multi Scale ◽  
Metallic Additive

Abstract One of significant challenges in the metallic additive manufacturing (AM) is the presence of many sources of uncertainty that leads to variability in microstructure and properties of AM parts. Consequently, it is extremely challenging to repeat the manufacturing of a high-quality product in mass production. A trial-and-error approach usually needs to be employed to attain a product with high quality. To achieve a comprehensive uncertainty quantification (UQ) study of AM processes, we present a physics-informed data-driven modeling framework, in which multi-level data-driven surrogate models are constructed based on extensive computational data obtained by multi-scale multi-physical AM models. It starts with computationally inexpensive metamodels, followed by experimental calibration of as-built metamodels and then efficient UQ analysis of AM process. For illustration purpose, this study specifically uses the thermal level of AM process as an example, by choosing the temperature field and melt pool as quantity of interest. We have clearly showed the surrogate modeling in the presence of high-dimensional response (e.g. temperature field) during AM process, and illustrated the parameter calibration and model correction of an as-built surrogate model for reliable uncertainty quantification. The experimental calibration especially takes advantage of the high-quality AM benchmark data from National Institute of Standards and Technology (NIST). This study demonstrates the potential of the proposed data-driven UQ framework for efficiently investigating uncertainty propagation from process parameters to material microstructures, and then to macro-level mechanical properties through a combination of advanced AM multi-physics simulations, data-driven surrogate modeling and experimental calibration.

Heart Watch: Dynamical Systems Based Real Time Data Driven ECG Synthesis

2021 ◽  
Author(s):  
Ashutosh Simha ◽  
Suryansh Sharma ◽  
Sujay Narayana ◽  
R. Venkatesh Prasad
Keyword(s):  
Dynamical Systems ◽  
Real Time ◽  
Data Driven ◽  
Time Data ◽  
Real Time Data

scholarly journals Multidimensional Approximation of Nonlinear Dynamical Systems

2019 ◽  
Vol 14 (6) ◽  
Author(s):  
Patrick Gelß ◽  
Stefan Klus ◽  
Jens Eisert ◽  
Christof Schütte
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Dynamical Systems ◽  
Measurement Data ◽  
Data Driven ◽  
High Dimensional ◽  
Data Sets ◽  
Nonlinear Dynamical ◽  
Tensor Network ◽  
Wide Range ◽  
Multidimensional Approximation

A key task in the field of modeling and analyzing nonlinear dynamical systems is the recovery of unknown governing equations from measurement data only. There is a wide range of application areas for this important instance of system identification, ranging from industrial engineering and acoustic signal processing to stock market models. In order to find appropriate representations of underlying dynamical systems, various data-driven methods have been proposed by different communities. However, if the given data sets are high-dimensional, then these methods typically suffer from the curse of dimensionality. To significantly reduce the computational costs and storage consumption, we propose the method multidimensional approximation of nonlinear dynamical systems (MANDy) which combines data-driven methods with tensor network decompositions. The efficiency of the introduced approach will be illustrated with the aid of several high-dimensional nonlinear dynamical systems.

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