Deep learning‐based reduced order models for the real‐time simulation of the nonlinear dynamics of microstructures

Reduced order modeling of nonlinear microstructures through Proper Orthogonal Decomposition

(2022) Giorgio Gobat et al.   MECHANICAL SYSTEMS AND SIGNAL PROCESSING

Generalization of the Neville–Aitken interpolation algorithm on Grassmann manifolds: Applications to reduced order model

(2021) Rolando Mosquera et al.   INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS

A Comprehensive Deep Learning-Based Approach to Reduced Order Modeling of Nonlinear Time-Dependent Parametrized PDEs

(2021) Stefania Fresca et al.   JOURNAL OF SCIENTIFIC COMPUTING

A physics-informed deep learning framework for inversion and surrogate modeling in solid mechanics

(2021) Ehsan Haghighat et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Model order reduction based on direct normal form: application to large finite element MEMS structures featuring internal resonance

(2021) Andrea Opreni et al.   NONLINEAR DYNAMICS

Direct computation of nonlinear mapping via normal form for reduced-order models of finite element nonlinear structures

(2021) Alessandra Vizzaccaro et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition

(2021) Stefania Fresca et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Machine Learning Approach to Model Order Reduction of Nonlinear Systems via Autoencoder and LSTM Networks

(2021) Thomas Simpson et al.   JOURNAL OF ENGINEERING MECHANICS

Deep learning-based reduced order models in cardiac electrophysiology

(2020) Stefania Fresca et al.   PLoS One

Nonlinear Response of PZT-Actuated Resonant Micromirrors

(2020) Attilio Frangi et al.   JOURNAL OF MICROELECTROMECHANICAL SYSTEMS

Numerical Modelling of Non-Linearities in MEMS Resonators

(2020) Valentina Zega et al.   JOURNAL OF MICROELECTROMECHANICAL SYSTEMS

Review for order reduction based on proper orthogonal decomposition and outlooks of applications in mechanical systems

(2019) Kuan Lu et al.   MECHANICAL SYSTEMS AND SIGNAL PROCESSING

A Taylor series-based continuation method for solutions of dynamical systems

(2019) Louis Guillot et al.   NONLINEAR DYNAMICS

Construction of reduced-order models for fluid flows using deep feedforward neural networks

(2019) Hugo F. S. Lui et al.   JOURNAL OF FLUID MECHANICS

Micro-beam resonator parametrically excited by electro-thermal Joule’s heating and its use as a flow sensor

(2019) Ben Torteman et al.   NONLINEAR DYNAMICS

A Nonlinear Rate Microsensor utilising Internal Resonance

(2019) Atabak Sarrafan et al.   Scientific Reports

Reduced order modelling of the non-linear stiffness in MEMS resonators

(2019) Attilio Frangi et al.   INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS

Data-driven discovery of coordinates and governing equations

(2019) Kathleen Champion et al.   PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA

Feasibility study of a resonant accelerometer with bistable electrostatically actuated cantilever as a sensing element

(2019) Omer HaLevy et al.   INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS

Model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders

(2019) Kookjin Lee et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Numerical approximation of parametrized problems in cardiac electrophysiology by a local reduced basis method

(2018) Stefano Pagani et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Reduced order modeling for nonlinear structural analysis using Gaussian process regression

(2018) Mengwu Guo et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Automated computation of autonomous spectral submanifolds for nonlinear modal analysis

(2018) Sten Ponsioen et al.   JOURNAL OF SOUND AND VIBRATION

Sparse identification of nonlinear dynamics for model predictive control in the low-data limit

(2018) E. Kaiser et al.   PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES

Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

(2018) M. Raissi et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Data-driven reduced order modeling for time-dependent problems

(2018) Mengwu Guo et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Model identification of reduced order fluid dynamics systems using deep learning

(2017) Z. Wang et al.   INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS

Self-induced parametric amplification in ring resonating gyroscopes

(2017) Pavel M. Polunin et al.   INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS

Designing flows to resolve human and environmental water needs in a dam-regulated river

(2017) William Chen et al.   Nature Communications

Flow sensing by buckling monitoring of electrothermally actuated double-clamped micro beams

(2016) Y. Kessler et al.   APPLIED PHYSICS LETTERS

Exploiting nonlinear amplitude-frequency dependence for temperature compensation in silicon micromechanical resonators

(2016) M. Defoort et al.   APPLIED PHYSICS LETTERS

Numerical computation of nonlinear normal modes in mechanical engineering

(2016) L. Renson et al.   JOURNAL OF SOUND AND VIBRATION

Discovering governing equations from data by sparse identification of nonlinear dynamical systems

(2016) Steven L. Brunton et al.   PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA

Nonlinear-Based MEMS Sensors and Active Switches for Gas Detection

(2016) Adam Bouchaala et al.   SENSORS

The harmonic balance method for bifurcation analysis of large-scale nonlinear mechanical systems

(2015) T. Detroux et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Threshold Shock Sensor Based on a Bistable Mechanism: Design, Modeling, and Measurements

(2015) Attilio Frangi et al.   JOURNAL OF MICROELECTROMECHANICAL SYSTEMS

Self-induced parametric amplification arising from nonlinear elastic coupling in a micromechanical resonating disk gyroscope

(2015) Sarah H. Nitzan et al.   Scientific Reports

A review of indirect/non-intrusive reduced order modeling of nonlinear geometric structures

(2013) Marc P. Mignolet et al.   JOURNAL OF SOUND AND VIBRATION

A comparison of model reduction techniques from structural dynamics, numerical mathematics and systems and control

(2013) B. Besselink et al.   JOURNAL OF SOUND AND VIBRATION

Nonlinear model order reduction based on local reduced-order bases

(2012) David Amsallem et al.   INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING

Design of nonlinear springs for attaining a linear response in gap-closing electrostatic actuators

(2012) Ben Rivlin et al.   INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES

Finding Structure with Randomness: Probabilistic Algorithms for Constructing Approximate Matrix Decompositions

(2011) N. Halko et al.   SIAM REVIEW

Nonlinear Dynamics and Its Applications in Micro- and Nanoresonators

(2010) Jeffrey F. Rhoads et al.   JOURNAL OF DYNAMIC SYSTEMS MEASUREMENT AND CONTROL-TRANSACTIONS OF THE ASME

Nonlinear Model Reduction via Discrete Empirical Interpolation

(2010) Saifon Chaturantabut et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

Phase Feedback for Nonlinear MEM Resonators in Oscillator Circuits

(2009) R.M.C. Mestrom et al.   IEEE-ASME TRANSACTIONS ON MECHATRONICS

Interpolation Method for Adapting Reduced-Order Models and Application to Aeroelasticity

(2008) D. Amsallem et al.   AIAA JOURNAL

A general multipurpose interpolation procedure: the magic points

(2008) Yvon Maday et al.   COMMUNICATIONS ON PURE AND APPLIED ANALYSIS

Nonlinear normal modes, Part I: A useful framework for the structural dynamicist

(2008) G. Kerschen et al.   MECHANICAL SYSTEMS AND SIGNAL PROCESSING