Deep learning for solution and inversion of structural mechanics and vibrations

Haghighat, Ehsan; Bekar, Ali Can; Madenci, Erdogan; Juanes, Rubén

doi:10.1088/978-0-7503-3487-7ch1

Cited by 9 publications

(5 citation statements)

References 33 publications

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“…The advent of PINNs [29,30] has resulted in a new era of modeling across engineering applications, spanning from solid materials to fluid dynamics [31][32][33][34]. Within the domain of fluid dynamics, PINN has been applied to solve fluid flow problems [35][36][37][38].…”

Section: Pinn and Related Literaturementioning

confidence: 99%

Physics-informed neural network for turbulent flow reconstruction in composite porous-fluid systems

Jang,

Jadidi,

Rezaeiravesh

et al. 2024

Mach. Learn.: Sci. Technol.

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This study explores the implementation of Physics-Informed Neural Networks (PINN) to analyze turbulent flow in composite porous-fluid systems. These systems are composed of a fluid-saturated porous medium and an adjacent fluid, where the flow properties are exchanged across the porous-fluid interface. The PINN model employs a novel approach combining supervised learning and enforces fidelity to flow physics through penalization by the Reynolds-Averaged Navier-Stokes (RANS) equations. Two cases were simulated for this purpose: solid block, i.e., porous media with zero porosity, and porous block with a defined porosity. The effect of providing internal training data on the accuracy of the PINN predictions for prominent flow features including leakage, channeling effect and wake recirculation were investigated. Additionally, L2 norm error, which evaluates the prediction accuracy for flow variables was studied. Furthermore, PINN training time in both cases with internal training data were considered in this study. The results showed that the PINN predictions achieved high accuracy for the prominent flow features compared to the reference RANS data. In addition, second-order internal training data in the wall-normal direction reduced the L2 norm error by 100% for the solid block case, while for the porous block case, providing training data at the porous-fluid interface, increased the prediction accuracy by nearly 40% for second-order statistics. The study elucidates the impact of the internal training data distribution on the PINN training in complex turbulent flow dynamics, underscoring the necessity of turbulent second-order statistics variables in PINN training and an additional velocity gradient treatment to enhance PINN prediction.

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Section: Pinn and Related Literaturementioning

confidence: 99%

Physics-informed neural network for turbulent flow reconstruction in composite porous-fluid systems

Jang,

Jadidi,

Rezaeiravesh

et al. 2024

Mach. Learn.: Sci. Technol.

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“…PINN can be broadly categorized into forward and inverse problems. 49,50 The forward problem seeks solutions to differential equations, while the inverse problem involves inferring mathematical model parameters from observational data. Using limited data from experimental voltage signals, we aim to estimate and validate the mechanical damping ratio, voltage source, and piezoelectric capacitance through experimentation.…”

Section: Introductionmentioning

confidence: 99%

Physics-informed neural network for parameter identification in a piezoelectric harvester

Bai,

Yeh,

Shu

2024

Active and Passive Smart Structures and Integrated Systems XVIII

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The article aims to develop a physics-informed neural network (PINN) for parameter identification in a piezoelectric harvester using experimental sampling data. The advantage of PINN lies in its efficient inverse calculation of parameters with minimal sampled signals. For instance, with a single piezoelectric oscillator, the data collection process requires only two sets of piezoelectric voltage waveforms acquired at different electric loads and excitation frequencies. The training process involves minimizing the loss function, which comprises the model-based differential equations and the sampled time-domain voltage signals. The results successfully achieve inverse parameter identification, covering mechanical damping ratio, capacitance, and voltage source (force magnitude divided by the piezoelectric constant). In addition, the voltage frequency response, based on the inverse parameters, agrees well with experimental observations, confirming the model's reliability.

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“…In contrast, physics-informed deep learning incorporates the governing equations of physics into its models, leveraging physical laws to enhance modelling robustness [14][15]. The advent of Physics-Informed Neural Networks (PINNs) has helped in a new era of numerical modelling across engineering applications, spanning from solid materials to fluid dynamics [16][17]. Within the domain of fluid dynamics, while the effectiveness of PINNs in solving Navier-Stokes equations for laminar flows has been demonstrated in several studies [18][19], the utilization of PINNs to address turbulent flows with complex flow physics has garnered relatively scant attention in the literature [20].…”

Section: Introductionmentioning

confidence: 99%

Physics Informed Neural Network in Turbulent Porous Flow: Pore-scale Flow Reconstruction

Jang,

Jadidi,

Mahmoudi

2024

Proceedings of the 9th World Congress on Momentum, Heat and Mass Transfer

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Turbulence modelling in porous media presents challenges in Computational Fluid Dynamics (CFD). While various modelling approaches have been employed to analyze turbulent flow properties, achieving both precision and cost-effectiveness remains a significant hurdle. In recent years, Deep Learning (DL), with its capacity for solving nonlinear model, has emerged as a promising solution to address these challenges. The advent of Physics-Informed Neural Networks (PINN) has expanded the scope of Deep learning applications in turbulent flow modelling. However, applying PINN to complex flow physics within porous media remains an underexplored territory. This study employs PINN to solve the Reynolds-Averaged Navier-Stokes (RANS) equations in a composite porous-fluid system, guided by supervised learning and penalized by the RANS equation to ensure fidelity to flow physics. The research aims to enhance flow prediction accuracy and explore the influence of data distribution on PINN performance in complex flow scenarios in composite porous-fluid systems. Results showed that using porous-fluid interface training data provides better accuracy, with improvements of 40% and 2% in second-order statistics. This research contributes to advancing our understanding of turbulent flows in porous media and highlights the potential of PINN as a valuable tool for exploring complex flow physics.

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Deep learning for solution and inversion of structural mechanics and vibrations

Cited by 9 publications

References 33 publications

Physics-informed neural network for turbulent flow reconstruction in composite porous-fluid systems

Physics-informed neural network for turbulent flow reconstruction in composite porous-fluid systems

Physics-informed neural network for parameter identification in a piezoelectric harvester

Physics Informed Neural Network in Turbulent Porous Flow: Pore-scale Flow Reconstruction

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