scholarly journals Data Driven Solutions and Discoveries in Mechanics Using Physics Informed Neural Network

2020 ◽  
Author(s):  
Qi Zhang ◽  
Yilin Chen ◽  
Ziyi Yang
Keyword(s):  
Neural Network ◽  
Differential Equations ◽  
Automatic Differentiation ◽  
Numerical Solutions ◽  
Data Driven ◽  
Attractive Alternative ◽  
The Finite Element Method ◽  
The Neural Network ◽  
Engineering Problems ◽  
Free Parameters

Deep learning has achieved remarkable success in diverse computer science applications, however, its use in other traditional engineering fields has emerged only recently. In this project, we solved several mechanics problems governed by differential equations, using physics informed neural networks (PINN). The PINN embeds the differential equations into the loss of the neural network using automatic differentiation. We present our developments in the context of solving two main classes of problems: data-driven solutions and data-driven discoveries, and we compare the results with either analytical solutions or numerical solutions using the finite element method. The remarkable achievements of the PINN model shown in this report suggest the bright prospect of the physics-informed surrogate models that are fully differentiable with respect to all input coordinates and free parameters. More broadly, this study shows that PINN provides an attractive alternative to solve traditional engineering problems.

scholarly journals Data-Driven Solutions and Discoveries in Mechanics Using Physics Informed Neural Network

2020 ◽  
Author(s):  
Qi Zhang ◽  
Yilin Chen ◽  
Ziyi Yang
Keyword(s):  
Neural Network ◽  
Differential Equations ◽  
Automatic Differentiation ◽  
Numerical Solutions ◽  
Data Driven ◽  
Attractive Alternative ◽  
The Finite Element Method ◽  
The Neural Network ◽  
Engineering Problems ◽  
Free Parameters

Deep learning has achieved remarkable success in diverse computer science applications, however, its use in other traditional engineering fields has emerged only recently. In this project, we solved several mechanics problems governed by differential equations, using physics informed neural networks (PINN). The PINN embeds the differential equations into the loss of the neural network using automatic differentiation. We present our developments in the context of solving two main classes of problems: data-driven solutions and data-driven discoveries, and we compare the results with either analytical solutions or numerical solutions using the finite element method. The remarkable achievements of the PINN model shown in this report suggest the bright prospect of the physics-informed surrogate models that are fully differentiable with respect to all input coordinates and free parameters. More broadly, this study shows that PINN provides an attractive alternative to solve traditional engineering problems.

scholarly journals Discretization and machine learning approximation of BSDEs with a constraint on the Gains-process

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Idris Kharroubi ◽  
Thomas Lim ◽  
Xavier Warin
Keyword(s):  
Neural Network ◽  
Machine Learning ◽  
Neural Networks ◽  
Differential Equations ◽  
Numerical Experiments ◽  
Optimization Problem ◽  
Learning Approach ◽  
The Neural Network ◽  
Machine Learning Approach ◽  
Mesh Grid

AbstractWe study the approximation of backward stochastic differential equations (BSDEs for short) with a constraint on the gains process. We first discretize the constraint by applying a so-called facelift operator at times of a grid. We show that this discretely constrained BSDE converges to the continuously constrained one as the mesh grid converges to zero. We then focus on the approximation of the discretely constrained BSDE. For that we adopt a machine learning approach. We show that the facelift can be approximated by an optimization problem over a class of neural networks under constraints on the neural network and its derivative. We then derive an algorithm converging to the discretely constrained BSDE as the number of neurons goes to infinity. We end by numerical experiments.

Estimation of Site Amplification from Geotechnical Array Data Using Neural Networks

2021 ◽  
Author(s):  
Daniel Roten ◽  
Kim B. Olsen
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Site Response ◽  
Site Amplification ◽  
Data Driven ◽  
Vertical Array ◽  
The Neural Network ◽  
Simplifying Assumptions ◽  
The Mean ◽  
Fully Connected

ABSTRACT We use deep learning to predict surface-to-borehole Fourier amplification functions (AFs) from discretized shear-wave velocity profiles. Specifically, we train a fully connected neural network and a convolutional neural network using mean AFs observed at ∼600 KiK-net vertical array sites. Compared with predictions based on theoretical SH 1D amplifications, the neural network (NN) results in up to 50% reduction of the mean squared log error between predictions and observations at sites not used for training. In the future, NNs may lead to a purely data-driven prediction of site response that is independent of proxies or simplifying assumptions.

scholarly journals Application of deep neural network reveals novel effects of maternal pre-conception exposure to nicotine on rat pup behavior

2020 ◽  
Author(s):  
Reza Torabi ◽  
Serena Jenkins ◽  
Allonna Harker ◽  
Ian Q. Whishaw ◽  
Robbin Gibb ◽  
...  
Keyword(s):  
Neural Network ◽  
Motor Development ◽  
Deep Neural Network ◽  
Data Driven ◽  
Nicotine Exposure ◽  
Movement Initiation ◽  
Warm Up ◽  
Rat Pups ◽  
The Neural Network ◽  
Data Driven Approach

We present a deep neural network for data-driven analyses of infant rat behavior in an open field task. The network was applied to study the effect of maternal nicotine exposure prior to conception on offspring motor development. The neural network outperformed human expert designed animal locomotion measures in distinguishing rat pups born to nicotine exposed dams versus control dams. Notably, the network discovered novel movement alterations in posture, movement initiation and a stereotypy in warm-up behavior (the initiation of movement along specific dimensions) that were predictive of nicotine exposure. The results suggest that maternal preconception nicotine exposure delays and alters offspring motor development. In summary, we demonstrated that a deep neural network can automatically assess animal behavior with high accuracy, and that it offers a data-driven approach to investigating pharmacological effects on brain development.

scholarly journals ‘Ring Breaker’: Neural Network Driven Synthesis Prediction of the Ring System Chemical Space

2020 ◽  
Author(s):  
Amol Thakkar ◽  
Nidhal Selmi ◽  
Jean-Louis Reymond ◽  
Ola Engkvist ◽  
Esben Jannik Bjerrum
Keyword(s):  
Neural Network ◽  
Chemical Space ◽  
Ring System ◽  
Data Driven ◽  
Ring Systems ◽  
The Neural Network ◽  
Synthetic Accessibility ◽  
Synthesis Planning ◽  
Data Driven Approach ◽  
Synthetic Routes

<p></p><p>Ring systems in pharmaceuticals, agrochemicals and dyes are ubiquitous chemical motifs. Whilst the synthesis of common ring systems is well described, and novel ring systems can be readily computationally enumerated, the synthetic accessibility of unprecedented ring systems remains a challenge. ‘Ring Breaker’ uses a data-driven approach to enable the prediction of ring-forming reactions, for which we have demonstrated its utility on frequently found and unprecedented ring systems, in agreement with literature syntheses. We demonstrate the performance of the neural network on a range of ring fragments from the ZINC and DrugBank databases and highlight its potential for incorporation into computer aided synthesis planning tools. These approaches to ring formation and retrosynthetic disconnection offer opportunities for chemists to explore and select more efficient syntheses/synthetic routes. </p><br><p></p>

scholarly journals Solving parametric PDE problems with artificial neural networks

2020 ◽  
pp. 1-15
Author(s):  
YUEHAW KHOO ◽  
JIANFENG LU ◽  
LEXING YING
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Artificial Neural Networks ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Time Evolution ◽  
Random Coefficients ◽  
Numerical Partial Differential Equations ◽  
The Neural Network ◽  
Physical Quantities

The curse of dimensionality is commonly encountered in numerical partial differential equations (PDE), especially when uncertainties have to be modelled into the equations as random coefficients. However, very often the variability of physical quantities derived from PDE can be captured by a few features on the space of the coefficient fields. Based on such observation, we propose using neural network to parameterise the physical quantity of interest as a function of input coefficients. The representability of such quantity using a neural network can be justified by viewing the neural network as performing time evolution to find the solutions to the PDE. We further demonstrate the simplicity and accuracy of the approach through notable examples of PDEs in engineering and physics.

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