scholarly journals Optimization with learning-informed differential equation constraints and its applications

2021 ◽  
Author(s):  
Michael Hintermüller ◽  
Kostas Papafitsoros ◽  
Guozhi Dong
Keyword(s):  
Neural Network ◽  
Differential Equation ◽  
Optimal Control ◽  
Artificial Neural Network ◽  
Optimization Problems ◽  
Elliptic Partial Differential Equations ◽  
Data Driven ◽  
General Context ◽  
Constrained Optimization Problems ◽  
Semilinear Elliptic

Inspired by applications in optimal control of semilinear elliptic partial differential equations and physics-integrated imaging,  differential equation constrained optimization problems with constituents that are only accessible through data-driven techniques are studied. A particular focus is on the analysis and on numerical methods for problems with machine-learned components. For a rather general context, an error analysis is provided, and particular properties resulting from artificial neural network based approximations are addressed. Moreover, for each of the two inspiring applications analytical details are presented and numerical results are provided.

Feed-forward artificial neural network provides data-driven inference of functional connectivity

2019 ◽  
Vol 29 (9) ◽  
pp. 091101 ◽  
Author(s):  
Nikita Frolov ◽  
Vladimir Maksimenko ◽  
Annika Lüttjohann ◽  
Alexey Koronovskii ◽  
Alexander Hramov
Keyword(s):  
Neural Network ◽  
Artificial Neural Network ◽  
Functional Connectivity ◽  
Data Driven ◽  
Feed Forward ◽  
Artificial Neural

Artificial Neural Network for Solving the Inventory Control Problem in Fuzzy Environments

2021 ◽  
pp. 126-143
Author(s):  
Mostafijur Rahaman ◽  
Sankar Prasad Mondal ◽  
Shariful Alam
Keyword(s):  
Neural Network ◽  
Differential Equation ◽  
Neural Networks ◽  
Artificial Neural Network ◽  
Artificial Neural Networks ◽  
Inventory Control ◽  
Solution Procedure ◽  
Control Problems ◽  
Fuzzy Environment ◽  
Artificial Neural

In this chapter, different inventory control problems are formulated in fuzzy environment and solved by artificial neural network. Due to present the non-linearity associated with the differential equation in fuzzy environment, the solution procedure may be very complicated. To avoid the situation, artificial neural networks play an important role. In this chapter, different inventory control problems are formulated in fuzzy environment and solved by artificial neural network. Due to present the non-linearity associated with the differential equation in fuzzy environment, the solution procedure may be very complicated. To avoid the situation, artificial neural networks play an important role.

scholarly journals Data-driven modeling to optimize the injection well placement for waterflooding in heterogeneous reservoirs applying artificial neural networks and reducing observation cost

2020 ◽  
Vol 38 (6) ◽  
pp. 2413-2435 ◽  
Author(s):  
Xinwei Xiong ◽  
Kyung Jae Lee
Keyword(s):  
Neural Network ◽  
Artificial Neural Network ◽  
Injection Well ◽  
Data Driven ◽  
Well Placement ◽  
Heterogeneous Reservoirs ◽  
Modeling Approach ◽  
Artificial Neural ◽  
Well Data ◽  
Data Driven Modeling

Secondary recovery methods such as waterflooding are often applied to depleted reservoirs for enhancing oil and gas production. Given that a large number of discretized elements are required in the numerical simulations of heterogeneous reservoirs, it is not feasible to run multiple full-physics simulations. In this regard, we propose a data-driven modeling approach to efficiently predict the hydrocarbon production and greatly reduce the computational and observation cost in such problems. We predict the fluid productions as a function of heterogeneity and injection well placement by applying artificial neural network with small number of training dataset, which are obtained with full-physics simulation models. To improve the accuracy of predictions, we utilize well data at producer and injector to achieve economic and efficient prediction without requiring any geological information on reservoir. The suggested artificial neural network modeling approach only utilizing well data enables the efficient decision making with reduced computational and observation cost.

scholarly journals An Optimal Implementation on FPGA of a Hopfield Neural Network

2011 ◽  
Vol 2011 ◽  
pp. 1-9 ◽  
Author(s):  
W. Mansour ◽  
R. Ayoubi ◽  
H. Ziade ◽  
R. Velazco ◽  
W. EL Falou
Keyword(s):  
Neural Network ◽  
Artificial Neural Network ◽  
High Performance ◽  
Optimization Problems ◽  
Parallel Architecture ◽  
Hopfield Neural Network ◽  
Noise Removal ◽  
Combinatorial Optimization Problems ◽  
Artificial Neural Network Ann ◽  
Optimal Implementation

The associative Hopfield memory is a form of recurrent Artificial Neural Network (ANN) that can be used in applications such as pattern recognition, noise removal, information retrieval, and combinatorial optimization problems. This paper presents the implementation of the Hopfield Neural Network (HNN) parallel architecture on a SRAM-based FPGA. The main advantage of the proposed implementation is its high performance and cost effectiveness: it requires O(1) multiplications and O(log⁡ N) additions, whereas most others require O(N) multiplications and O(N) additions.

MATHEMATICAL-ARTIFICIAL NEURAL NETWORK HYBRID MODEL TO PREDICT ROLL FORCE DURING HOT ROLLING OF STEEL

2013 ◽  
Vol 02 (01) ◽  
pp. 1350004 ◽  
Author(s):  
S. RATH ◽  
P. P. SENGUPTA ◽  
A. P. SINGH ◽  
A. K. MARIK ◽  
P. TALUKDAR
Keyword(s):  
Neural Network ◽  
Mathematical Model ◽  
Artificial Neural Network ◽  
Flow Stress ◽  
Mathematical Models ◽  
Hybrid Model ◽  
Data Driven ◽  
Roll Force ◽  
Hot Strip ◽  
Artificial Neural

Accurate prediction of roll force during hot strip rolling is essential for model based operation of hot strip mills. Traditionally, mathematical models based on theory of plastic deformation have been used for prediction of roll force. In the last decade, data driven models like artificial neural network have been tried for prediction of roll force. Pure mathematical models have accuracy limitations whereas data driven models have difficulty in convergence when applied to industrial conditions. Hybrid models by integrating the traditional mathematical formulations and data driven methods are being developed in different parts of world. This paper discusses the methodology of development of an innovative hybrid mathematical-artificial neural network model. In mathematical model, the most important factor influencing accuracy is flow stress of steel. Coefficients of standard flow stress equation, calculated by parameter estimation technique, have been used in the model. The hybrid model has been trained and validated with input and output data collected from finishing stands of Hot Strip Mill, Bokaro Steel Plant, India. It has been found that the model accuracy has been improved with use of hybrid model, over the traditional mathematical model.

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