A Constrained Backpropagation Approach for the Adaptive Solution of Partial Differential Equations

Rudd, Keith; Muro, Gianluca Di; Ferrari, Silvia

doi:10.1109/tnnls.2013.2277601

Cited by 55 publications

(46 citation statements)

References 19 publications

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“…In the context of PDEs single hidden layer ANNs have traditionally been used to solve PDEs since one hidden layer with sufficiently many neurons is sufficient for approximating any function and as all gradients that are needed can be computed in analytical closed form [21,22,26]. More recently there is a limited but emerging literature on the use of deep ANNs to solve PDEs [31,30,7,4,29,8,33]. In general ANNs have the benefits that they are smooth, analytical functions which can be evaluated at any point inside, or even outside, the domain without reconstruction.…”

Section: Introductionmentioning

confidence: 99%

A unified deep artificial neural network approach to partial differential equations in complex geometries

2018

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In this paper we use deep feedforward artificial neural networks to approximate solutions to partial differential equations in complex geometries. We show how to modify the backpropagation algorithm to compute the partial derivatives of the network output with respect to the space variables which is needed to approximate the differential operator. The method is based on an ansatz for the solution which requires nothing but feedforward neural networks and an unconstrained gradient based optimization method such as gradient descent or a quasi-Newton method.We show an example where classical mesh based methods cannot be used and neural networks can be seen as an attractive alternative. Finally, we highlight the benefits of deep compared to shallow neural networks and device some other convergence enhancing techniques.

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Section: Introductionmentioning

confidence: 99%

A unified deep artificial neural network approach to partial differential equations in complex geometries

2018

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“…In the first phase, a multi-layered perceptron (MLP) network based on a gradient descent learning algorithm is used by the neuro-fuzzy model to adapt the parameters of the fuzzy model [16]. Learning from data and approximate reasoning is simplifies by this architecture, as well as knowledge acquisition.…”

Section: A Hybrid Neural Fuzzy Inference Systemmentioning

confidence: 99%

Energy flexibility assessment of a multi agent-based smart home energy system

Gazafroudi

Pinto

Prieto‐Castrillo

et al. 2017

2017 IEEE 17th International Conference on Ubiquitous Wireless Broadband (ICUWB)

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Abstract-Power systems worldwide are complex and challenging environments. The increasing necessity for an adequate integration of renewable energy sources is resulting in a rising complexity in power systems operation. Multi-agent based simulation platforms have proven to be a good option to study the several issues related to these systems. In a smaller scale, a home energy management system would be effective for the both sides of the network. It can reduce the electricity costs of the demand side, and it can assist to relieve the grid congestion in peak times. This paper represents a domestic energy management system as part of a multi-agent system that models the smart home energy system. Our proposed system consists of energy management and predictor systems. This way, homes are able to transact with the local electricity market according to the energy flexibility that is provided by the electric vehicle, and it can manage produced electrical energy of the photovoltaic system inside of the home.

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“…In the learning phase, the neuro-fuzzy model in the HyFIS uses a multilayered perceptron (MLP) network based on a gradient descent learning algorithm for adapting the parameters of the fuzzy model [13]. The architecture simplifies learning from data and approximate reasoning, as well as knowledge acquisition.…”

Section: ) Hybrid Neural Fuzzy Inference System (Hyfis)mentioning

confidence: 99%

Energy consumption forecasting using neuro-fuzzy inference systems: Thales TRT building case study

Jozi

Pinto

Praça

et al. 2017

2017 IEEE Symposium Series on Computational Intelligence (SSCI)

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Electrical energy consumption forecasting is, nowadays, essential in order to deal with the new paradigm of consumers' active participation in the power and energy system. The uncertainty related to the variability of consumption is associated to numerous factors, such as consumers' habits, the environmental temperature, luminosity, etc. Current forecasting methods are not suitable to deal with such a combination of input variables, with often highly variable influence on the out-comesthe actual energy consumption. This paper presents a study on the application of five different methods based on fuzzy rulebased systems. This type of method is able to find associations between the distinct input variables, thus creating rules that support and improve the actual forecasting process. A case study is presented, showing the results of applying these five methods to predict the consumption of a real building: the Thales TRT building, in France.

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A Constrained Backpropagation Approach for the Adaptive Solution of Partial Differential Equations

Cited by 55 publications

References 19 publications

A unified deep artificial neural network approach to partial differential equations in complex geometries

A unified deep artificial neural network approach to partial differential equations in complex geometries

Energy flexibility assessment of a multi agent-based smart home energy system

Energy consumption forecasting using neuro-fuzzy inference systems: Thales TRT building case study

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