Sensitivity-Analysis-Driven Surrogate Model for Molten Salt Reactors Control

Cervi, Eric; Lu, Xuefei; Cammi, Antonio; Maio, Francesco Di; Zio, Enrico

doi:10.3390/jne3040016

Cited by 2 publications

(3 citation statements)

References 44 publications

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“…with corresponding constraints for the right, top and bottom sides. If Equation ( 29) holds and Equation (30) holds for all sides then the boundary conditions for the left side, i = 1, can be implemented with:…”

Section: Inputsmentioning

confidence: 99%

“…The approach described in this article is a new and alter-obtained through this new approach are identical to those obtained by standard codes, but the advantage of performing all operations through an AI library is that the code will run efficiently on all architectures. Furthermore, through the neural networks, the latest developments can be realised for methods such as sensitivities [30] , uncertainty quantification [31,32] and data assimilation [33]. Although AI is becoming popular for nuclear engineering, it is often through surrogate modelling, which requires training a neural network.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Solving the Discretised Neutron Diffusion Equations using Neural Networks

Phillips¹,

Heaney²,

Boyang³

et al. 2023

Preprint

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This paper presents a new approach which uses the tools within Artificial Intelligence (AI) software libraries as an alternative way of solving partial differential equations (PDEs) that have been discretised using standard numerical methods. In particular, we describe how to represent numerical discretisations arising from the finite volume and finite element methods by pre-determining the weights of convolutional layers within a neural network. As the weights are defined by the discretisation scheme, no training of the network is required and the solutions obtained are identical (accounting for solver tolerances) to those obtained with standard codes often written in Fortran or C++. We also explain how to implement the Jacobi method and a multigrid solver using the functions available in AI libraries. For the latter, we use a U-Net architecture which is able to represent a sawtooth multigrid method. A benefit of using AI libraries in this way is that one can exploit their power and their built-in technologies. For example, their executions are already optimised for different computer architectures, whether it be CPUs, GPUs or new-generation AI processors.In this article, we apply the proposed approach to eigenvalue problems in reactor physics where neutron transport is described by diffusion theory. For a fuel assembly benchmark, we demonstrate that the solution obtained from our new approach is the same (accounting for solver tolerances) as that obtained from the same discretisation coded in a standard way using Fortran. We then proceed to solve a reactor core benchmark using the new approach.

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Section: Inputsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Solving the Discretised Neutron Diffusion Equations using Neural Networks

Phillips¹,

Heaney²,

Boyang³

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

“…Ultimately solutions obtained through this new approach are identical to those obtained by standard codes, but the advantage of performing all operations through an AI library is that the code will run on all architectures (that support AI libraries) without the need for modification. Furthermore, through the neural networks, the latest developments can be realised for methods such as sensitivities, 32 uncertainty quantification 33,34 and data assimilation. 35 Although AI is becoming popular for nuclear engineering, it is often through surrogate modelling, which requires training a neural network.…”

Section: Introductionmentioning

confidence: 99%

Solving the discretised neutron diffusion equations using neural networks

Phillips

Heaney

Chen

et al. 2023

Numerical Meth Engineering

View full text Add to dashboard Cite

This paper presents a new approach which uses the tools within artificial intelligence (AI) software libraries as an alternative way of solving partial differential equations (PDEs) that have been discretised using standard numerical methods. In particular, we describe how to represent numerical discretisations arising from the finite volume and finite element methods by pre‐determining the weights of convolutional layers within a neural network. As the weights are defined by the discretisation scheme, no training of the network is required and the solutions obtained are identical (accounting for solver tolerances) to those obtained with standard codes often written in Fortran or C++. We also explain how to implement the Jacobi method and a multigrid solver using the functions available in AI libraries. For the latter, we use a U‐Net architecture which is able to represent a sawtooth multigrid method. A benefit of using AI libraries in this way is that one can exploit their built‐in technologies to enable the same code to run on different computer architectures (such as central processing units, graphics processing units or new‐generation AI processors) without any modification. In this article, we apply the proposed approach to eigenvalue problems in reactor physics where neutron transport is described by diffusion theory. For a fuel assembly benchmark, we demonstrate that the solution obtained from our new approach is the same (accounting for solver tolerances) as that obtained from the same discretisation coded in a standard way using Fortran. We then proceed to solve a reactor core benchmark using the new approach. For both benchmarks we give timings for the neural network implementation run on a CPU and a GPU, and a serial Fortran code run on a CPU.

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Sensitivity-Analysis-Driven Surrogate Model for Molten Salt Reactors Control

Cited by 2 publications

References 44 publications

Solving the Discretised Neutron Diffusion Equations using Neural Networks

Solving the Discretised Neutron Diffusion Equations using Neural Networks

Solving the discretised neutron diffusion equations using neural networks

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