A classical density functional from machine learning and a convolutional neural network
We use machine learning methods to approximate a classical density functional. As a study case, we choose the model problem of a Lennard Jones fluid in one dimension where there is no exact solution available and training data sets must be obtained from simulations. After separating the excess fr...
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| Format: | Article |
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2019-02-01
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| Series: | SciPost Physics |
| Online Access: | https://scipost.org/SciPostPhys.6.2.025 |
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doaj-7b67fe2bcdee4c7097030752988e02d72020-11-24T21:17:55ZengSciPostSciPost Physics2542-46532019-02-016202510.21468/SciPostPhys.6.2.025A classical density functional from machine learning and a convolutional neural networkShang-Chun Lin, Martin OettelWe use machine learning methods to approximate a classical density functional. As a study case, we choose the model problem of a Lennard Jones fluid in one dimension where there is no exact solution available and training data sets must be obtained from simulations. After separating the excess free energy functional into a "repulsive" and an "attractive" part, machine learning finds a functional in weighted density form for the attractive part. The density profile at a hard wall shows good agreement for thermodynamic conditions beyond the training set conditions. This also holds for the equation of state if it is evaluated near the training temperature. We discuss the applicability to problems in higher dimensions.https://scipost.org/SciPostPhys.6.2.025 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Shang-Chun Lin, Martin Oettel |
| spellingShingle |
Shang-Chun Lin, Martin Oettel A classical density functional from machine learning and a convolutional neural network SciPost Physics |
| author_facet |
Shang-Chun Lin, Martin Oettel |
| author_sort |
Shang-Chun Lin, Martin Oettel |
| title |
A classical density functional from machine learning and a convolutional neural network |
| title_short |
A classical density functional from machine learning and a convolutional neural network |
| title_full |
A classical density functional from machine learning and a convolutional neural network |
| title_fullStr |
A classical density functional from machine learning and a convolutional neural network |
| title_full_unstemmed |
A classical density functional from machine learning and a convolutional neural network |
| title_sort |
classical density functional from machine learning and a convolutional neural network |
| publisher |
SciPost |
| series |
SciPost Physics |
| issn |
2542-4653 |
| publishDate |
2019-02-01 |
| description |
We use machine learning methods to approximate a classical density
functional. As a study case, we choose the model problem of a Lennard Jones
fluid in one dimension where there is no exact solution available and training
data sets must be obtained from simulations. After separating the excess free
energy functional into a "repulsive" and an "attractive" part, machine learning
finds a functional in weighted density form for the attractive part. The
density profile at a hard wall shows good agreement for thermodynamic
conditions beyond the training set conditions. This also holds for the equation
of state if it is evaluated near the training temperature. We discuss the
applicability to problems in higher dimensions. |
| url |
https://scipost.org/SciPostPhys.6.2.025 |
| work_keys_str_mv |
AT shangchunlinmartinoettel aclassicaldensityfunctionalfrommachinelearningandaconvolutionalneuralnetwork AT shangchunlinmartinoettel classicaldensityfunctionalfrommachinelearningandaconvolutionalneuralnetwork |
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1726011320880332800 |