UntitledSource: Journal of Computing and Information Science in Engineering:;2022:;volume( 023 ):;issue: 003::page 31008-1DOI: 10.1115/1.4055316Publisher: The American Society of Mechanical Engineers (ASME)
Abstract: Data sparsity is still the main challenge to apply machine learning models to solve complex scientific and engineering problems. The root cause is the “curse of dimensionality” in training these models. Training algorithms need to explore and exploit in a very high-dimensional parameter space to search the optimal parameters for complex models. In this study, a new scheme of multifidelity physics-constrained neural networks with minimax architecture is proposed to improve the data efficiency of training neural networks by incorporating physical knowledge as constraints and sampling data with various fidelities. In this new framework, fully connected neural networks with two levels of fidelities are combined to improve the prediction accuracy. The low-fidelity neural network is used to approximate the low-fidelity data, whereas the high-fidelity neural network is adopted to approximate the correlation function between the low-fidelity and high-fidelity data. To systematically search the optimal weights of various losses for reducing the training time, the Dual-Dimer algorithm is adopted to search high-order saddle points of the minimax optimization problem. The proposed framework is demonstrated with two-dimensional heat transfer, phase transition, and dendritic growth problems, which are fundamental in materials modeling. With the same set of training data, the prediction error of the multifidelity physics-constrained neural network with minimax architecture can be two orders of magnitude lower than that of the multifidelity neural network with minimax architecture.
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| contributor author | Liu, Dehao | |
| contributor author | Pusarla, Pranav | |
| contributor author | Wang, Yan | |
| date accessioned | 2023-08-16T18:30:52Z | |
| date available | 2023-08-16T18:30:52Z | |
| date copyright | 12/9/2022 12:00:00 AM | |
| date issued | 2022 | |
| identifier issn | 1530-9827 | |
| identifier other | jcise_23_3_031008.pdf | |
| identifier uri | http://yetl.yabesh.ir/yetl1/handle/yetl/4292071 | |
| description abstract | Data sparsity is still the main challenge to apply machine learning models to solve complex scientific and engineering problems. The root cause is the “curse of dimensionality” in training these models. Training algorithms need to explore and exploit in a very high-dimensional parameter space to search the optimal parameters for complex models. In this study, a new scheme of multifidelity physics-constrained neural networks with minimax architecture is proposed to improve the data efficiency of training neural networks by incorporating physical knowledge as constraints and sampling data with various fidelities. In this new framework, fully connected neural networks with two levels of fidelities are combined to improve the prediction accuracy. The low-fidelity neural network is used to approximate the low-fidelity data, whereas the high-fidelity neural network is adopted to approximate the correlation function between the low-fidelity and high-fidelity data. To systematically search the optimal weights of various losses for reducing the training time, the Dual-Dimer algorithm is adopted to search high-order saddle points of the minimax optimization problem. The proposed framework is demonstrated with two-dimensional heat transfer, phase transition, and dendritic growth problems, which are fundamental in materials modeling. With the same set of training data, the prediction error of the multifidelity physics-constrained neural network with minimax architecture can be two orders of magnitude lower than that of the multifidelity neural network with minimax architecture. | |
| publisher | The American Society of Mechanical Engineers (ASME) | |
| type | Journal Paper | |
| journal volume | 23 | |
| journal issue | 3 | |
| journal title | Journal of Computing and Information Science in Engineering | |
| identifier doi | 10.1115/1.4055316 | |
| journal fristpage | 31008-1 | |
| journal lastpage | 31008-10 | |
| page | 10 | |
| tree | Journal of Computing and Information Science in Engineering:;2022:;volume( 023 ):;issue: 003 | |
| contenttype | Fulltext |