5:15 PM - 7:15 PM
[MGI31-P01] Evaluation of a Surrogate Model for Atmospheric Simulation Using PINNs
In atmospheric simulations, numerical simulation methods, such as the finite element method, are commonly used. These numerical methods have been used to simulate atmospheric circulation on Earth. To improve the accuracy of these simulations, it is necessary to increase both spatial and temporal resolution. This means an increase in computational demands and processing time. To accelerate simulations, there have been some attempts to create surrogate models using machine learning techniques like neural networks. However, these machine learning methods have some disadvantages in ensuring the physical laws and the high cost of gathering the learning data.
To solve these problems, recently Physics-Informed Neural Networks (PINNs) have been proposed. PINNs incorporate governing equations of physical phenomena such as partial differential equations and boundary conditions into the loss function of standard neural networks. The model has some advantages in ensuring the physical laws and in principle allowing training to use only the initial distribution of physical quantities. In this study, neural networks and PINNs were applied to atmospheric simulation and then compared to examine whether PINNs can be a surrogate model for atmospheric simulations in numerical methods.
Both PINNs and neural networks were implemented to take variables such as spherical coordinates, date, and elapsed time since the simulation started as inputs. Both the models had a total of nine hidden layers and output four physical quantities: east-west wind, north-south wind, atmospheric pressure, and temperature. In the neural network, only error loss based on the differences from the truth data was used. In PINNs, the loss function included not only error loss but also physical losses related to the four physical quantities like east-west wind, north-south wind, atmospheric density, and temperature and boundary condition losses. In physical losses, the partial differential equations were modified. For training in neural networks, truth data outputs from a General Circulation Model (GCM) were prepared, consisting of surface-level physical quantities on a 64x128 grid at hourly intervals for two days. In PINNs, in addition to the truth data, physical losses were calculated for an additional two days without truth data. In addition, PINNs adopts a method in which physical losses are incorporated into the loss function during the learning process.
For validation, the models were evaluated using data from the two days following the training period, and the outputs were compared to the truth data. During training, both PINNs and neural networks have sufficient learning in error loss. In addition, PINNs also showed a reduction in physical loss. After that, outputs were evaluated using validation data, but it was hard to say that PINNs is superior to neural networks in accuracy. Specifically, the neural network did not improve the results for the three physical quantities except for atmospheric pressure. Furthermore, the outputs of east-west and north-south wind from PINNs became uniform distributions. Causes for this might include the omission of friction effects from the physical losses, inaccuracies in spatial partial derivatives due to limited learning on surface level, and the failure of information from the initial distribution to propagate effectively in the temporal direction through physical losses during training.
To solve these problems, recently Physics-Informed Neural Networks (PINNs) have been proposed. PINNs incorporate governing equations of physical phenomena such as partial differential equations and boundary conditions into the loss function of standard neural networks. The model has some advantages in ensuring the physical laws and in principle allowing training to use only the initial distribution of physical quantities. In this study, neural networks and PINNs were applied to atmospheric simulation and then compared to examine whether PINNs can be a surrogate model for atmospheric simulations in numerical methods.
Both PINNs and neural networks were implemented to take variables such as spherical coordinates, date, and elapsed time since the simulation started as inputs. Both the models had a total of nine hidden layers and output four physical quantities: east-west wind, north-south wind, atmospheric pressure, and temperature. In the neural network, only error loss based on the differences from the truth data was used. In PINNs, the loss function included not only error loss but also physical losses related to the four physical quantities like east-west wind, north-south wind, atmospheric density, and temperature and boundary condition losses. In physical losses, the partial differential equations were modified. For training in neural networks, truth data outputs from a General Circulation Model (GCM) were prepared, consisting of surface-level physical quantities on a 64x128 grid at hourly intervals for two days. In PINNs, in addition to the truth data, physical losses were calculated for an additional two days without truth data. In addition, PINNs adopts a method in which physical losses are incorporated into the loss function during the learning process.
For validation, the models were evaluated using data from the two days following the training period, and the outputs were compared to the truth data. During training, both PINNs and neural networks have sufficient learning in error loss. In addition, PINNs also showed a reduction in physical loss. After that, outputs were evaluated using validation data, but it was hard to say that PINNs is superior to neural networks in accuracy. Specifically, the neural network did not improve the results for the three physical quantities except for atmospheric pressure. Furthermore, the outputs of east-west and north-south wind from PINNs became uniform distributions. Causes for this might include the omission of friction effects from the physical losses, inaccuracies in spatial partial derivatives due to limited learning on surface level, and the failure of information from the initial distribution to propagate effectively in the temporal direction through physical losses during training.