Loss Function for Deep Learning in Physical Systems

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  • 物理システムにおける深層学習のための損失関数

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<p>Accurate simulation of physical systems is required in various fields of real-world systems. To automatically build a model from the data, recent studies have attempted to use deep learning to build models of the system. Neural ordinary differential equation (Neural ODE), which treats the output of a neural network as the time derivative of the input, has brought development to this research field. However, the training strategy of Neural ODE and related methods still needs to be established. We proposed the error-analytic strategy as a new strategy for training time series datasets to be more accurate in long-term predictions. The proposed strategy is inspired by error analysis techniques in numerical analysis and is derived by replacing numerical errors with modeling errors. Our strategy can capture a long-term error and hence improve the performance of long-term predictions.</p>

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