変分的積分法を用いたベイジアンニューラルネットワークの応用

抄録

In numerical analysis, the conservation of structure, i.e., whether the essential properties of physical phenomena can be reproduced numerically, is of great importance. On the other hand, neural networks that can learn conservation laws has recently received great attention. These models take important structure of physical problems into consideration, which are often ignored in traditional models that directly learn using data, consequently exhibiting long-term accurate prediction and interpretability. In the current study, we construct neural network models based on variational integrator, a typical kind of structure-preserving method. In addition, we introduce Bayesian framework to measure uncertainty of the model and evaluate the models quantitively. Illustrative examples are studied.