Data-driven derivation of partial differential equations using neural network model

Koyamada, Koji*; Yu, L.*; Kawamura, Takuma; Konishi, Katsumi*

International Journal of Modeling, Simulation, and Scientific Computing, 12(2), p.2140001_1 - 2140001_19, 2021/04

https://doi.org/10.1142/S1793962321400018

With the improvement of sensors technologies in various fields such as fluid dynamics, meteorology, and space observation, it is an important issue to derive explanatory models using partial differential equations (PDEs) for the big data obtained from them. In this paper, we propose a technique for estimating linear PDEs with higher-order derivatives for spatiotemporally discrete point cloud data. The technique calculates the time and space derivatives from a neural network (NN) trained on the point cloud data, and estimates the derivative term of the PDE using regression analysis techniques. In the experiment, we computed the error of the estimated PDEs for various meta-parameters for the PDEs with exact solutions. As a result, we found that increasing the hierarchy of NNs to match the order of the derivative terms in the exact solution PDEs and adopting L1 regularization with LASSO as the method of regression analysis increased the accuracy of the model.

Multivariate analysis approach to predicting event timing based on temporal knowledge base for application to computerized system for radiological emergency response

Ishigami, Tsutomu; *; *; *; Kobayashi, Kensuke

Probabilistic Safety Assessment and Management,Vol. 2, p.947 - 952, 1991/00

no abstracts in English

Current status of uncertainty analysis methods for computer models

Ishigami, Tsutomu

JAERI-M 89-190, 66 Pages, 1989/11

JAERI-M-89-190.pdf:1.5MB

no abstracts in English