TY - JOUR
T1 - PRIMER ON SOLVING DIFFERENTIAL EQUATIONS USING MACHINE LEARNING TECHNIQUES
AU - Bakthavatchalam, Tamil Arasan
AU - Murugan, Selvakumar
AU - Ramamoorthy, Suriyadeepan
AU - Sankarasubbu, Malaikannan
AU - Ramaswamy, Radha
AU - Sethuraman, Vijayalakshmi
AU - Malomed, Boris A.
N1 - Publisher Copyright:
© 2022, Publishing House of the Romanian Academy. All rights reserved.
PY - 2022
Y1 - 2022
N2 - Machine Learning (ML) has shown a substantial impact on computational sciences in recent years. The adaptation of ML techniques to deal with various systems in physical sciences has gained ground in addition to the existing numerical methods. In this work, we introduce the readers to machine learning with special reference to Artificial Neural Networks (ANNs) that can solve ordinary differential equations (ODEs) and partial differential equations (PDEs) including those which are subject to specific symmetries. This paper will be helpful for graduate and undergraduate students as an introductory material to early career researchers interested in applying ML techniques to solve problems in computational sciences. In particular, we choose elementary differential equations that describe systems from various fields of science to illustrate the proficiency of ANNs to capture the regularities that underlie such systems in the hope of adding ML techniques to the physicists’ toolbelt.
AB - Machine Learning (ML) has shown a substantial impact on computational sciences in recent years. The adaptation of ML techniques to deal with various systems in physical sciences has gained ground in addition to the existing numerical methods. In this work, we introduce the readers to machine learning with special reference to Artificial Neural Networks (ANNs) that can solve ordinary differential equations (ODEs) and partial differential equations (PDEs) including those which are subject to specific symmetries. This paper will be helpful for graduate and undergraduate students as an introductory material to early career researchers interested in applying ML techniques to solve problems in computational sciences. In particular, we choose elementary differential equations that describe systems from various fields of science to illustrate the proficiency of ANNs to capture the regularities that underlie such systems in the hope of adding ML techniques to the physicists’ toolbelt.
KW - Deep Learning
KW - Differential Equations
KW - Differential Programming
KW - Machine Learning
KW - Mathematical Modelling
KW - Neural Networks
KW - Nonlinear Dynamics
KW - Numerical Methods
UR - http://www.scopus.com/inward/record.url?scp=85133482537&partnerID=8YFLogxK
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AN - SCOPUS:85133482537
SN - 1221-1451
VL - 74
JO - Romanian Reports in Physics
JF - Romanian Reports in Physics
IS - 2
M1 - 113
ER -