IEEE Computational Intelligence Magazine - May 2021 - 14
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Can Transfer Neuroevolution
Tractably Solve Your
Differential Equations?
Jian Cheng Wong
Agency for Science, Technology and Research (A*STAR) and
Nanyang Technological University, SINGAPORE
Abhishek Gupta
Agency for Science, Technology and Research (A*STAR), SINGAPORE
Yew-Soon Ong
Agency for Science, Technology and Research (A*STAR) and
Nanyang Technological University, SINGAPORE
Abstract-This paper introduces neuroevolution for solving
differential equations. The solution is obtained through optimizing a deep neural network whose loss function is defined
by the residual terms from the differential equations. Recent
studies have focused on learning such physics-informed neural networks through stochastic gradient descent (SGD) variants, yet
they face the difficulty of obtaining an accurate solution due to
optimization challenges. In the context of solving differential
Digital Object Identifier 10.1109/MCI.2021.3061854
Date of current version: 12 April 2021
14
IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE | MAY 2021
equations, we are faced with the problem of finding globally
optimum parameters of the network, instead of being concerned with out-of-sample generalization. SGD, which searches
along a single gradient direction, is prone to become trapped in
local optima, so it may not be the best approach here. In contrast, neuroevolution carries out a parallel exploration of
diverse solutions with the goal of circumventing local optima.
It could potentially find more accurate solutions with better
optimized neural networks. However, neuroevolution can be
slow, raising tractability issues in practice. With that in mind, a
Corresponding Author: Jian Cheng Wong (Email: wongj@ihpc.a-star.edu.sg).
1556-603X/21©2021IEEE
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IEEE Computational Intelligence Magazine - May 2021
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