Prediction of thickness undulations in coating of liquid films by means of physics-informed machine learning

2022 Fiscal Year Final Research Report

• Project/Area Number: 19K04175
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 19010:Fluid engineering-related
• Research Institution: Tokyo City University
• Principal Investigator: Shiratori Suguru 東京都市大学, 理工学部, 准教授 (10803447)
• Project Period (FY): 2019-04-01 – 2023-03-31
• Keywords: 液膜流れ / 物理法則の機械学習 / 膜厚ムラ / データ同化

Outline of Final Research Achievements

This research applied Physics-Informed Neural Network (PINN), to efficiently predict various film thickness irregularities that occur in the liquid film coating process in microfabrication technologies such as semiconductor device and various color filter manufacturing methods. The effectiveness of PINN was investigated by applying it to the partial differential equation of liquid film flow, which includes a fourth-order spatial derivative and a fourth-order nonlinearity, for which was not validated. We found that for proper learning, it is effective to (1) densely place the spatio-temporal residual points where the solution changes rapidly, (2) use double precision floating-point operation, and (3) reduce the number of automatic differentiation operations by introducing intermediate variables and reducing the highest order of derivatives in the partial differential equation.

Free Research Field

流体工学

Academic Significance and Societal Importance of the Research Achievements

液膜に生じる膜厚ムラを予測するシミュレーション方法として、従来の有限差分法等の計算法では時間発展計算に長時間を要するため、膜厚ムラを回避・抑制するための最適塗布条件の探索に供するのは非現実的状況にあった。本研究で有効性を検証したPhysics-informed neural networkは一度学習計算を終えれば、任意の時刻と位置における膜厚を即時に計算することができるため、最適塗布条件への活用が現実的になると期待される。