The 83rd JSAP Autumn Meeting 2022 Highlighted Presentations
October 24, 2022

High-speed prediction of thermal convection by using physics-informed neural networks (PINNs)

Neural network creates a digital twin that can control
reality
Yuto Takehara, Yasunori Okano
Graduate School of Engineering Science, Osaka University

Summary• A digital twin was created using a physics-informed neural network (PINN), a neuralnetwork that learns the governing equations of physical laws, to make fast predictions offlow and heat transfer in real systems.
• The first ever case study was conducted to apply PINNs to a real-world system, and its
physical consistency for flow and temperature were confirmed.
• The research will pave the way for industrial applications such as crystal growth
processes for silicon carbide (SiC).

A research group led by Yuto Takehara and Yasunori Okano of the Graduate School of Engineering
Science, Osaka University, used physics-informed neural networks (PINNs), neural networks that learn thegoverning equations of physical laws, to perform fast predictions of flow and heat transfer in real systems. A
digital twin was created. This twin was successfully used to accurately predict all flow and temperaturechanges inside the target under various conditions. The research suggests the potential of using digital twinsin scientific research and for a wide range of industrial applications.

DetailDigital twin is a new technology that controls reality
A digital twin is another reality reconstructed in a digital space based on various data collectedfrom real objects. The digital twin is considered an important technology that will support the fourthindustrial revolution, and in the future, it is expected to become more useful and realistic in various
applications, including industrial ones. A digital twin is a kind of simulator; however, its mainfeature is that it is a twin, or another reality. The digital twin is based on the same physical laws as
actual reality; however, its parameters can be changed. In other words, it is possible to try things
that are impossible in reality or to observe things that cannot be observed owing to physicallimitations. Furthermore, the numerical values obtained using the digital twin can be used to control
reality, improve processes, and make new discoveries.
A research group led by Yuto Takehara of the Graduate School of Engineering Science at OsakaUniversity used physics-informed neural networks (PINNs), neural networks that learn thegoverning equations of physical laws, to perform fast predictions of flow and heat transfer in realsystems. A digital twin was created. The neural network can accurately predict any flow andtemperature changes inside the object under various conditions.
Digital twins have been created in the past. However, Takehara noted that “There have been
problems with conventional techniques for reproducing phenomena. Numerical calculations aretime-consuming and computationally expensive, and machine learning has the disadvantage thatthe predicted values do not always satisfy the actual physical laws.” In this research, thesedrawbacks were overcome by using PINNs while developing a physically consistent digital twinthat can achieve the speedups that are important in practical applications.
Neural network that learns the laws of physics
The PINN used in this study is an ordinary neural network with a part that solves the governing
equations of physical laws. Then, based on temperature predictions, this neural network is trained
to ensure that the predicted temperatures satisfy the governing equations for all parameters, wherethe boundary conditions and governing equations are zero (Figure 1). Experiments are currently
being conducted on various subjects. In particular, in an experiment of the growth process of bulk
silicon single crystals used in semiconductor wafers (Czochralski [Cz] method), the flow andtemperature at all locations in the silicon melt were instantly predicted when the temperature of aportion of the real crystal growth process was provided as an input. Numerical calculations used ingeneral reproduction technology cannot achieve real-time operation because of the large amountof calculations required to reconfigure the computational grid when parameters such as the reactor
size are changed. To achieve real-time operation, this study exploited the ability of PINNs to
instantaneously predict all values when parameters are changed.
Conventional PINNs are used to predict motion and direction in a fluid. The novelty of this researchis that we have included a temperature index to enable the prediction of heat conduction.
Furthermore, this is the first time that PINNs has been applied to a real-world system, and its
physical consistency has been confirmed rather than being simply predicted (Figure 2).
In the future, this research could be applied to the crystal growth process of silicon carbide (SiC)
and to industrial applications of physically consistent digital twins.

We aim to apply this technology to the crystal growth process of SiC used in power and otherdevices. Currently, we do not know what the internal temperature distribution is like when certain
controls are applied during crystal growth. Through this research, we can predict all internal
temperature distributions when good crystals are produced. Takehara notes that by using thesetemperature data, all the controls that will produce good crystals can be quantified.
The PINNs used in this research can find various applications. In the future, it may become
possible to capture previously undetectable phenomena in reality through the digital twin and tobetter control hitherto uncontrollable factors.

Figures

Figure 1. Structure of PINNs. A regular neural network (left) predicts the temperature at coordinates (x, y, z) andthe parameters (T1, T2, T3, l). The governing equations are computed from the predicted temperatures (right).
Learning is performed to satisfy the boundary conditions and governing equations.
Figure 2.
The parameters considered include the Tr (crucible top temperature), Th (crucible bottom temperature), Tl(crucible bottom center temperature), and l (liquid surface height). Numerical temperature predictions for (Tr, Th,Tl, l) = (1700 K, 1700 K, 1696 K, 0.3 m) (top) and (1691 K, 1687 K, 1690 K, 0.12 m) (bottom) for different liquidheights (left) and when using PINNs (right). This figure shows that PINNs can accurately predict temperature
distributions for different geometries without reconfiguring the computational grid as in numerical calculations.
This result shows that real-time temperature control is possible.

Numerical (left) and PINN (right) predictions for (Tr, Th, Tl, l) = (1698 K, 1700 K, 1690 K, 0.3 m). Both thetemperature profile (left) and streamline (right) are predicted.