IEEE Power & Energy Magazine - May/June 2022 - 41

Increases During Training
Prediction Contradicts Physics
Frequency
Frequency
Prediction in Line With Physics
Frequency
NN
Physical Model
Derivative
Time
(a)
(b)
Time
(c)
figure 7. The training process for physics-informed neural networks, showing the evolution of neural network output during
training (orange) versus ground truth (blue). NN: neural network. (a) At the start of training, the neural network output
contradicts the physical model. (b) As the training progresses, the neural network output fits the physical model better.
(c) After sufficient training, the neural network output is in line with the physical model.
Figure 7(b) and (c) show how the neural network adjusts its
parameters so that the derivatives of the predicted trajectory
can fit what the differential equations describing the
system dictate.
Physics-informed neural networks may lead to much better
predictions while requiring much fewer training data.
This can remove significant barriers. Instead of creating
large training databases by randomly sampling thousands of
trajectories to train a network with sufficient accuracy, we
can now directly include governing equations in the training
process and let the neural network train until it minimizes
the prediction error.
Where Does This Lead Us?
The two directions we presented, neural network verification
and physics-informed neural networks, aim to build trust
with grid operators, utilities, and other potential users and
improve network performance while requiring much fewer
data. They arguably remove the most important barrier
when it comes to the safety-critical operations of energy systems:
ML tools no longer need to be considered a black box;
instead, they can be trusted. Such methods can also further
help to develop systematic approaches that identify regions
where the neural network demonstrates poor performance
and then systematically improve it through retraining.
There are still many steps needed until ML tools are
embraced inside the control room. For instance, scalable
algorithms that can apply to very large neural networks and
power grids need to be developed. Expertise in power systems,
operations research, and ML is necessary to arrive
at production-level algorithms. Once achieved, gaining the
trust of system operators will be a deciding step toward the
wider adoption of ML algorithms across energy systems.
This includes safety-critical operations, where ML can drastically
accelerate computation speed and enable the management
of millions of controllable appliances and converterconnected
devices.
may/june 2022
For Further Reading
A. Venzke and S. Chatzivasileiadis, " Verification of neural
network behaviour: Formal guarantees for power system
applications, " IEEE Trans. Smart Grid, vol. 12, no. 1, pp.
383-397, Jan. 2021, doi: 10.1109/TSG.2020.3009401.
A. Venzke, G. Qu, S. Low, and S. Chatzivasileiadis,
" Learning optimal power flow: Worst-case guarantees for
neural networks, " in Proc. 2020 IEEE Int. Conf. Commun.,
Control, Comput. Technol. Smart Grids (SmartGridComm),
pp. 1-7, doi: 10.1109/SmartGridComm47815.2020.9302963.
G. S. Misyris, A. Venzke, and S. Chatzivasileiadis,
" Physics-informed neural networks for power systems, " 2020,
in Proc. IEEE Power & Energy Society General Meeting,
2020, pp. 1-5, doi: 10.1109/PESGM41954.2020.9282004.
L. Duchesne, E. Karangelos, and L. Wehenkel, " Recent
developments in machine learning for energy systems reliability
management, " Proc. IEEE, vol. 108, no. 9, pp. 1656-
1676, 2020, doi: 10.1109/JPROC.2020.2988715.
V. Tjeng, K. Xiao, and R. Tedrake, " Evaluating robustness
of neural networks with mixed integer programming, "
2017, arXiv:1711.07356.
M. Raissi, P. Perdikaris, and G. E. Karniadakis, " Physicsinformed
neural networks: A deep learning framework for
solving forward and inverse problems involving non-linear
partial differential equations, " J. Comput. Phys., vol. 378,
pp. 686-707, Feb. 2019, doi: 10.1016/j.jcp.2018.10.045.
Biographies
Spyros Chatzivasileiadis is with the Technical University of
Denmark, Kongens Lyngby, 2800, Denmark.
Andreas Venzke was previously with the Technical University
of Denmark, Kongens Lyngby, 2800, Denmark.
Jochen Stiasny is with the Technical University of Denmark,
Kongens Lyngby, 2800, Denmark.
Georgios Misyris was previously with the Technical University
of Denmark, Kongens Lyngby, 2800, Denmark.
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