Digital Twin Generalization with Meta and Geometric Deep
Learning
Raffael Theiler, Olga Fink
ENAC IIC IMOS
´
Ecole Polytechnique F
´
ed
´
erale de Lausanne (EPFL)
Lausanne, CH-1015, Lausanne
{raffael.theiler, olga.fink}@epfl.ch
ABSTRACT
Deep digital twins (DDTs) are deep neural networks that en-
code the behavior of complex physical systems. DDTs are
excellent system representations due to their ability to con-
tinuously adapt to operational changes and their capability to
capture complex relationships between system components
and processes that cannot be explicitly modeled. For this
challenge, DDTs benefit greatly from recent success in ge-
ometric deep learning (GDL) which allows the integration of
information from multiple systems based on schematic rep-
resentations. A major challenge in training DDTs is their
dependence on the quality and representativeness of training
data, especially under the dynamic conditions typical in prog-
nostics and health management (PHM). Recent developments
in differentiable simulation present new opportunities for op-
timizing the training data representativeness. In this the-
sis, we propose a novel meta-learning framework that trains
DDTs using the output from differentiable simulators. This
setup enables active optimization of training data sampling
through gradient computation, enhancing training speed, ro-
bustness, and data representativeness. We extend this frame-
work to address challenges in multi-system data integration
in power grids and fault detection in railway traction net-
works. By applying our framework, we aim to tackle signifi-
cant challenges in forecasting, anomaly detection and sensor-
fault analysis using advanced data fusion techniques. Our
approach promises substantial improvements in DDT robust-
ness and operational efficiency, with its effectiveness to be
demonstrated through empirical studies on both simple and
complex case studies within the power systems domain.
1. INTRODU CTION
Power systems are a paramount example of complex sys-
tems (Cuadra, Salcedo-Sanz, Del Ser, Jim
´
enez-Fern
´
andez, &
Raffael Theiler et al. This is an open-access article distributed under the
terms of the Creative Commons Attribution 3.0 United States License, which
permits unrestricted use, distribution, and reproduction in any medium, pro-
vided the original author and source are credited.
Geem, 2015). Conventional and data-driven methods have
been developed for the analysis of power systems (Liao, Bak-
Jensen, Radhakrishna Pillai, Wang, & Wang, 2022), and other
industrial assets (Hu, Miao, Si, Pan, & Zio, 2022) over many
years. Yet, they suffer from non-stationary behaviors of com-
plex systems such as changes in environmental and oper-
ational conditions (Soleimani, Campean, & Neagu, 2021).
Such non-stationarity poses a challenge to traditional data-
driven machine learning which is trained on the i.i.d assump-
tion that data are identically and independently distributed
with balanced training and testing sets (Jardine, Lin, & Ban-
jevic, 2006). However, the requirement for balanced amounts
of healthy and unhealthy data across different operational
states cannot be met in the industrial environment due to the
long operational lifespans of critical assets and the challenges
in storing and processing the associated data (Booyse, Wilke,
& Heyns, 2020). The resulting imbalance violates the i.i.d as-
sumption. Therefore, sophisticated approaches for the oper-
ation and maintenance of industrial systems with data-driven
models are required to ensure robust and reliable operation.
Enhancing the generalization ability of the data-driven model
with respect to these conditions becomes essential in both in-
dustry and academic fields (Wang et al., 2022).
For operation and maintenance, Digital twins (DT) have been
one of the emerging tools applied for industrial systems. They
are virtual representations of these industrial systems that
can be used to approximate the behavior in a digital envi-
ronment (Booyse et al., 2020). DTs are different from data-
driven simulators because they make use of additional (real-
time) sensory information from the physical system for on-
line updates of the system state to real operational and en-
vironmental scenarios. The most prominent application of
DT is for control. However, they have been increasingly ap-
plied for fault detection, diagnostics, and prognostics where
DTs continuously represent the system to help engineers bet-
ter identify deviations from expected behavior to take correc-
tive action. Furthermore, DTs are used for prognostics and
health management (PHM), where the DT can approximate
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