=Paper=
{{Paper
|id=Vol-3432/paper29
|storemode=property
|title=Causality Prediction with Neural-Symbolic Systems: A Case Study in Smart Grids
|pdfUrl=https://ceur-ws.org/Vol-3432/paper29.pdf
|volume=Vol-3432
|authors=Katrin Schreiberhuber,Marta Sabou,Fajar J. Ekaputra,Peter Knees,Peb Ruswono Aryan,Alfred Einfalt,Ralf Mosshammer
|dblpUrl=https://dblp.org/rec/conf/nesy/SchreiberhuberS23
}}
==Causality Prediction with Neural-Symbolic Systems: A Case Study in Smart Grids==
https://ceur-ws.org/Vol-3432/paper29.pdf
Causality Prediction with Neural-Symbolic Systems:
A Case Study in Smart Grids
Katrin Schreiberhuber1,2,∗ , Marta Sabou1,2 , Fajar J. Ekaputra1,2 , Peter Knees2 ,
Peb Ruswono Aryan2 , Alfred Einfalt3 and Ralf Mosshammer3
1
Vienna University of Economics and Business, Welthandelsplatz 1, 1020 Vienna, Austria
2
TU Wien – Faculty of Informatics, Favoritenstr. 9-11, 1040 Vienna, Austria
3
Siemens AG Österreich, Siemensstr. 90, 1210 Vienna, Austria
Abstract
In complex systems, such as smart grids, explanations of system events benefit both system operators
and users. Deriving causality knowledge as a basis for explanations has been addressed with rule-based,
symbolic AI systems. However, these systems are limited in their scope to discovering causalities that
can be inferred by their rule base. To address this gap, we propose a neural-symbolic architecture
that augments symbolic approaches with sub-symbolic components, in order to broaden the scope of
the identified causalities. Concretely, we use Knowledge Graph Embeddings (KGE) to solve causality
knowledge derivation as a link prediction problem. Experimental results show that the neural-symbolic
approach can predict causality knowledge with a good performance and has the potential to predict
causalities that were not present in the symbolic system, thus broadening the causality knowledge scope
of symbolic approaches.
Keywords
Knowledge Graph, Knowledge Graph Embedding, Explainability, Causality, Smart Grid
1. Introduction
Causality knowledge enables advanced applications such as explaining events in complex (en-
gineering) systems. For example, in the smart grid domain, the event of an electrical vehicle
failing to load at full capacity could be due to: (i) an increased energy demand in the area due
to low temperatures or (ii) reduced energy production due to low solar radiation in the area.
Explanations of such reasons depend on understanding actual causalities [1], that is, concrete
events that happen in the underlying energy grid and their causal relations (e.g., low levels of
solar radiation at a concrete time/location cause low power generation at PV-station A). We
focus on the problem of deriving such actual causality knowledge. Typically, this means starting
out with a system (e.g., grid) topology and time-series data describing the evolution of variables
NESY 2023: 17th International Workshop on Neural-Symbolic Learning and Reasoning, Certosa di Pontignano, Siena,
Italy
∗
Corresponding author.
Envelope-Open katrin.schreiberhuber@wu.ac.at (K. Schreiberhuber); marta.sabou@wu.ac.at (M. Sabou);
fajar.ekaputra@wu.ac.at (F. J. Ekaputra); peter.knees@tuwien.ac.at (P. Knees); peb.aryan@tuwien.ac.at
(P. R. Aryan); alfred.einfalt@siemens.com (A. Einfalt); ralf.mosshammer@siemens.com (R. Mosshammer)
Orcid 0000-0003-1815-8167 (K. Schreiberhuber); 0000-0001-9301-8418 (M. Sabou); 0000-0003-4569-2496 (F. J. Ekaputra);
0000-0003-3906-1292 (P. Knees); 0000-0002-1698-1064 (P. R. Aryan)
© 2023 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR
Workshop
Proceedings
http://ceur-ws.org
ISSN 1613-0073
CEUR Workshop Proceedings (CEUR-WS.org)
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Katrin Schreiberhuber et al. CEUR Workshop Proceedings 1–12
in that system (e.g., solar radiation, power production) as input and deriving individual events
and causal relations between them as output.
Such task of actual causality knowledge derivation was addressed with deterministic (symbolic)
approaches, such as graph-traversal algorithms [2][3] and rule/logic-based solvers [4][5][6].
These approaches are limited in their scope by the rules they rely on, being unable to discov-
er/learn causalities beyond those that can be deduced by rule inference. At the same time, we
are not aware of any machine learning (sub-symbolic) approach that addresses such a complex
problem spanning the large knowledge gap from time-series based variables as input to actual
causalities as output. The recent trend in Artificial Intelligence towards the development of
neural-symbolic (NeSy) approaches [7] focuses on the complementary combination of symbolic
and sub-symbolic AI approaches. For example, the Semantic Web community proposed tech-
niques such as KGE and deductive reasoning [8], and has seen rapid growth in systems that
combine Semantic Web and Machine Learning components (a particular type of neural-symbolic
systems) [9]. Therefore, in this paper we investigate:
• (RQ1) What is the causality prediction performance of a neural-symbolic approach com-
pared to existing knowledge?
• (RQ2) To what extent can the neural-symbolic system predict new knowledge?
We address our research questions in the context of a smart grid use case (detailed in Sect. 2).
We rely on the use of a domain-specific simulation environment to generate input data (i.e.,
a smart grid topology and time-series data of a number of key parameters generated over a
set period of time). As a baseline, we consider a symbolic, knowledge graph-based approach
to solving this problem [10], described in Sect. 3. We extend this system with a sub-symbolic
component by applying KGEs for link prediction, where predicted links are causal relations (see
Sect. 4). We set up an experiment (i) to compare the performance of the various KGE algorithms
and (ii) to investigate the derivation of causality knowledge with a neural-symbolic approach
(Sect. 5). As such, the contributions of this paper are:
• a neural-symbolic architecture for deriving causality knowledge;
• experimental evidence in a concrete case study about the performance of KGE as a
particular implementation of a NeSy approach for causality derivation.
Our empirical investigations show that the proposed neural-symbolic system predicts causal-
ity links with an average hits@5 of 0.24 using TransE. Performance differs between event types,
achieving up to 0.6 for some event types. Moreover, the trained models capture the latent
semantics of the causality relations being able to predict (a) causalities for event types that they
were not trained on; (b) indirect causality links that were not explicitly present in the training
data. 1
1
implementation of our investigations is released at https://github.com/Kat-rin-sc/ExpCPSKGE
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Katrin Schreiberhuber et al. CEUR Workshop Proceedings 1–12
Figure 1: (a) Example energy community, including key events and their causal relations. (b) Corre-
sponding BIFROST simulation.
2. Causality-based Event Explanations in Smart Grids
In the use case domain of smart grids, being able to explain complex events is crucial for saving
energy and costs, but also to ensure the grid’s stability. Consider for example, the energy
community (EC) (also referred to as an (energy) village) depicted in Fig. 1(a) consisting of houses
H1-H4 (equipped with PV cells, batteries) connected to a flexibility operator S1 which informs
EC members about best trading actions (selling/buying energy) depending on the energy price
on the market M1. The EC is served by transformer T1, to which other office buildings (B1, B2)
and eCar charging stations (C1, C2) are connected.
In this setting complex event explanations can be derived consisting of chains of causality
links between concrete events that happened previously. For example, the event of slow charging
at C1 (event e8) is caused because of reducing an overload at transformer T1 (e7). On its term,
e7 was caused by the EC members (i) consuming a high amount of energy (e4-6) because a “buy”
command of S1 (e3) in line with low energy prices (e1) and discharged batteries of some houses
and (ii) producing less energy as usual due to reduced solar radiation (e2). Other event types
(see Table 1) that require explanations include the overloading or normalisation of a transformer,
or lowering/peaking in energy demand of customers.
We employ BIFROST [11], a smart grid simulator, to construct such scenarios, as in Fig. 1(b),
and to simulate the behavior thereof over a period of time (typically, a day). As a result, the
evolution of several physical measures (e.g., voltage levels) is computed leading to time-series
data with a chosen time frequency (usually 1 hour).
3. ExpCPS: Symbolic AI Solution
We build on an existing approach to derive system event explanations using symbolic AI, called
ExpCPS [2, 10] and depicted in Fig. 2. The input is provided by BIFROST. Core to the system is
a semantic knowledge structure, the ExpCPS KG, which stores (a) a semantic representation
of the simulated scenario and (b) additional knowledge necessary for deriving explanations
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Katrin Schreiberhuber et al. CEUR Workshop Proceedings 1–12
Figure 2: Neural-symbolic architecture for causality detection combining the ExpCPS symbolic approach
(top layer) and sub-symbolic models for learning causalities from ExpCPS KG (bottom layer).
and which is inferred using symbolic techniques such as rules. The workflow for deriving the
ExpCPS KG and explanation of events (see symbolic approach in Fig. 2) consists of the following
components (color coded and labelled in Fig. 2):
(A) In a Data Integration process, static topology data including physical components of the
simulated village (i.e. building, EV-charging station, underground cable) are represented
as instances of the F e a t u r e O f I n t e r e s t concept. S e n s o r s are placed at these features to
measure their state at different times during a simulation (i.e. loading of a transformer).
Dynamic data corresponding to the sensor measurements during the simulation are stored
as O b s e r v a t i o n s (i.e., o b s e r v e d D a t a at a t i m e s t a m p ).
(B) An Event Detection process identifies anomalies in the dynamic measurement data which
are stored as instances of different types of E v e n t s (see Table 1) in ExpCPS KG.
(C) Device Causality Derivation uses type causality rules defined by domain experts to derive
device causality in the energy community (see an example in Fig 5, Appendix). Type
causality [1] represents general relations between entity types in a system (i.e. the power
consumed by a residential house influences the loading of a transformer). Based on this
knowledge, potential causes between specific instances of sensors in the energy commu-
nity can be derived, called device causality. It captures the relation between two devices
in a physical context (i.e. “power consumption at p o w e r m e t e r M 1 influences transformer
load at l o a d i n g s e n s o r L 6 ” –device causality– is derived from “power consumption at a
powermeter influences transformer load” –type causality).
(D) The rule-based Event Causality Derivation algorithm considers device causalities between
sensors and events in the system to derive a set of actual causalities. Actual causality
focuses on particular events that happened in a system at a specific time and place (i.e.
P e a k i n g D e m a n d E 3 causes O v e r l o a d i n g E 4 ), which make up an event explanation. To find
explanations of a certain event (i.e. O v e r l o a d i n g E 4 ), multiple steps need to be taken: (i)
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Katrin Schreiberhuber et al. CEUR Workshop Proceedings 1–12
Event Type Definition
Overloading/Normalizing transformer is overloading/normalizing
Lowering/Peaking Demand active power demand of energy consumers is lowering/peaking
Flex Request Approved/Rejected, states of a flexibility contribution program, where energy
Flex Unavailable State consumers adhere to requests to use more or less energy
Table 1
Definitions of event types relevant for actual causality prediction
find the sensor, which registered the event (i.e. l o a d i n g s e n s o r L 6 ), (ii) find sensors, which
are connected to this sensor registering the event by device causality (i.e. p o w e r m e t e r M 1
influences l o a d i n g s e n s o r L 6 ) , (iii) check for events, which happened at these sensors (i.e.
P e a k i n g D e m a n d E 3 is registered at p o w e r m e t e r M 1 ) and (iv) add the causality relation to the
KG (i.e.P e a k i n g D e m a n d E 3 cause O v e r l o a d i n g E 4 ). For a full explanation path, these steps
need to be repeated recursively for each event added in (iv).
Limitation. While ExpCPS successfully addresses the causality-based explanation gener-
ation problem, its scope is limited by the rule-based mechanism it relies on which leads to a
deterministic behavior, i.e,. identifying only those causalities that can be derived by rules, but
not being able to learn other plausible causalities by itself.
4. Proposed Sub-Symbolic Extension
Our hypothesis is that the symbolic ExpCPS system can be extended with sub-symbolic compo-
nents in order to increase the scope of the learned causalities. To test this hypothesis, we propose
a neural-symbolic architecture (Fig.2) which complements the symbolic ExpCPS approach with a
sub-symbolic layer trained on the existing ExpCPS KG to derive new actual causalities, leading
to extended system explanations. Concretely we make use of KGE methods, which use relations
between KG entities to embed the components of a KG into a continuous vector space as a basis
for downstream tasks such as KG completion, relation extraction or entity classification [12].
We formalise the problem as a link prediction problem: in the ExpCPS KG causalities between
events are represented as RDF-triples, e.g.: ( O v e r l o a d E v e n t C , c a u s e d B y , P e a k i n g D e m a n d E v e n t A ) .
The role of KGE is to predict the tail entities (i.e., objects) in such causality triples (i.e., the
potential causes for the head entity. i.e., the subject of the triple). We focus on evaluating the
performance of this prediction task (RQ1) and whether the neural-symbolic system can predict
new knowledge beyond what ExpCPS provides (RQ2).
Rather than replacing the original ExpCPS architecture, the aim of using KGE is to enhance the
existing system. The proposed sub-symbolic approach should be an extension of the symbolic
system, training the models on the KG, which was created using the ExpCPS approach (see Fig.
2)
Training Data Architecture. We make use of two villages, representing energy community
setups in BIFROST with different topologies, to create the training/test and validation envi-
ronment. For each village the corresponding ExpCPS KG is derived using the ExpCPS system
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Katrin Schreiberhuber et al. CEUR Workshop Proceedings 1–12
Topology Observations Events Device Causality Actual Causality
Village 1 004 sensors 25 067 observations 107 events 57 potential causes 85 actual causes
A 379 FOIs in 24h between sensors between events
23 feature types
Village 1 203 sensors 30 075 observations 191 events 77 potential causes validation data:
B 379 FOIs in 24h between sensors 133 actual causes
24 feature types between events
Table 2
Overview of village A and village B - actual causality in Village B (grey brackground) is used as validation
data, while the rest is randomly split for training and testing (FOI = feature of interest)
with characteristics captured in Table 2. The training/test data consists of the entire KG derived
for village A. Since KGEs cannot predict any relations of instances which are unknown in the
training phase, the topology, observation, events and device causality of village B are included in
the training set as well. The validation data (i.e., ground truth) consists of the “Actual Causality”
knowledge of village B, which we try to predict.
In this setup, a KGE model can learn actual causality embeddings from all information in the
village A ExpCPS KG. Moreover, it is equipped with information about the topology, observations
and device causalities of village B, but no actual causalities. By testing the performance of
embedding models on predicting actual causalities for a set of events in Village B, we can test
their ability to represent actual causality. As the buildings and events are different in the two
villages, we can ensure that village A data is only used to train actual causalities overall, but no
direct information on actual causality in village B is used in training. Thus, there is no data leak
between training and validation data.
Knowledge Graph Embeddings We chose four embedding methods based on their compu-
tational intensity and their ability to represent various types of relations. TransE [13], TransH
[14] and TTransE [15] are translational embedding models, meaning that they aim to use
relations as a “translation” from one entity to another. TransE is one of the earliest proposed
embedding approaches. TransH extends the idea of TransE by using separate Hyperplanes for
different types of relations. TTransE adds temporal information in the form of timestamps to
each RDF triple [12]. We chose ComplEx [16], a high-performing [17] semantic matching model
which leverage latent semantics present in the vector embeddings of entities and relations to
measure the plausibility of triples.
For each KGE method, hyperparameter optimization (HPO) using grid search was conducted
on loss function, model embedding dimensions, optimizer, negative sampler and number of
epochs (see Table 3 in the Appendix for HPO search space and optimized setup of each embedding
model). For HPO, the training/test data was split randomly into training and test set, training
each setup on the training data and testing the performance on test data. For final evaluation,
each model was trained on the full set of training and test data using the optimized setup and
was tasked to predict actual causalities for events in the validation data. The results were then
evaluated on their prediction performance of actual causalities in the validation data.
For Village B, explanations for 17 events (of event types shown in Table 1) exist in the valida-
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Katrin Schreiberhuber et al. CEUR Workshop Proceedings 1–12
Figure 3: Event explanation of O v e r l o a d E v e n t 2 . Green node is the explained event. Colored circles show
the predictions of the respective models ( TransE, TransH, ComplEx, TTransE)
tion data. Each explanation contains one to twelve cause events. For example, for the event
O v e r l o a d E v e n t 2 there is only one direct cause in the validation data (F l e x R e q u e s t R e j e c t e d E v e n t 1 )
, but four events are indirectly causing the event (D i s c h a r g i n g E v e n t 1 9 , F l e x C o n t r i b u t e d E v e n t 2 0 , 2 1
a n d 2 2 )(see Fig. 3).
Evaluation Setup The proposed system predicts the most fitting causes for an event in
the validation data according to the embedding model trained on the training and test set of
the ExpCPS KG (see Table 2). For evaluation, we measure the performance of causality link
prediction on validation events with the hits@5 metric, which captures the percentage of true
predictions in the five top-ranked predictions of a model.
True predictions are determined in two ways. First, the set of actual causalities in the
validation data, which were also determined by the symbolic system, (i.e., actual causality data
for village B in Table 2) are considered definitely true. Second, the models’ predictions that
were not present in the validation data were checked by experts in an evaluation workshop and
labelled on their likelihood to be true on a scale from 1 to 4 (1 - definitely false, 2 - probably
false, 3 - probably true, 4 - definitely true). From the above example, F l e x R e q u e s t R e j e c t e d : 1 is
a true cause of O v e r l o a d i n g : 2 according to the validation data, thus it is true. Moreover, a KGE
model might also suggest D i s c h a r g i n g : 4 to be a cause of O v e r l o a d i n g : 2 , which was analysed by
experts and labeled as probably true. Overall, each prediction which is not definitely true is
evaluated by experts to determine its likelihood to be a missing link in the graph. Accordingly,
two performance metrics are defined: (a) defHits@5 includes predictions which are definitely
true because they were present in the validation data; (b) probHits@5 includes predictions,
which are either probably or definitely true, based on expert evaluation and ground truth data.
Therefore, the improvement from defHits@5 to probHits@5 shows the potential of a KGE method
to increase the knowledge base created by the symbolic ExpCPS approach.
5. Evaluation Results
Performance of KGE methods. In Fig. 4, the comparison between defHits@5 and prob-
Hits@5 is visualised overall and per event type (see Table 4 in the appendix for a tabular
representation of these values). Overall, TransE performed best on link prediction for defHits@5
and probHits@5. TransH and ComplEx benefited the most from including probable hits in the
performance metric as their result improved by 0.09 from defHits@5 to probHits@5.
While probHits@5 increase model performances for some types of events, general performance
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Katrin Schreiberhuber et al. CEUR Workshop Proceedings 1–12
Figure 4: Link Prediction Performance of all four models overall(left) and per event type(right). Solid
colors represent defHits@5, transparent colors represent probHits@5.
rankings between the four models hardly ever change between defHits@10 and probHits@5.
Even though TransE does not perform best for each event type individually, it does outperform
other models overall, being able to always predict at least a probable cause for each event type.
Predicting event types absent from the training data. The event types F l e x R e q u e s t R e j e c t e d
and F l e x U n a v a i l a b l e S t a t e did not occur in Village A. Therefore, there was no explanation of
these event types known to the trained KGE models. As expected, all KGE models perform
poorly when trying to find and explanation for F l e x U n a v a i l a b l e S t a t e event types. Surprisingly,
predictions on F l e x R e q u e s t R e j e c t e d event types are good, especially with TransE and TransH.
As there was no event of type F l e x R e q u e s t R e j e c t e d present in the trainig data of Village A, it
is impressive that performance on this event type is among the best compared to other event
types. Furthermore, as this causality was not learned by the KGE models explicitly, these
results suggest that the KGE models “picked up” on the latent semantic implications of causality
sufficiently to be able to predict causal events of event types unseen during training.
Predicting indirect causality. Indirect causalities are causes of a cause of an event , e.g.,
in Fig 3, for the O v e r l o a d i n g E v e n t : 2 the direct cause is F l e x R e q u e s t R e j e c t e d E v e n t : 1 ; while the
other 4 events in the figure are indirect causalities. We observed that the KGE models were able
to predict such indirect causalities. Fig. 3 shows that none of the KGE models could predict the
immediate cause event for O v e r l o a d i n g E v e n t : 2 , but three of the indirect causes were predicted
by TransE and TransH. Indirect causalities are ground-truth data which was never directly
connected to the effect events in the original KG. Therefore, the behavior of predicting such
causalities shows that the KGE models could represent actual causality relations and apply these
semantics to the data beyond simple reconstruction of existing direct relations.
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Katrin Schreiberhuber et al. CEUR Workshop Proceedings 1–12
6. Related Work
Topics related to system explainability include anomaly detection and root-cause analysis (RCA),
both of which can be tackled by methods such as Failure Mode and Effect Analysis [18] and
Fault Tree Analysis [19]. These methods apply a human-oriented approach, where causes
of potential anomalies need to be specified by domain experts. However, they are at risk of
inconsistent terminology and ambiguous knowledge. As an extension, the use of ontologies
has been proposed to remove ambiguity from causality knowledge [20]. Moreover, semantic
technologies enable researchers to use existing general-purpose knowledge about a system for
analysing its behaviour [21]. RCA methods primarily employ deterministic and probabilistic
techniques [22] and are hampered by the increasing complexity of the growing graphs.
KGEs could address this situation by better scaling to such large graphs. Yet, work on using
KGEs for predicting causality relations is limited to rather recent endeavours. For example,
Khatiwada et al [23] have investigated the use of KGE for predicting causal relations for news
events based on Wikidata Knowledge. However, the sparsity of causal relations in the Wikidata
KG limits the capabilities of KGE predictions.
7. Conclusions
We propose a neural-symbolic approach for causality link prediction which we implement
and test in a smart grid setting, where we extended a symbolic system (ExpCPS) with KGE,
investigating four KGE methods. Performance evaluations showed that links are predicted with
an average hits@5 of 0.24 using TransE (and up to 0.6 for some event types). More interestingly,
the approach was able to discover new knowledge such as (i) explanations of event types which
were not present in the training data and (ii) indirect causalities (only present implicitly in the
training data).
Acknowledgements. The master thesis work of Katrin Schreiberhuber has been funded by
the Career Grant proposals scheme of the Faculty of Informatics in TU Wien. This work has
been funded by the FFG SENSE project (project Nr. FO999894802) and the Austrian Science
Fund (FWF) [P33526].
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A. Appendix
Figure 5: Inference of actual causality from type causality
Parameter Potential Values TransE TransH ComplEx TTransE
dimensions 32,64,128 64 64 64 32
loss function margin ranking, soft- margin margin softplus cross
plus, cross entropy ranking ranking entropy
loss loss
optimizer Adam, SGD Adam Adam Adam Adam
learning rate 0.001, 0.01, 0.1 0.001 0.001 0.001 0.01
epochs max 100, early stop- 100 30 80 45
ping
Table 3
hyperparameter optimization search space and final model setups
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Katrin Schreiberhuber et al. CEUR Workshop Proceedings 1–12
event type model defHits@5 probHits@5
TransE 0.17* 0.23*
FlexRequest TransH 0.07 0.17
Approved ComplEx 0.10 0.23
TTransE 0.03 0.03
TransE 0.50* 0.70*
FlexRequest TransH 0.50* 0.70*
Rejected** ComplEx 0.10 0.10
TTransE 0.30 0.40
TransE 0.00 0.07
Flex TransH 0.00 0.13*
Unavailable
State** ComplEx 0.00 0.00
TTransE 0.00 0.00
TransE 0.20 0.20
Lowering TransH 0.40* 0.40*
Demand ComplEx 0.00 0.40*
TTransE 0.40* 0.40*
TransE 0.60* 0.60*
TransH 0.40 0.60*
Normalizing
ComplEx 0.20 0.20
TTransE 0.20 0.20
TransE 0.40* 0.40*
TransH 0.40* 0.40*
Overloading
ComplEx 0.00 0.10
TTransE 0.10 0.10
TransE 0.20* 0.20*
Peaking TransH 0.20* 0.20*
Demand ComplEx 0.00 0.00
TTransE 0.20* 0.20*
TransE 0.24* 0.30*
TransH 0.20 0.29
Overall
ComplEx 0.06 0.15
TTransE 0.11 0.13
* best result in this category
** event type is not present in the training data
Table 4
Link Prediction Performance over all event types and models. Best-performing models per event type
are in bold.
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