NeSy4PPM is the first Python-based library for Predictive Process Monitoring (PPM) that integrates neural models with symbolic background knowledge to improve sufix prediction under specific contextual circumstances. It supports sufix prediction while ensuring compliance with various types of background knowledge, including declare, MP-Declare, ProbDeclare, and procedural models such as Petri nets and BPMN. In this paper, we present the functionalities of NeSy4PPM and empirically evaluate its performance in terms of prediction eficiency, compliance with the input background knowledge, and overall efectiveness.
0.1 https://nesy4ppm.readthedocs.io/en/latest/ https://github.com/JamilaOUKHARIJANE/NeSy4PPM https://youtu.be/ig4QQGxu49M
Predictive Process Monitoring (PPM) has received growing attention in recent years as organizations increasingly aim to anticipate the future evolution of ongoing process instances using historical execution data 1[]. One of the main tasks in this domain is sufix prediction, which aims to forecast the remaining sequence of activities until a trace is completed.
Although various tools and frameworks have been developed for sufix prediction, they primarily focus on stationary processes (i.e., processes that do not evolve over time) and rely mainly on neural models, lacking support for incorporating background knowleℬd ge )(, such as constraints or logical rules in the prediction taskN. eSy4PPM is the first general-purpose Python library for Neuro-Symbolic PPM that supports both stationary and evolving processes, i.e., those that evolve due to concept drift. It addresses sufix prediction for both activity sequences and activity–resource pairs by combining neural models (e.g., LSTM, Transformer) with diverse types ℬof , including probabilistic, declarative, and procedural knowledge.
NeSy4PPM provides an end-to-end pipeline, from data preprocessing to prediction evaluation, and enables users to integrate symbolℬic
to enhance neural predictions at testing time and better manage process changes over time. The library is modular, extensible, and designed to support both single-attribute (activity) and multi-attribute (activity and resource) sufix prediction tasks.
CEUR
ceur-ws.org
Probabilistic declarative BK type
> is the sub-trace obtained by removing the prefix, i.e., > = ⟨ ⟩ log is a set of traces, where each tra creepresents an execution of a business process. An event is a tuple(, , , ) where is the case id, ∈
is the activity name, is the timestamp of the event, and ∈ ℛ is the allocated resource for activ i.tyWe denote the components of an event= (, , , ) the notation. , . , . , and. . Given a trace = ⟨ 1, 2, … , ⟩, the prefix ≤ of length ∈ {1, … , } the sub-trace including the first events of , i.e., ≤ = ⟨ ⟩=1 , with | ≤ | = . The corresponding sufix using
is =+1 , with | > | = − .
xes csv
1. Data preprocessing 2. Prefixes extraction
3. Prefixes encoding Shrinked index-based
2.1. Data Preprocessing The Data Preprocessing package transforms event logs into neural-compatible inputs. It handles event log loading, prefix extraction, and encoding into formats suitable for Neural Network (NN) models: 1. Data loading. This step supports two configurations: (i) asingle event log, automatically split into training and test sets based on the chronological order of trace start timestamps and a user-defined train/test ratio; or (ii) a pair osefparate training and test logs. Logs can be provided in .xes, .xes.gz, or.csv format. 2. Prefix extraction.
All possible prefixes are extracted from the training log traces. Each prefix is turned into an input–label pa(ir,)
for NN training. Given a trac e= ⟨ 1, … , ⟩, this step generates training pairs by selecting prefixe⟨s ⟩=1 as input , and the subsequent event +1 as
the target labe l, for each = 1, … , − 1 . Specifically, +1 . serves as the next activity lab e l, and +1 . as the next resource label. 3. Prefixes encoding. Since NN inputs must be numerical, prefixes are transformed into feature vectors using one of the following methodso:ne-hot, index-based, shrinked index-based, or multi-encoders, which we describe in more detail below. Since vectorhsave variable lengths, zero-padding is applied to ensure fixed-size inputs for NN training. matrix of these row vectors.
In one-hot encoding, each even t = ⟨ , ⟩ is represented by a binary vect or= [ , v ], wherev andv are one-hot vectors for activit y ∈ and resourc e ∈ ℛ. The feature vecto r for prefix is a In index-based encoding, each even t is represented a s = [ , ], where and are indices in
andℛ. The feature vecto r is the concatenation of th e vectors. Both encodings can be adapted for activity-only sequences by omitting the resource vector.
In shrinked index-based encoding, a unique integer index is assigned to each activity–resource pair , resulting in = ( , ). The feature vecto r is then ( , ) using a joint index function obtained by concatenating the values. embeddings are computed a s = Ẽ ⋅ + Ẽ ⋅ , whereẼ = E ⊕ (E ⊗ E ) andẼ = E ⊕ (E ⊗ E ), with
In multi-encoders, separate embeddingsE andE are created for activities and resources. Combined and as alignment weights computed via a shared modulat3o]r. [ 2.2. Training For training, NeSy4PPM implements state-of-the-art NN architectures, supporting both LSTM (Long Short-Term Memory)4[] and Transformer3[] models. This component is responsible for learning predictive models from the encoded input d ataand corresponding target lab el.sIn its basic configuration, the selected NN model learns to predict the next activ̂ i.tyIf the target label s also include resource information , the NN is trained in a multi-output setting to jointly predict the next activity ̂ and its associated resour c ê. 2.3. Prediction Prediction in NeSy4PPM is performed using an autoregressive Symbolic[Neuro] component according to Kautz’s taxonomy 5[, Section 2], where anNN model is invoked as a subroutine within a symbolic reasoner that checks the compliance of tNheN predictions withℬ (see Figure2). This component takes as input a prefix ≤ , a trained NN model, anℬd .
The prediction process begins by encoding the input prefi x ≤ using the same encoding method applied during training. The encoded prefix is then passed to thsearch predictor, which performs sufix prediction via beam search in an autoregressive manner. At each prediction stℎe,pthe predictor evaluates possible continuations based on: (i) the probability distribution over next activities and resources predicted by thterained NN, and (ii) aℬ
compliance score. These are combined using a
weight ∈ [
Here, ( NN( ≤+ℎ−1 , ), NN( ≤+ℎ−1 .)) computes an aggregation (we implemented the average, but other strategies are possible) of the predicted probabilities for the next activity and resource, and the compliance function(⟨ ≤+ℎ−1 , , ⟩, ℬ )
returns a score in[
[
The search predictor is modular and configurable, supporting various settings across four dimensions. Prediction modes include purely neural prediction (wit=h 0 ), BK-contextualized predictio n>( 0 ), and BK-filtered prediction, in which the full predicted trace is retained only if compliantℬw ith upon termination.Search strategies include beam search for exploring multiple candidate continuations and greedy search for selecting only the most likely continuation. The predictor supports diℬferent types as described above. Finally, this NeSy component supports variporuedsiction targets, allowing for prediction of both activity and resource, or activity only. This flexible configuration enables adaptation to a wide range of predictive monitoring scenarios and knowledge models. 2.4. Evaluation To evaluate the performance of neuro-symbolic predictions,Etvhaeluation package supports the following metrics: (i) theDamerau-Levenshtein Similarity (DLS) between the predicted sufix ̂> and the ground truth sufix > ; (ii) the Jaccard similarity between the predicted sufix ̂> and the ground truth sufix
> ; (iii) the Compliance, defined as the proportion of predicted traces (i.e., the prefix concatenated with the predicted sufix) that satisfyℬ (i.e., declare orMP-Declare constraints); (iv) the Fitness, representing the degree to which the predicted traces align with a procedural model; and (v) Computation time, referring to the average and standard deviation of prediction times.
The maturity of NeSy4PPM is demonstrated by its support for a broad range of features, including: (i) multipleencoding methods; (ii) neural architectures, including LSTM and Transformer models; (iii) symbolicℬ
representations, including declarative modedlesc(lare, MP-Declare, ProbDeclare) and procedural models (Petri nets and BPMN); (iv) predicstieoanrch strategies, such as greedy and beam search; (v)prediction modes, including purely neuraℬl, -contextualized, andℬ -filtered predictions; and (vi)prediction targets, supporting both single-attribute (activity) and multi-attribute (activity and resource) prediction tasks. These features enable flexible and comprehensive evaluation across diverse experimental configurations.
In addition, we evaluated the computational performance and prediction accurNaecSyyo4PfPM using two real-world event logs: Helpd1esaknd Request For Paymen2t, under concept drift assumptions. For each log, traces were chronologically sorted: the first 80% were used for training, and the remaining 20% for testing. To simulate concept drift,ℬ
was mined from under-represented behaviors in the
Encoder
One-hot
Index-based [
One-hot seeerrcaydhG ++( MP-Declare) IISSOMnnhhnddurreeelii-nnxxthi--kk-bboeeeaatnddssceeiionndddddeeerxxs--bbaasseedd
Multi-encoders one-hot Index-based Shrinked index-based Multi-encoders
One-hot [
Multi-encoders training set using theDeclareMiner3 tool, selecting constraints with less than 20% support. We extracted two MP-Declare constraints for the Helpdesk log and eight for the Request For Payment log. We then retained only those traces in the test sets that were compliant with the respective constraints. This resulted inMP-Declare-compliant test sets containing 820 traces for Helpdesk and 445 traces for Request For Payment.
We performed experiments using diferent prediction configurations, including Greedy Search )( and Beam Search ( ) with a beam size of = 3 . For each strategy, we evaluated: (i) purely neural predictions, (ii) filtered predictions ( ), and (iii) contextualized predictions ( ). All experiments used a Transformer architecture as the NN model.
Table1 reports the average and standard deviation of prediction times (in seconds), as well as
prediction accuracy using the DLS and compliance metrics for both activity and resource prediction,
across all combinations of prediction metho d s –[
From the table, we observe that while the use of in combination with greedy or beam search introduces additional computational overhead duℬe toconformance checking, it leads to a clear improvement in prediction accuracy. These results highlight the efectiveness of integrating symbolicℬ into the prediction algorithm. Notabl y+, achieves the best DLS scores for both activity and resource prediction, as well as the highest compliance on both logs. We acknowledge that this comes at the cost of increased computational time.
In contrast, the purely neural predictions methods a(nd ) struggle with resource prediction, confirming that NN models alone fail to capture drifts in resource allocation. Alth o +u gh and + methods apply symbolicℬ as a post-prediction filter, their overall performance remains similar to the purely neural predictions methods in terms of both prediction accuracy and compliance. This limited improvement can be attributed to the restricted beam size: when activity-resource pairs representing drift are rare or unseen during training, the NN model assigns them low probabilities. As a result, these pairs are often excluded from the beam due to the prioritization of higher-probability candidates.
As future work, we plan to implement multi-threading to parallelize the beam search to reduce the computational time. Furthermore, we aim to integrate fu zzy compliance checking to support reasoning under uncertainty10[], incorporateℬ into the training phase via the loss function11[], and include explanation techniques to enhance interpretability. This study was partially funded by the European Union - NextGenerationEU, in the framework of the iNEST - Interconnected Nord-Est Innovation Ecosystem (iNEST ECS00000043 – CUP I43C22000250006). The views and opinions expressed are solely those of the authors and do not necessarily reflect those of the European Union, nor can the European Union be held responsible for them. The study was also supported by Fondazione Cariverona within the ReSS-Pro project.
The authors have not employed any Generative AI tools.