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A Unified Particle Filter LSTM for Data-Driven Process Simulation
Parvin Malekzadeh, Opher Baron, Dmitry Krass
TL;DR
Event logs partially reveal process conditions, while standard recurrent models reduce each observed history to one deterministic state. The Unified PF-LSTM maintains weighted recurrent-state hypotheses, summarizes their belief with a weighted mean and MGF features, and predicts routing and timing. Across three real-world emergency-department datasets, it outperforms alternative data-driven baselines in reproducing routing, durations, and system-level behavior, especially for more complex settings.
Problem
Event logs provide only partial process-state information, so one observed history may correspond to multiple latent conditions that standard recurrent representations do not preserve.
Method
Unified PF-LSTM maintains and updates weighted recurrent-state hypotheses, then uses their weighted mean and MGF-based features to predict next activities and conditional sojourn-time quantiles.
Results
The framework outperforms alternative data-driven baselines across three real-world emergency-department datasets in routing, activity-duration, and system-level behavior reproduction.
Takeaways & Limitations
Particle-based belief representations support complete case-trajectory generation while representing latent-state uncertainty and variability in routing and sojourn times.
Takeaways & Limitations
The particle-based model requires more computation than the two baselines, although vectorized GPU evaluation is expected to reduce wall-clock time.
Abstract
from arXiv · showhide
Data-driven process simulation aims to generate realistic case trajectories from historical event logs without requiring an explicitly specified model of the underlying dynamics. Deep sequence models can capture complex temporal dependencies through next-activity probabilities and conditional time distributions. However, event logs provide only a partial view of the underlying process state, often recording activity completions without the corresponding service-start times. Consequently, the same observed process history may be consistent with multiple plausible latent process conditions, whereas standard recurrent models compress each process prefix into a single deterministic recurrent state. We propose a Unified Particle Filter LSTM (Unified PF-LSTM) that maintains and sequentially updates a weighted set of recurrent-state hypotheses. We summarize this particle belief using its weighted mean and learned features based on the moment-generating function. The resulting representation is used to predict a categorical distribution over the next activity and conditional quantiles of the current activity's sojourn time. The framework is trained end-to-end from event-log data and evaluated on three real-world emergency department datasets. The results show that the proposed framework consistently outperforms the considered data-driven baselines in reproducing routing, duration, and system-level behavior across all datasets, with particularly strong gains in settings where complex process dynamics are only partially reflected in the available event logs.
1 Introduction
Data-driven process simulation learns routing and timing from event logs, but partial observability leaves multiple plausible process conditions. Unified PF-LSTM addresses this by maintaining particle-based recurrent-state beliefs and outperforms considered baselines on three emergency-department datasets.
- Data-driven simulation learns generative process models directly from event logs, reducing the need to fully specify underlying dynamics.
- Standard LSTMs compress variable-length process prefixes into a single deterministic recurrent state despite uncertainty in the underlying process state.
- Partial event logs can conflate waiting and service time, making identical observed histories consistent with different latent process conditions.
- PF-LSTM maintains a weighted particle approximation of recurrent-state beliefs and updates particle importance through a differentiable filtering procedure.
- MGF-based learned features augment the weighted mean to preserve information about the particle belief’s shape efficiently.
- The framework uses shared belief representations for next-activity probabilities and conditional sojourn-time quantiles, outperforming baselines across three emergency departments.The evaluation covers over 120,000 patient visits and 1,200,000 station visits, with particularly strong accuracy gains for complex, partially observed processes.
2 Problem Formulation
The problem formulation represents each case as an activity trace with transition times, dynamic system features, and static attributes. Given this history, the model estimates next-activity probabilities and conditional sojourn-time quantiles.
- Each case is represented as a sequence of visited activities and times spent until transitions to subsequent events.
- The observation at step k combines the current activity, the previous transition time, and dynamic features describing case and system conditions.Dynamic features may include elapsed process time, system population, activity-level census, and congestion measures.
- Given H_k, the model estimates the conditional probability of each possible next activity, including END as the terminal activity.
- The model represents the current activity’s sojourn-time distribution using conditional quantiles at multiple probability levels.Quantile representations avoid imposing a parametric duration distribution and accommodate skewness, heavy tails, or heteroscedasticity.
3 Methodology
The Unified PF-LSTM represents partial observability with a weighted set of recurrent-state hypotheses, summarizes that belief, and jointly predicts routing and sojourn-time outcomes. It is trained end to end and includes validation safeguards for recursive simulation.
- Motivation: Partial event logs can conflate waiting and service time, creating uncertainty about latent process conditions and motivating a particle-based representation.The framework addresses unavailable, noisy, or delayed factors affecting routing and sojourn times.
- Particle belief: The PF-LSTM maintains weighted recurrent-state particles that represent plausible latent process conditions and updates their relative importance sequentially.Particles are propagated, weighted by compatibility, and soft-resampled through a differentiable computational graph.
- Belief representation: The particle belief is summarized by a weighted hidden-state mean and trainable moment-generating-function features before prediction.The MGF features evaluate trainable linear projections of particle states, apply exponentiation, and aggregate them using particle weights.
- Prediction and training: The shared belief representation feeds a routing head for next-activity probabilities and a timing head for conditional sojourn-time quantiles.The two heads are trained with categorical cross-entropy and quantile Huber losses under the joint objective L = LRouting + LTiming.
- Prediction and training: The model is trained end to end through the particle transition, particle weights, MGF matrix, and two prediction heads, while the validator is trained separately.Gradients from both task losses propagate through the shared belief representation; validator parameters are excluded from the unified objective.
- Recursive simulation: During recursive simulation, a separately trained routing validator filters implausible next activities before the main routing probabilities are renormalized.The validator uses activity history and static case attributes, and safeguards against transitions induced by outlier-driven system conditions.
4 Experimental Evaluation
The evaluation compares Unified PF-LSTM with established baselines on three emergency-department datasets, assessing simulation fidelity, errors, sensitivity, and computational cost. The proposed model closely reproduces observed system-level distributions and improves errors across datasets, especially for more complex processes, while requiring more computation.
- Experimental setup: The study evaluates routing and activity sojourn-time distributions using patient event logs from three emergency departments.The datasets comprise patient-level activity sequences and completion timestamps, with dynamic features describing congestion and workload.
- Experimental setup: The proposed model is compared with a fifth-order Markov routing model combined with a random survival forest for sojourn-time prediction.The baseline models routing and timing separately, whereas the LSTM baseline provides a sequential joint representation.
- System-level fidelity: Across all three datasets, Unified PF-LSTM-generated TPIA and LOS distributions closely follow the observed distributions.TPIA and LOS are used as key indicators of emergency-department operations.
- Error performance: The LSTM improves upon the RSF timing + 5-Markov routing framework, while Unified PF-LSTM reduces both mean and 90th-percentile errors across all datasets and measures.Larger improvements are observed for EDs B and C, which have more complex process structures.
- Error performance: TPIA errors are generally larger than LOS errors because TPIA is more sensitive to early routing mistakes.Duration errors can partially offset when aggregated into total LOS.
- Sensitivity and ablation: Increasing particles generally improves performance from P = 1 to P = 30, but P = 20 is selected to balance predictive performance and efficiency.The particle-based model requires more computation because each observation is propagated through multiple particles; GPU parallelization is expected to reduce runtime.
- Sensitivity and ablation: MGF features improve over a mean-only belief representation, particularly for ED B, while improvements become minor beyond M = 8.The MGF features capture distributional information beyond the mean, including dispersion and multimodality.
- Sensitivity and ablation: Increasing predicted quantiles from Nq = 10 to Nq = 50 improves conditional sojourn-time representation, but Nq = 20 is chosen because further gains are minor and computation increases.The default configuration uses Nq = 20.
5 Conclusion and Future Directions
The Unified PF-LSTM represents latent process-state uncertainty with particle-based beliefs and MGF-based features, enabling complete trajectory generation. Across three real-world emergency-department datasets, it outperformed alternative data-driven baselines, especially in more complex settings; future work targets broader deployment and adaptation.
- The Unified PF-LSTM maintains particle-based beliefs over recurrent-state hypotheses and uses MGF-based features to represent latent process conditions under partial observability.
- Across three real-world emergency-department datasets, the framework outperformed alternative data-driven baselines in routing, activity durations, and system-level performance measures.
- The strongest improvements occurred in more complex settings with differing levels of process complexity and information availability.
- Future Directions: Future work may extend the framework to other service systems and investigate online adaptation under changing operating conditions.
- Future Directions: Additional directions include counterfactual analysis and integration with reinforcement learning for policy evaluation, optimization, and operational decision-making.