We consider the problem of quantitative predictive monitoring (QPM) of stochastic systems, i.e., predicting at runtime the degree of satisfaction of a desired temporal logic property from the current state of the system. Since computational efficiency is key to enable timely intervention against predicted violations, several state-of-the-art QPM approaches rely on fast machine-learning surrogates to provide prediction intervals for the satisfaction values, using conformal inference to offer statistical guarantees. However, these QPM methods suffer when the monitored agent exhibits multi-modal dynamics, whereby certain modes may yield high satisfaction values while others critically violate the property. Existing QPM methods are mode-agnostic and so would yield overly conservative and uninformative intervals that lack meaningful mode-specific satisfaction information. To address this problem, we present GenQPM, a method that leverages deep generative models, specifically score-based diffusion models, to reliably approximate the probabilistic and multi-modal system dynamics without requiring explicit model access. GenQPM employs a mode classifier to partition the predicted trajectories by dynamical mode. For each mode, we then apply conformal inference to produce statistically valid, mode-specific prediction intervals. We demonstrate the effectiveness of GenQPM on a benchmark of agent navigation and autonomous driving tasks, resulting in prediction intervals that are significantly more informative (less conservative) than mode-agnostic baselines.

We study the problem of predictive runtime monitoring of black-box dynamical systems with quantitative safety properties. The black-box setting stipulates that the exact semantics of the dynamical system and the controller are unknown, and that we are only able to observe the state of the controlled (aka, closed-loop) system at finitely many time points. We present a novel framework for predicting future states of the system based on the states observed in the past. The numbers of past states and of predicted future states are parameters provided by the user. Our method is based on a combination of Taylor's expansion and the backward difference operator for numerical differentiation. We also derive an upper bound on the prediction error under the assumption that the system dynamics and the controller are smooth. The predicted states are then used to predict safety violations ahead in time. Our experiments demonstrate practical applicability of our method for complex black-box systems, showing that it is computationally lightweight and yet significantly more accurate than the state-of-the-art predictive safety monitoring techniques.

This tutorial focuses on efficient methods to predictive monitoring (PM), the problem of detecting at runtime future violations of a given requirement from the current state of a system. While performing model checking at runtime would offer a precise solution to the PM problem, it is generally computationally expensive. To address this scalability issue, several lightweight approaches based on machine learning have recently been proposed. These approaches work by learning an approximate yet efficient surrogate (deep learning) model of the expensive model checker. A key challenge remains to ensure reliable predictions, especially in safety-critical applications. We review our recent work on predictive monitoring, one of the first to propose learning-based approximations for CPS verification of temporal logic specifications and the first in this context to apply conformal prediction (CP) for rigorous uncertainty quantification. These CP-based uncertainty estimators offer statistical guarantees regarding the generalization error of the learning model, and they can be used to determine unreliable predictions that should be rejected. In this tutorial, we present a general and comprehensive framework summarizing our approach to the predictive monitoring of CPSs, examining in detail several variants determined by three main dimensions: system dynamics (deterministic, non-deterministic, stochastic), state observability, and semantics of requirements' satisfaction (Boolean or quantitative).

Reinforcement learning has been increasingly applied in monitoring applications because of its ability to learn from previous experiences and can make adaptive decisions. However, existing machine learning-based health monitoring applications are mostly supervised learning algorithms, trained on labels and they cannot make adaptive decisions in an uncertain complex environment. This study proposes a novel and generic system, predictive deep reinforcement learning (PDRL) with multiple RL agents in a time series forecasting environment. The proposed generic framework accommodates virtual Deep Q Network (DQN) agents to monitor predicted future states of a complex environment with a well-defined reward policy so that the agent learns existing knowledge while maximizing their rewards. In the evaluation process of the proposed framework, three DRL agents were deployed to monitor a subject's future heart rate, respiration, and temperature predicted using a BiLSTM model. With each iteration, the three agents were able to learn the associated patterns and their cumulative rewards gradually increased. It outperformed the baseline models for all three monitoring agents. The proposed PDRL framework is able to achieve state-of-the-art performance in the time series forecasting process. The proposed DRL agents and deep learning model in the PDRL framework are customized to implement the transfer learning in other forecasting applications like traffic and weather and monitor their states. The PDRL framework is able to learn the future states of the traffic and weather forecasting and the cumulative rewards are gradually increasing over each episode.

Predictive process monitoring is an exceedingly active field of research. At its core, the fundamental component of predictive monitoring is the abstraction technique it uses to obtain a fixed-length representation of the process component subject to the prediction (often, but not always, process traces). In the earlier approaches, the need for such abstraction was overcome through model-aware techniques, employing process models and replay techniques on partial traces to abstract a flat representation of event sequences. Such process models are mostly automatically discovered from a set of available complete traces, and require perfect fitness on training instances (and, seldomly, also on unseen test instances). For instance, van der Aalst et al. [van_der_aalst_time_2011] proposed a time prediction framework based on replaying partial traces on a transition system, effectively clustering training instances by control-flow information.

Predictive monitoring of business processes is concerned with the prediction of ongoing cases on a business process. Lately, the popularity of deep learning techniques has propitiated an ever-growing set of approaches focused on predictive monitoring based on these techniques. However, the high disparity of process logs and experimental setups used to evaluate these approaches makes it especially difficult to make a fair comparison. Furthermore, it also difficults the selection of the most suitable approach to solve a specific problem. In this paper, we provide both a systematic literature review of approaches that use deep learning to tackle the predictive monitoring tasks. In addition, we performed an exhaustive experimental evaluation of 10 different approaches over 12 publicly available process logs.

Predictive Business Process Monitoring is becoming an essential aid for organizations, providing online operational support of their processes. This paper tackles the fundamental problem of equipping predictive business process monitoring with explanation capabilities, so that not only the what but also the why is reported when predicting generic KPIs like remaining time, or activity execution. We use the game theory of Shapley Values to obtain robust explanations of the predictions. The approach has been implemented and tested on real-life benchmarks, showing for the first time how explanations can be given in the field of predictive business process monitoring.