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.

Thermoacoustic instability in annular combustors, essential to aero engines and modern gas turbines, can severely impair operational stability and efficiency, accurately recognizing and understanding various combustion modes is the prerequisite for understanding and controlling combustion instabilities. However, the high-dimensional spatial-temporal dynamics of turbulent flames typically pose considerable challenges to mode recognition. Based on the bidirectional temporal and nonlinear dimensionality reduction models, this study introduces a two-layer bidirectional long short-term memory variational autoencoder, Bi-LSTM-VAE model, to effectively recognize dynamical modes in annular combustion systems. Specifically, leveraging 16 pressure signals from a swirl-stabilized annular combustor, the model maps complex dynamics into a low-dimensional latent space while preserving temporal dependency and nonlinear behavior features through the recurrent neural network structure. The results show that the novel Bi-LSTM-VAE method enables a clear representation of combustion states in two-dimensional state space. Analysis of latent variable distributions reveals distinct patterns corresponding to a wide range of equivalence ratios and premixed fuel and air mass flow rates, offering novel insights into mode classification and transitions, highlighting this model's potential for deciphering complex thermoacoustic phenomena.

Combustion instability in gas turbines and rocket engines, as one of the most challenging problems in combustion research, arises from the complex interactions among flames, which are also influenced by chemical reactions, heat and mass transfer, and acoustics. Identifying and understanding combustion instability is essential to ensure the safe and reliable operation of many combustion systems, where exploring and classifying the dynamical behaviors of complex flame systems is a core take. To facilitate fundamental studies, the present work concerns dynamical mode recognition of coupled flame oscillators made of flickering buoyant diffusion flames, which have gained increasing attention in recent years but are not sufficiently understood. The time series data of flame oscillators are generated by fully validated reacting flow simulations. Due to limitations of expertise-based models, a data-driven approach is adopted. In this study, a nonlinear dimensional reduction model of variational autoencoder (VAE) is used to project the simulation data onto a 2-dimensional latent space. Based on the phase trajectories in latent space, both supervised and unsupervised classifiers are proposed for datasets with well known labeling and without, respectively. For labeled datasets, we establish the Wasserstein-distance-based classifier (WDC) for mode recognition; for unlabeled datasets, we develop a novel unsupervised classifier (GMM-DTWC) combining dynamic time warping (DTW) and Gaussian mixture model (GMM). Through comparing with conventional approaches for dimensionality reduction and classification, the proposed supervised and unsupervised VAE-based approaches exhibit a prominent performance for distinguishing dynamical modes, implying their potential extension to dynamical mode recognition of complex combustion problems.

Oscillatory combustion in aero engines and modern gas turbines often has significant adverse effects on their operation, and accurately recognizing various oscillation modes is the prerequisite for understanding and controlling combustion instability. However, the high-dimensional spatial-temporal data of a complex combustion system typically poses considerable challenges to the dynamical mode recognition. Based on a two-layer bidirectional long short-term memory variational autoencoder (Bi-LSTM-VAE) dimensionality reduction model and a two-dimensional Wasserstein distance-based classifier (WDC), this study proposes a promising method (Bi-LSTM-VAE-WDC) for recognizing dynamical modes in oscillatory combustion systems. Specifically, the Bi-LSTM-VAE dimension reduction model was introduced to reduce the high-dimensional spatial-temporal data of the combustion system to a low-dimensional phase space; Gaussian kernel density estimates (GKDE) were computed based on the distribution of phase points in a grid; two-dimensional WD values were calculated from the GKDE maps to recognize the oscillation modes. The time-series data used in this study were obtained from numerical simulations of circular arrays of laminar flame oscillators. The results show that the novel Bi-LSTM-VAE method can produce a non-overlapping distribution of phase points, indicating an effective unsupervised mode recognition and classification. Furthermore, the present method exhibits a more prominent performance than VAE and PCA (principal component analysis) for distinguishing dynamical modes in complex flame systems, implying its potential in studying turbulent combustion.

Many nonlinear dynamical phenomena can be effectively modeled by a system that switches among a set of conditionally linear dynamical modes. We consider two such models: the switching linear dynamical system (SLDS) and the switching vector autoregressive (VAR) process. In this paper, we present a nonparametric approach to the learning of an unknown number of persistent, smooth dynamical modes by utilizing a hierarchical Dirichlet process prior. We develop a sampling algorithm that combines a truncated approximation to the Dirichlet process with an efficient joint sampling of the mode and state sequences. The utility and flexibility of our model are demonstrated on synthetic data, sequences of dancing honey bees, and the IBOVESPA stock index.

Ocean dynamics constitute a source of incertitude in determining the ocean's role in complex climatic phenomena. Current observation systems have difficulty achieving sufficiently statistic precision for three-dimensional oceanic data. It is crucial knowledge to describe the behavior of internal ocean structures. We present a data-driven approach that explores latent class regressions and deep neural networks in modeling ocean dynamics in the extensions of Gulf Stream and Kuroshio currents. The obtained results show a promising direction of data-driven for understanding the ocean's characteristics (salinity, temperature) in both spatial and temporal dimensions in the turbulent regions. Our source codes are publicly available at https://github.com/v18nguye/gulfstream-lrm and at https://github.com/sagudelor/Kuroshio.

Many nonlinear dynamical phenomena can be effectively modeled by a system that switches among a set of conditionally linear dynamical modes. We consider two such models: the switching linear dynamical system (SLDS) and the switching vector autoregressive (VAR) process. In this paper, we present a nonparametric approach to the learning of an unknown number of persistent, smooth dynamical modes by utilizing a hierarchical Dirichlet process prior. We develop a sampling algorithm that combines a truncated approximation to the Dirichlet process with an efficient joint sampling of the mode and state sequences. The utility and flexibility of our model are demonstrated on synthetic data, sequences of dancing honey bees, and the IBOVESPA stock index.

We propose a Bayesian nonparametric approach to the problem of jointly modeling multiple related time series. Our approach is based on the discovery of a set of latent, shared dynamical behaviors. Using a beta process prior, the size of the set and the sharing pattern are both inferred from data. We develop efficient Markov chain Monte Carlo methods based on the Indian buffet process representation of the predictive distribution of the beta process, without relying on a truncated model. In particular, our approach uses the sum-product algorithm to efficiently compute Metropolis-Hastings acceptance probabilities, and explores new dynamical behaviors via birth and death proposals. We examine the benefits of our proposed feature-based model on several synthetic datasets, and also demonstrate promising results on unsupervised segmentation of visual motion capture data.

Many nonlinear dynamical phenomena can be effectively modeled by a system that switches among a set of conditionally linear dynamical modes. We consider two such models: the switching linear dynamical system (SLDS) and the switching vector autoregressive (VAR) process. In this paper, we present a nonparametric approach to the learning of an unknown number of persistent, smooth dynamical modes by utilizing a hierarchical Dirichlet process prior. We develop a sampling algorithm that combines a truncated approximation to the Dirichlet process with an efficient joint sampling of the mode and state sequences. The utility and flexibility of our model are demonstrated on synthetic data, sequences of dancing honey bees, and the IBOVESPA stock index.