Analog quantum simulators provide access to many-body dynamics beyond the reach of classical computation. However, extracting physical insights from experimental data is often hindered by measurement noise, limited observables, and incomplete knowledge of the underlying microscopic model. Here, we develop a machine learning approach based on a variational autoencoder (VAE) to analyze interference measurements of tunnel-coupled one-dimensional Bose gases, which realize the sine-Gordon quantum field theory. Trained in an unsupervised manner, the VAE learns a minimal latent representation that strongly correlates with the equilibrium control parameter of the system. Applied to non-equilibrium protocols, the latent space uncovers signatures of frozen-in solitons following rapid cooling, and reveals anomalous post-quench dynamics not captured by conventional correlation-based methods. These results demonstrate that generative models can extract physically interpretable variables directly from noisy and sparse experimental data, providing complementary probes of equilibrium and non-equilibrium physics in quantum simulators. More broadly, our work highlights how machine learning can supplement established field-theoretical techniques, paving the way for scalable, data-driven discovery in quantum many-body systems.

As modern power systems continue to evolve, accurate power load forecasting remains a critical issue. The phase space reconstruction method can effectively retain the chaotic characteristics of power load from a system dynamics perspective and thus is a promising knowledge-based preprocessing method for power load forecasting. However, limited by its fundamental theory, there is still a gap in implementing a multi-step forecasting scheme in current studies. To bridge this gap, this study proposes a novel multi-step forecasting approach by integrating the PSR with neural networks. Firstly, the useful features in the phase trajectory obtained from the preprocessing of PSR are discussed in detail. Through mathematical derivation, the equivalent characterization of the PSR and another time series preprocessing method, patch segmentation, is demonstrated for the first time. Based on this prior knowledge, an image-based modeling perspective with the global and local feature extraction strategy is introduced. Subsequently, a novel deep learning model, namely PSR-GALIEN, is designed for end-to-end processing, in which the Transformer Encoder and 2D-convolutional neural networks are employed for the extraction of the global and local patterns in the image, and a multi-layer perception based predictor is used for the efficient correlation modeling. Then, extensive experiments are conducted on five real-world benchmark datasets to verify the effectiveness as well as to have an insight into the detailed properties. The results show that, comparing it with six state-of-the-art deep learning models, the forecasting performance of PSR-GALIEN consistently surpasses these baselines, which achieves superior accuracy in both intra-day and day-ahead forecasting scenarios. At the same time, a visualization-based method is proposed to explain the attributions of the forecasting results.

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.

In systems biology, attractor landscape analysis of gene regulatory networks is recognized as a powerful computational tool for studying various cellular states from proliferation and differentiation to senescence and apoptosis. Therefore, accurate identification of attractors plays a critical role in determination of the cell fates. On the other hand, in a real biological circuit, genetic/epigenetic alterations as well as varying environmental factors drastically take effect on the location, characteristics, and even the number of attractors. The central question is: Given a temporal gene expression profile of a real gene regulatory network, how can the attractors be robustly identified in the presence of huge amount of uncertainty? This paper addresses this question using a novel approach based on Zadeh Computing with Words. The proposed scheme could effectively identify the attractors from temporal gene expression data in terms of both fuzzy logic-based and linguistic descriptions which are simply interpretable by human experts. Therefore, this method can be considered as an effective step towards interpretable artificial intelligence. Without loss of generality, genetic toggle switch is considered as the case study. The nonlinear dynamics of this benchmark gene regulatory network is computationally modeled by the notion of uncertain stochastic differential equations. The results of in-silico study demonstrate the efficiency and robustness of the proposed method.

In current model-free reinforcement learning (RL) algorithms, stability criteria based on sampling methods are commonly utilized to guide policy optimization. However, these criteria only guarantee the infinite-time convergence of the system's state to an equilibrium point, which leads to sub-optimality of the policy. In this paper, we propose a policy optimization technique incorporating sampling-based Lyapunov stability. Our approach enables the system's state to reach an equilibrium point within an optimal time and maintain stability thereafter, referred to as "optimal-time stability". To achieve this, we integrate the optimization method into the Actor-Critic framework, resulting in the development of the Adaptive Lyapunov-based Actor-Critic (ALAC) algorithm. Through evaluations conducted on ten robotic tasks, our approach outperforms previous studies significantly, effectively guiding the system to generate stable patterns.