Traditional reinforcement learning (RL) assumes the agents make decisions based on Markov decision processes (MDPs) with one-step transition models. In many real-world applications, such as energy management and stock investment, agents can access multi-step predictions of future states, which provide additional advantages for decision making. However, multi-step predictions are inherently high-dimensional: naively embedding these predictions into an MDP leads to an exponential blow-up in state space and the curse of dimensionality. Moreover, existing RL theory provides few tools to analyze prediction-augmented MDPs, as it typically works on one-step transition kernels and cannot accommodate multi-step predictions with errors or partial action-coverage. We address these challenges with three key innovations: First, we propose the \emph{Bayesian value function} to characterize the optimal prediction-aware policy tractably. Second, we develop a novel \emph{Bellman-Jensen Gap} analysis on the Bayesian value function, which enables characterizing the value of imperfect predictions. Third, we introduce BOLA (Bayesian Offline Learning with Online Adaptation), a two-stage model-based RL algorithm that separates offline Bayesian value learning from lightweight online adaptation to real-time predictions. We prove that BOLA remains sample-efficient even under imperfect predictions.

Flight trajectory prediction is a critical time series task in aviation. While deep learning methods have shown significant promise, the application of large language models (LLMs) to this domain remains underexplored. This study pioneers the use of LLMs for flight trajectory prediction by reframing it as a language modeling problem. Specifically, We extract features representing the aircraft's position and status from ADS-B flight data to construct a prompt-based dataset, where trajectory waypoints are converted into language tokens. The dataset is then employed to fine-tune LLMs, enabling them to learn complex spatiotemporal patterns for accurate predictions. Comprehensive experiments demonstrate that LLMs achieve notable performance improvements in both single-step and multi-step predictions compared to traditional methods, with LLaMA-3.1 model achieving the highest overall accuracy. However, the high inference latency of LLMs poses a challenge for real-time applications, underscoring the need for further research in this promising direction.

Deep learning models are often trained to approximate dynamical systems that can be modeled using differential equations. These models are optimized to predict one step ahead and produce calibrated predictions if the predictive model can quantify uncertainty, such as deep ensembles. At inference time, multi-step predictions are generated via autoregression, which needs a sound uncertainty propagation method (e.g., Trajectory Sampling) to produce calibrated multi-step predictions. This paper introduces an approach named HopCast that uses the Modern Hopfield Network (MHN) to learn the residuals of a deterministic model that approximates the dynamical system. The MHN predicts the density of residuals based on a context vector at any timestep during autoregression. This approach produces calibrated multi-step predictions without uncertainty propagation and turns a deterministic model into a calibrated probabilistic model. This work is also the first to benchmark existing uncertainty propagation methods based on calibration errors with deep ensembles for multi-step predictions.

Early fault detection and timely maintenance scheduling can significantly mitigate operational risks in NPPs and enhance the reliability of operator decision-making. Therefore, it is necessary to develop an efficient Prognostics and Health Management (PHM) multi-step prediction model for predicting of system health status and prompt execution of maintenance operations. In this study, we propose a novel predictive model that integrates reinforcement learning with Long Short-Term Memory (LSTM) neural networks and the Expert Fuzzy Evaluation Method. The model is validated using parameter data for 20 different breach sizes in the Main Steam Line Break (MSLB) accident condition of the CPR1000 pressurized water reactor simulation model and it demonstrates a remarkable capability in accurately forecasting NPP parameter changes up to 128 steps ahead (with a time interval of 10 seconds per step, i.e., 1280 seconds), thereby satisfying the temporal advance requirement for fault prognostics in NPPs. Furthermore, this method provides an effective reference solution for PHM applications such as anomaly detection and remaining useful life prediction.

We propose and experimentally demonstrate an innovative stock index prediction method using a weighted optical reservoir computing system. We construct fundamental market data combined with macroeconomic data and technical indicators to capture the broader behavior of the stock market. Our approach shows significant higher performance than state-of-the-art methods such as linear regression, decision trees, and neural network architectures including long short-term memory. It captures well the market's high volatility and nonlinear behaviors despite limited data, demonstrating great potential for real-time, parallel, multi-dimensional data processing and predictions.

Uncertainty quantification has become crucial in many scientific domains where black-box machine learning models are often used [1]. Conformal prediction has emerged as a popular and modern technique for uncertainty quantification by providing valid predictive inference for those black-box models [8, 2]. Time series prediction aims to forecast future values based on a sequence of observations sequentially ordered in time [3]. With recent advances in machine learning, numerous models have been proposed and adopted for various time series prediction tasks. The increased use of black-box machine learning models necessitates uncertainty quantification, particularly in high-stakes time series prediction tasks such as medical event prediction, stock prediction, and weather forecasting. While conformal prediction can provide valid predictive inference for uncertainty quantification, applying conformal prediction to time series is challenging since time series data often violate the exchangeability assumption.

The aim of this paper is to present a novel physics-based framework for the identification of dynamical systems, in which the physical and structural insights are reflected directly into a backpropagation-based learning algorithm. The main result is a method to compute in closed form the gradient of a multi-step loss function, while enforcing physical properties and constraints. The derived algorithm has been exploited to identify the unknown inertia matrix of a space debris, and the results show the reliability of the method in capturing the physical adherence of the estimated parameters.

Chlorophyll concentration can well reflect the nutritional status and algal blooms of water bodies, and is an important indicator for evaluating water quality. The prediction of chlorophyll concentration change trend is of great significance to environmental protection and aquaculture. However, there is a complex and indistinguishable nonlinear relationship between many factors affecting chlorophyll concentration. In order to effectively mine the nonlinear features contained in the data. This paper proposes a time-series decomposition adaptive graph-time convolutional network ( AGTCNSD ) prediction model. Firstly, the original sequence is decomposed into trend component and periodic component by moving average method. Secondly, based on the graph convolutional neural network, the water quality parameter data is modeled, and a parameter embedding matrix is defined. The idea of matrix decomposition is used to assign weight parameters to each node. The adaptive graph convolution learns the relationship between different water quality parameters, updates the state information of each parameter, and improves the learning ability of the update relationship between nodes. Finally, time dependence is captured by time convolution to achieve multi-step prediction of chlorophyll concentration. The validity of the model is verified by the water quality data of the coastal city Beihai. The results show that the prediction effect of this method is better than other methods. It can be used as a scientific resource for environmental management decision-making.

While looking at a static image alone it is difficult to discern (without direct supervision) between background and foreground objects, or discern individual objects at all. Where does one object start and another end? Only by observing the objects interacting with each other over time can we fully learn their properties. Prediction of video sequences using only video frames is especially difficult as images are a discrete 2D projection of the real world. Many difficulties in frame-to-frame video prediction come from the fact that our system must perform several sub-tasks sequentially in order to create an output that not only looks realistic, but also matches real world data. We argue that these two requirements, predicting a realistic frame and predicting a frame that matches a target frame from the data-set, conflict with each other during training causing poor performance. In order to create plausible predictions in dynamic natural video sequences, we loosen the constraint of matching the target frames exactly. By doing so, we acknowledged that there are some things in the next frame that are not possible to predict at all, let alone with any accuracy.