Related papers: Hybrid Forecasting of Chaotic Processes: Using Mac…

A machine-learning approach called "reservoir computing" has been used successfully for short-term prediction and attractor reconstruction of chaotic dynamical systems from time series data. We present a theoretical framework that describes…

Robust model predictive control algorithms are essential for addressing unavoidable errors due to the uncertainty in predicting real-world systems. However, the formulation of such algorithms typically results in a trade-off between…

Accurate time-series forecasting is crucial in various scientific and industrial domains, yet deep learning models often struggle to capture long-term dependencies and adapt to data distribution shifts over time. We introduce Future-Guided…

Data-driven forecasts of air quality have recently achieved more accurate short-term predictions. Despite their success, most of the current data-driven solutions lack proper quantifications of model uncertainty that communicate how much to…

For real-life nonlinear systems, the exact form of nonlinearity is often not known and the known governing equations are often based on certain assumptions and approximations. Such representation introduced model-form error into the system.…

Probabilistic models help us encode latent structures that both model the data and are ideally also useful for specific downstream tasks. Among these, mixture models and their time-series counterparts, hidden Markov models, identify…

Simultaneous load forecasting across multiple entities (e.g., regions, buildings) is crucial for the efficient, reliable, and cost-effective operation of power systems. Accurate load forecasting is a challenging problem due to the inherent…

A hallmark of chaotic dynamics is the loss of information with time. Although information loss is often expressed through a connection to Lyapunov exponents -- valid in the limit of high information about the system state -- this picture…

As global climate change intensifies, accurate weather forecasting has become increasingly important, affecting agriculture, energy management, environmental protection, and daily life. This study introduces a hybrid model combining…

Advances in machine learning have revolutionized capabilities in applications ranging from natural language processing to marketing to health care. Here, we demonstrate the efficacy of machine learning in predicting chaotic behavior in…

In data-driven modelling of complex dynamic processes, it is often desirable to combine different classes of models to enhance performance. Examples include coupled models of different fidelities, or hybrid models based on physical…

As the role played by statistical and computational sciences in climate and environmental modelling and prediction becomes more important, Machine Learning researchers are becoming more aware of the relevance of their work to help tackle…

Recent research has established the effectiveness of machine learning for data-driven prediction of the future evolution of unknown dynamical systems, including chaotic systems. However, these approaches require large amounts of measured…

An extremely challenging problem of significant interest is to predict catastrophes in advance of their occurrences. We present a general approach to predicting catastrophes in nonlinear dynamical systems under the assumption that the…

A chaotic system is a highly volatile system characterized by its sensitive dependence on initial conditions and outside factors. Chaotic systems are prevalent throughout the world today: in weather patterns, disease outbreaks, and even…

In nonlinear dynamical systems, tipping refers to a critical transition from one steady state to another, typically catastrophic, steady state, often resulting from a saddle-node bifurcation. Recently, the machine-learning framework of…

Recent research has demonstrated Reservoir Computing's capability to model various chaotic dynamical systems, yet its application to Hamiltonian systems remains relatively unexplored. This paper investigates the effectiveness of Reservoir…

Mathematical models are crucial for optimizing and controlling chemical processes, yet they often face significant limitations in terms of computational time, algorithm complexity, and development costs. Hybrid models, which combine…

Recent innovations in diffusion probabilistic models have paved the way for significant progress in image, text and audio generation, leading to their applications in generative time series forecasting. However, leveraging such abilities to…

Chaotic dynamics, commonly seen in weather systems and fluid turbulence, are characterized by their sensitivity to initial conditions, which makes accurate prediction challenging. Recent approaches have focused on developing data-driven…