Related papers: Analysis of Empirical Mode Decomposition-based Loa…

Dynamic mode decomposition (DMD) is a versatile approach that enables the construction of low-order models from data. Controller design tasks based on such models require estimates and guarantees on predictive accuracy. In this work, we…

Electrical impedance tomography (EIT) is an imaging modality in which the conductivity distribution inside a target is reconstructed based on voltage measurements from the surface of the target. Reconstructing the conductivity distribution…

Recently, there has been growing interest in incorporating textual information into foundation models for time series forecasting. However, it remains unclear whether and under what conditions such multimodal integration consistently yields…

Dynamic mode decomposition (DMD) provides a principled approach to extract physically interpretable spatial modes from time-resolved flow field data, along with a linear model for how the amplitudes of these modes evolve in time. Recently,…

Multiscale modeling and analysis of multiphysics coupling processes in highly heterogeneous media present significant challenges. In this paper, we propose a novel multiphysics embedding localized orthogonal decomposition (ME-LOD) method…

The well-developed ETS (ExponenTial Smoothing or Error, Trend, Seasonality) method incorporating a family of exponential smoothing models in state space representation has been widely used for automatic forecasting. The existing ETS method…

Electric vehicles (EVs) have the potential to reduce grid stress through smart charging strategies while simultaneously meeting user demand. This requires accurate forecasts of key charging parameters, such as energy demand and connection…

Transformer-based methods have achieved state-of-the-art performance in time series forecasting (TSF) by capturing positional and semantic topological relationships among input tokens. However, it remains unclear whether existing…

Accurate spatiotemporal forecasting is critical for numerous complex systems but remains challenging due to complex volatility patterns and spectral entanglement in conventional graph neural networks (GNNs). While decomposition-integrated…

This work proposes a new framework of model reduction for parametric complex systems. The framework employs a popular model reduction technique dynamic mode decomposition (DMD), which is capable of combining data-driven learning and physics…

Handling anomalies is a critical preprocessing step in multivariate time series prediction. However, existing approaches that separate anomaly preprocessing from model training for multivariate time series prediction encounter significant…

Machine learning methods have been adopted in the literature as contenders to conventional methods to solve the energy time series forecasting (TSF) problems. Recently, deep learning methods have been emerged in the artificial intelligence…

Two ocean models are considered for geophysical flow simulations: the multi-layer shallow water equations and the multi-layer primitive equations. For the former, we investigate the parallel performance of exponential time differencing…

Recent progress in time-series forecasting has led to rapidly increasing architectural complexity, yet many reported State-of-the-Art gains are statistically fragile or misattributed. We argue that progress requires a shift from model…

Time series forecasting is a critical task in various domains, where accurate predictions can drive informed decision-making. Traditional forecasting methods often rely on current observations of variables to predict future outcomes,…

Energy-Based Models (EBMs) have proven to be a highly effective approach for modelling densities on finite-dimensional spaces. Their ability to incorporate domain-specific choices and constraints into the structure of the model through…

The use of machine learning for time series prediction has become increasingly popular across various industries thanks to the availability of time series data and advancements in machine learning algorithms. However, traditional methods…

This chapter describes modal decompositions in the framework of matrix factorizations. We highlight the differences between classic space-time decompositions and 2D discrete transforms and discuss the general architecture underpinning…

Mode-based model-reduction is used to reduce the degrees of freedom of high dimensional systems, often by describing the system state by a linear combination of spatial modes. Transport dominated phenomena, ubiquitous in technical and…

The simulation of atmospheric flows by means of traditional discretization methods remains computationally intensive, hindering the achievement of high forecasting accuracy in short time frames. In this paper, we apply three reduced order…