Related papers: Time Series Forecasting Using Manifold Learning

Time-series data exists in every corner of real-world systems and services, ranging from satellites in the sky to wearable devices on human bodies. Learning representations by extracting and inferring valuable information from these time…

Purpose: To develop a deep learning method on a nonlinear manifold to explore the temporal redundancy of dynamic signals to reconstruct cardiac MRI data from highly undersampled measurements. Methods: Cardiac MR image reconstruction is…

Advancements in modern science have led to the increasing availability of non-Euclidean data in metric spaces. This paper addresses the challenge of modeling relationships between non-Euclidean responses and multivariate Euclidean…

The contribution of this work is twofold: (1) We introduce a collection of ensemble methods for time series forecasting to combine predictions from base models. We demonstrate insights on the power of ensemble learning for forecasting,…

Multivariate Time Series (MTS) forecasting involves modeling temporal dependencies within historical records. Transformers have demonstrated remarkable performance in MTS forecasting due to their capability to capture long-term…

In [C.W. Gear, T.J. Kaper, I.G. Kevrekidis, and A. Zagaris, Projecting to a Slow Manifold: Singularly Perturbed Systems and Legacy Codes, SIAM J. Appl. Dyn. Syst. 4 (2005) 711-732], we developed a class of iterative algorithms within the…

Algorithms proposed for solving high-dimensional optimization problems with no derivative information frequently encounter the "curse of dimensionality," becoming ineffective as the dimension of the parameter space grows. One feature of a…

In this paper, we show empirical evidence on how to construct the optimal feature selection or input representation used by the input layer of a feedforward neural network for the propose of forecasting spatial-temporal signals. The…

Time series prediction aims to predict future values to help stakeholders make proper strategic decisions. This problem is relevant in all industries and areas, ranging from financial data to demand to forecast. However, it remains…

We develop information-geometric techniques to analyze the trajectories of the predictions of deep networks during training. By examining the underlying high-dimensional probabilistic models, we reveal that the training process explores an…

Long-term time series forecasting (LTSF) offers broad utility in practical settings like energy consumption and weather prediction. Accurately predicting long-term changes, however, is demanding due to the intricate temporal patterns and…

Time-series forecasting plays an important role in many domains. Boosted by the advances in Deep Learning algorithms, it has for instance been used to predict wind power for eolic energy production, stock market fluctuations, or motor…

Deep learning methods are powerful tools in classifying multivariate time series data. Despite their high performance, these methods are hard to interpret, which diminishes their applications in high-risk domains such as healthcare. In this…

This article introduces a new data-driven approach that leverages a manifold embedding generated by the invertible neural network to improve the robustness, efficiency, and accuracy of the constitutive-law-free simulations with limited…

Time series analysis remains a major challenge due to its sparse characteristics, high dimensionality, and inconsistent data quality. Recent advancements in transformer-based techniques have enhanced capabilities in forecasting and…

Recurrent and convolutional neural networks are the most common architectures used for time series forecasting in deep learning literature. These networks use parameter sharing by repeating a set of fixed architectures with fixed parameters…

An increasing array of biomedical and computer vision applications requires the predictive modeling of complex data, for example images and shapes. The main challenge when predicting such objects lies in the fact that they do not comply to…

The goal of this paper is to test three classes of neural network (NN) architectures based on four-dimensional (4D) hypercomplex algebras for time series prediction. We evaluate different architectures, varying the input layers to include…

We present a novel kernel-based machine learning algorithm for identifying the low-dimensional geometry of the effective dynamics of high-dimensional multiscale stochastic systems. Recently, the authors developed a mathematical framework…

We present a novel method for learning reduced-order models of dynamical systems using nonlinear manifolds. First, we learn the manifold by identifying nonlinear structure in the data through a general representation learning problem. The…