Related papers: Non-autoregressive time-series methods for stable …

State-space models (SSMs) are a highly expressive model class for learning patterns in time series data and for system identification. Deterministic versions of SSMs (e.g. LSTMs) proved extremely successful in modeling complex time series…

In this paper we extend the hierarchical model reduction framework based on reduced basis techniques for the application to nonlinear partial differential equations. The major new ingredient to accomplish this goal is the introduction of…

Projection-based reduced order models are effective at approximating parameter-dependent differential equations that are parametrically separable. When parametric separability is not satisfied, which occurs in both linear and nonlinear…

Multivariate time series forecasting is an important machine learning problem across many domains, including predictions of solar plant energy output, electricity consumption, and traffic jam situation. Temporal data arise in these…

Recent advances in machine learning such as Long Short-Term Memory (LSTM) models and Transformers have been widely adopted in hydrological applications, demonstrating impressive performance amongst deep learning models and outperforming…

The increasing integration of renewable energy sources (RESs) into modern power systems presents significant opportunities but also notable challenges, primarily due to the inherent variability of RES generation. Accurate forecasting of RES…

This paper is based on a machine learning project at the Norwegian University of Science and Technology, fall 2020. The project was initiated with a literature review on the latest developments within time-series forecasting methods in the…

A nonintrusive model order reduction method for bilinear stochastic differential equations with additive noise is proposed. A reduced order model (ROM) is designed in order to approximate the statistical properties of high-dimensional…

This work explores the physics-driven machine learning technique Operator Inference (OpInf) for predicting the state of chaotic dynamical systems. OpInf provides a non-intrusive approach to infer approximations of polynomial operators in…

Long short-term memory (LSTM) is a robust recurrent neural network architecture for learning spatiotemporal sequential data. However, it requires significant computational power for learning and implementing from both software and hardware…

Time series subject to change in regime have attracted much interest in domains such as econometry, finance or meteorology. For discrete-valued regimes, some models such as the popular Hidden Markov Chain (HMC) describe time series whose…

Monitoring ground displacement is crucial for urban infrastructure stability and mitigating geological hazards. However, forecasting future deformation from sparse Interferometric Synthetic Aperture Radar (InSAR) time-series data remains a…

Identification of a linear time-invariant dynamical system from partial observations is a fundamental problem in control theory. Particularly challenging are systems exhibiting long-term memory. A natural question is how learn such systems…

We present a new scientific machine learning method that learns from data a computationally inexpensive surrogate model for predicting the evolution of a system governed by a time-dependent nonlinear partial differential equation (PDE), an…

We propose a family of high-order local discontinuous Galerkin (LDG) methods, built on a parametric representation and coupled with a semi-implicit backward Euler time discretization, for isotropic and anisotropic curve-shortening flows.…

This work formulates a new approach to reduced modeling of parameterized, time-dependent partial differential equations (PDEs). The method employs Operator Inference, a scientific machine learning framework combining data-driven learning…

Nonlinear dynamical systems with input delays pose significant challenges for prediction, estimation, and control due to their inherent complexity and the impact of delays on system behavior. Traditional linear control techniques often fail…

This paper introduces an iterative algorithm for training nonparametric additive models that enjoys favorable memory storage and computational requirements. The algorithm can be viewed as the functional counterpart of stochastic gradient…

Long Short-Term Memory (LSTM) is a well-known method used widely on sequence learning and time series prediction. In this paper we deployed stacked LSTM model in an application of weather forecasting. We propose a 2-layer spatio-temporal…

We study the problem of modeling a non-linear dynamical system when given a time series by deriving equations directly from the data. Despite the fact that time series data are given as input, models for dynamics and estimation algorithms…