Related papers: Non-autoregressive time-series methods for stable …
We present a simple and scalable implementation of next-generation reservoir computing (NGRC) for modeling dynamical systems from time-series data. The method uses a pseudorandom nonlinear projection of time-delay embedded inputs, allowing…
We introduce a Gaussian process-based model for handling of non-stationarity. The warping is achieved non-parametrically, through imposing a prior on the relative change of distance between subsequent observation inputs. The model allows…
In this article, an efficient sequential linear programming algorithm (SLP) for uncertainty analysis-based data-driven computational mechanics (UA-DDCM) is presented. By assuming that the uncertain constitutive relationship embedded behind…
This paper analyzes the stability-related properties of Long Short-Term Memory (LSTM) networks and investigates their use as the model of the plant in the design of Model Predictive Controllers (MPC). First, sufficient conditions…
An important problem in time-series analysis is modeling systems with time-varying dynamics. Probabilistic models with joint continuous and discrete latent states offer interpretable, efficient, and experimentally useful descriptions of…
Attention-based architectures have become ubiquitous in time series forecasting tasks, including spatio-temporal (STF) and long-term time series forecasting (LTSF). Yet, our understanding of the reasons for their effectiveness remains…
In this paper, we propose a probabilistic reduced-dimensional vector autoregressive (PredVAR) model with oblique projections. This model partitions the measurement space into a dynamic subspace and a static subspace that do not need to be…
We study a fundamental class of regression models called the second order linear model (SLM). The SLM extends the linear model to high order functional space and has attracted considerable research interest recently. Yet how to efficiently…
In this article we consider one-dimensional random systems of hyperbolic conservation laws. We first establish existence and uniqueness of random entropy admissible solutions for initial value problems of conservation laws which involve…
In this paper, we propose a predictive regression model for longitudinal images with missing data based on large deformation diffeomorphic metric mapping (LDDMM) and deep neural networks. Instead of directly predicting image scans, our…
This work addresses the development of a physics-informed neural network (PINN) with a loss term derived from a discretized time-dependent reduced-order system. In this work, first, the governing equations are discretized using a finite…
This paper proposes a new sequential model learning architecture to solve partially observable Markov decision problems. Rather than compressing sequential information at every timestep as in conventional recurrent neural network-based…
Projected Gradient Descent denotes a class of iterative methods for solving optimization programs. Its applicability to convex optimization programs has gained significant popularity for its intuitive implementation that involves only…
We investigate regression for variable length sequential data containing missing samples and introduce a novel tree architecture based on the Long Short-Term Memory (LSTM) networks. In our architecture, we employ a variable number of LSTM…
Charged particle dynamics under the influence of electromagnetic fields is a challenging spatiotemporal problem. Many high performance physics-based simulators for predicting behavior in a charged particle beam are computationally…
In this paper, we study nonparametric models allowing for locally stationary regressors and a regression function that changes smoothly over time. These models are a natural extension of time series models with time-varying coefficients. We…
In the current data-intensive era, big data has become a significant asset for Artificial Intelligence (AI), serving as a foundation for developing data-driven models and providing insight into various unknown fields. This study navigates…
In this study, a method for predicting unsteady aerodynamic forces under different initial conditions using a limited number of samples based on transfer learning is proposed, aiming to avoid the need for large-scale high-fidelity…
In this work, we present a machine learning approach for reducing the error when numerically solving time-dependent partial differential equations (PDE). We use a fully convolutional LSTM network to exploit the spatiotemporal dynamics of…
Computing reduced-order models using non-intrusive methods is particularly attractive for systems that are simulated using black-box solvers. However, obtaining accurate data-driven models can be challenging, especially if the underlying…