Related papers: Time-Delayed Transformers for Data-Driven Modeling…
In this paper, we explore the role of tensor algebra in balanced truncation (BT) based model reduction/identification for high-dimensional multilinear/linear time invariant systems. In particular, we employ tensor train decomposition (TTD),…
Time series forecasting is widely used in the fields of equipment life cycle forecasting, weather forecasting, traffic flow forecasting, and other fields. Recently, some scholars have tried to apply Transformer to time series forecasting…
Dynamic Mode Decomposition (DMD) is a model-order reduction approach, whereby spatial modes of fixed temporal frequencies are extracted from numerical or experimental data sets. The DMD low-rank or reduced operator is typically obtained by…
Human Trajectory Forecasting (HTF) predicts future human movements from past trajectories and environmental context, with applications in Autonomous Driving, Smart Surveillance, and Human-Robot Interaction. While prior work has focused on…
Deep learning algorithms provide a new paradigm to study high-dimensional dynamical behaviors, such as those in fusion plasma systems. Development of novel model reduction methods, coupled with detection of abnormal modes with plasma…
Streaming Dynamic Mode Decomposition (sDMD) (Hemati et al., Phys. Fluids 26(2014)) is a low-storage version of Dynamic Mode Decomposition (DMD) (Schmid, J. Fluid Mech. 656 (2010)), a data-driven method to extract spatio-temporal flow…
We use a data-driven approach to model a three-dimensional turbulent flow using cutting-edge Deep Learning techniques. The deep learning framework incorporates physical constraints on the flow, such as preserving incompressibility and…
The recent proposed orthogonal time frequency space (OTFS) modulation shows signifcant advantages than conventional orthogonal frequency division multiplexing (OFDM) for high mobility wireless communications. However, a challenging problem…
Denoising diffusion probabilistic models (DDPMs) are becoming the leading paradigm for generative models. It has recently shown breakthroughs in audio synthesis, time series imputation and forecasting. In this paper, we propose…
Understanding the complex interactions within dynamic multilayer networks is critical for advancements in various scientific domains. Existing models often fail to capture such networks' temporal and cross-layer dynamics. This paper…
We study stability of interacting nonlinear systems with time-delayed communications, using contraction theory and a simplified wave variable design inspired by robotic teleoperation. We show that contraction is preserved through specific…
Predicting the evolution of systems that exhibit spatio-temporal dynamics in response to external stimuli is a key enabling technology fostering scientific innovation. Traditional equations-based approaches leverage first principles to…
This paper is devoted to a discussion of the Discrete Fourier Transform (DFT) representation of a chaotic finite-duration sequence. This representation has the advantage that is itself a finite-duration sequence corresponding to samples…
It is difficult to analyze the stability of systems with time-varying delays. One approach is to construct a time-transformation that converts the system into a form with a constant delay but with a time-varying scalar appearing in the…
Deep neural networks are among the most widely applied machine learning tools showing outstanding performance in a broad range of tasks. We present a method for folding a deep neural network of arbitrary size into a single neuron with…
Temporal difference learning (TD) is a simple iterative algorithm used to estimate the value function corresponding to a given policy in a Markov decision process. Although TD is one of the most widely used algorithms in reinforcement…
Detecting and analyzing complex patterns in multivariate time-series data is crucial for decision-making in urban and environmental system operations. However, challenges arise from the high dimensionality, intricate complexity, and…
Addressing the resource waste caused by fixed computation paradigms in deep learning models under dynamic scenarios, this paper proposes a Transformer$^{-1}$ architecture based on the principle of deep adaptivity. This architecture achieves…
In this work we propose for the first time a transformer-based framework for unsupervised representation learning of multivariate time series. Pre-trained models can be potentially used for downstream tasks such as regression and…
Performing Data Assimilation (DA) at a low cost is of prime concern in Earth system modeling, particularly at the time of big data where huge quantities of observations are available. Capitalizing on the ability of Neural Networks…