Related papers: Reconstructing Nonlinear Dynamical Systems from Mu…

In many scientific disciplines, we are interested in inferring the nonlinear dynamical system underlying a set of observed time series, a challenging task in the face of chaotic behavior and noise. Previous deep learning approaches toward…

Dynamic Magnetic Resonance Imaging (dMRI) is widely used to assess various cardiac conditions such as cardiac motion and blood flow. To accelerate MR acquisition, techniques such as undersampling and Simultaneous Multi-Slice (SMS) are often…

Irregularly sampled time series (ISTS) data has irregular temporal intervals between observations and different sampling rates between sequences. ISTS commonly appears in healthcare, economics, and geoscience. Especially in the medical…

In real world clinical environments, training and applying deep learning models on multi-modal medical imaging data often struggles with partially incomplete data. Standard approaches either discard missing samples, require imputation or…

The identification and modeling of time-varying systems is a fundamental challenge in signal processing and system identification. To address this challenge, we propose a class of time-varying state-space model (SSM) based neural networks…

Molecular dynamics (MD) simulation is essential for various scientific domains but computationally expensive. Learning-based force fields have made significant progress in accelerating ab-initio MD simulation but are not fast enough for…

Spatial-temporal data modeling aims to mine the underlying spatial relationships and temporal dependencies of objects in a system. However, most existing methods focus on the modeling of spatial-temporal data in a single mode, lacking the…

A critical challenge in the data-driven modeling of dynamical systems is producing methods robust to measurement error, particularly when data is limited. Many leading methods either rely on denoising prior to learning or on access to large…

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,…

Research in modern data-driven dynamical systems is typically focused on the three key challenges of high dimensionality, unknown dynamics, and nonlinearity. The dynamic mode decomposition (DMD) has emerged as a cornerstone for modeling…

Accurate models are essential for design, performance prediction, control, and diagnostics in complex engineering systems. Physics-based models excel during the design phase but often become outdated during system deployment due to changing…

Time series data are inherently functions of time, yet current transformers often learn time series by modeling them as mere concatenations of time periods, overlooking their functional properties. In this work, we propose a novel objective…

In frequency division duplex (FDD) systems, acquiring channel state information (CSI) at the base station (BS) traditionally relies on limited feedback from mobile terminals (MTs). However, the accuracy of channel reconstruction from…

Statistic modeling and data-driven learning are the two vital fields that attract many attentions. Statistic models intend to capture and interpret the relationships among variables, while data-based learning attempt to extract information…

A new variational mode decomposition (VMD) based deep learning approach is proposed in this paper for time series forecasting problem. Firstly, VMD is adopted to decompose the original time series into several sub-signals. Then, a…

The effectiveness of recurrent neural networks can be largely influenced by their ability to store into their dynamical memory information extracted from input sequences at different frequencies and timescales. Such a feature can be…

Deep neural networks (DNNs) are widely used in pattern-recognition tasks for which a human comprehensible, quantitative description of the data-generating process, e.g., in the form of equations, cannot be achieved. While doing so, DNNs…

Improving the interpretability of deep neural networks has recently gained increased attention, especially when the power of deep learning is leveraged to solve problems in physics. Interpretability helps us understand a model's ability to…

Multivariate time series(MTS) is a universal data type related to many practical applications. However, MTS suffers from missing data problems, which leads to degradation or even collapse of the downstream tasks, such as prediction and…

The data-driven recovery of the unknown governing equations of dynamical systems has recently received an increasing interest. However, the identification of governing equations remains challenging when dealing with noisy and partial…