相关论文: DeepGraphDMD: Interpretable Spatio-Temporal Decomp…
The goal of this work is to address two limitations in autoencoder-based models: latent space interpretability and compatibility with unstructured meshes. This is accomplished here with the development of a novel graph neural network (GNN)…
Learning representations for graphs plays a critical role in a wide spectrum of downstream applications. In this paper, we summarize the limitations of the prior works in three folds: representation space, modeling dynamics and modeling…
The graph neural network (GNN) has demonstrated its superior performance in various applications. The working mechanism behind it, however, remains mysterious. GNN models are designed to learn effective representations for graph-structured…
Dynamic mode decomposition (DMD) is a popular data-driven framework to extract linear dynamics from complex high-dimensional systems. In this work, we study the system identification properties of DMD. We first show that DMD is invariant…
We introduce the Rigged Dynamic Mode Decomposition (Rigged DMD) algorithm, which computes generalized eigenfunction decompositions of Koopman operators. By considering the evolution of observables, Koopman operators transform complex…
Modern computational science and engineering applications are being improved by the advances in scientific machine learning. Data-driven methods such as Dynamic Mode Decomposition (DMD) can extract coherent structures from spatio-temporal…
Recent applications of pattern recognition techniques on brain connectome classification using functional connectivity (FC) are shifting towards acknowledging the non-Euclidean topology and dynamic aspects of brain connectivity across time.…
We introduce Variational Latent Mode Decomposition (VLMD), a new algorithm for extracting oscillatory modes and associated connectivity structures from multivariate signals. VLMD addresses key limitations of existing Multivariate Mode…
As neural networks grow in scale, their training becomes both computationally demanding and rich in dynamics. Amidst the flourishing interest in these training dynamics, we present a novel observation: Parameters during training exhibit…
We present a topology-based method for mesh-partitioning in three-dimensional discrete fracture network (DFN) simulations that take advantage of the intrinsic multi-level nature of a DFN. DFN models are used to simulate flow and transport…
Koopman operators model nonlinear dynamics as a linear dynamic system acting on a nonlinear function as the state. This nonstandard state is often called a Koopman observable and is usually approximated numerically by a superposition of…
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…
A novel unsupervised deep learning method is developed to identify individual-specific large scale brain functional networks (FNs) from resting-state fMRI (rsfMRI) in an end-to-end learning fashion. Our method leverages deep Encoder-Decoder…
Time series forecasting is an extensively studied subject in statistics, economics, and computer science. Exploration of the correlation and causation among the variables in a multivariate time series shows promise in enhancing the…
Understanding the training dynamics of deep neural networks (DNNs) is important as it can lead to improved training efficiency and task performance. Recent works have demonstrated that representing the wirings of static graph cannot capture…
Dynamic mode decomposition (DMD) is a powerful data-driven technique for construction of reduced-order models of complex dynamical systems. Multiple numerical tests have demonstrated the accuracy and efficiency of DMD, but mostly for…
Functional magnetic resonance imaging produces high dimensional data, with a less then ideal number of labelled samples for brain decoding tasks (predicting brain states). In this study, we propose a new deep temporal convolutional neural…
Accurate electricity demand forecasting is challenging due to the strong multi-periodicity of real-world demand series, which makes effective modeling of recurrent temporal patterns crucial. Decomposition techniques make such structure…
Multivariate time series classification (MTSC) is an important data mining task, which can be effectively solved by popular deep learning technology. Unfortunately, the existing deep learning-based methods neglect the hidden dependencies in…
Irregular Medical Time Series play a critical role in the clinical domain to better understand the patient's condition. However, inherent irregularity arising from heterogeneous sampling rates, asynchronous observations, and variable gaps…