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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…
Real-world network systems are inherently dynamic, with network topologies undergoing continuous changes over time. Previous works often focus on static networks or rely on complete prior knowledge of evolving topologies, whereas real-world…
Physics-Informed Neural Networks (PINNs) have shown continuous and increasing promise in approximating partial differential equations (PDEs), although they remain constrained by the curse of dimensionality. In this paper, we propose a…
Residential electricity demand forecasting is critical for efficient energy management and grid stability. Accurate predictions enable utility companies to optimize planning and operations. However, real-world residential electricity demand…
Many consequential real-world systems, like wind fields and ocean currents, are dynamic and hard to model. Learning their governing dynamics remains a central challenge in scientific machine learning. Dynamic Mode Decomposition (DMD)…
We introduce a generalization of temporal-difference (TD) learning to networks of interrelated predictions. Rather than relating a single prediction to itself at a later time, as in conventional TD methods, a TD network relates each…
Accurate and efficient plasma models are essential to understand and control experimental devices. Existing magnetohydrodynamic or kinetic models are nonlinear, computationally intensive, and can be difficult to interpret, while often only…
We introduce a new method for predicting the formation of links in real-world networks, which we refer to as the method of effective transitions. This method relies on the theory of isospectral matrix reductions to compute the probability…
How can we find patterns and anomalies in a tensor, or multi-dimensional array, in an efficient and directly interpretable way? How can we do this in an online environment, where a new tensor arrives each time step? Finding patterns and…
Seasonal time series exhibit intricate long-term dependencies, posing a significant challenge for accurate future prediction. This paper introduces the Multi-scale Seasonal Decomposition Model (MSSD) for seasonal time-series forecasting.…
In recent research, Tensor Product Representation (TPR) is applied for the systematic generalization task of deep neural networks by learning the compositional structure of data. However, such prior works show limited performance in…
Model order reduction plays a crucial role in simplifying complex systems while preserving their essential dynamic characteristics, making it an invaluable tool in a wide range of applications, including robotic systems, signal processing,…
We develop new dynamically orthogonal tensor methods to approximate multivariate functions and the solution of high-dimensional time-dependent nonlinear partial differential equations (PDEs). The key idea relies on a hierarchical…
Dynamic mode decomposition (DMD), which the family of singular-value decompositions (SVD), is a popular tool of data-driven regression. While multiple numerical tests demonstrated the power and efficiency of DMD in representing data (i.e.,…
Tensor network methods have been a key ingredient of advances in condensed matter physics and have recently sparked interest in the machine learning community for their ability to compactly represent very high-dimensional objects. Tensor…
Tensor network decomposition, originated from quantum physics to model entangled many-particle quantum systems, turns out to be a promising mathematical technique to efficiently represent and process big data in parsimonious manner. In this…
Learning complex network dynamics is fundamental for understanding, modeling, and controlling real-world complex systems. Though great efforts have been made to predict the future states of nodes on networks, the capability of capturing…
We establish connections between the problem of learning a two-layer neural network and tensor decomposition. We consider a model with feature vectors $\boldsymbol x \in \mathbb R^d$, $r$ hidden units with weights $\{\boldsymbol w_i\}_{1\le…
Graph-based change point detection (CPD) play an irreplaceable role in discovering anomalous graphs in the time-varying network. While several techniques have been proposed to detect change points by identifying whether there is a…
We present a new method for online prediction and learning of tensors ($N$-way arrays, $N >2$) from sequential measurements. We focus on the specific case of 3-D tensors and exploit a recently developed framework of structured tensor…