Related papers: Tensor Network Framework for Forecasting Nonlinear…
Accurately forecasting dynamic processes on graphs, such as traffic flow or disease spread, remains a challenge. While Graph Neural Networks (GNNs) excel at modeling and forecasting spatio-temporal data, they often lack the ability to…
In spite of the recent interest and advances in linear controllability of complex networks, controlling nonlinear network dynamics remains to be an outstanding problem. We develop an experimentally feasible control framework for nonlinear…
Deep learning has become a one-size-fits-all solution for technical and business domains thanks to its flexibility and adaptability. It is implemented using opaque models, which unfortunately undermines the outcome trustworthiness. In order…
Originating from condensed matter physics, tensor networks are compact representations of high-dimensional tensors. In this paper, the prowess of tensor networks is demonstrated on the particular task of one-class anomaly detection. We…
We present a data-driven and interpretable approach for reducing the dimensionality of chaotic systems using spectral submanifolds (SSMs). Emanating from fixed points or periodic orbits, these SSMs are low-dimensional inertial manifolds…
We present a framework for modeling multi-scale processes, and study its performance in the context of streamflow forecasting in hydrology. Specifically, we propose a novel hierarchical recurrent neural architecture that factorizes the…
Real-time particle transverse momentum ($p_T$) estimation in high-energy physics demands algorithms that are both efficient and accurate under strict hardware constraints. Static machine learning models degrade under high pileup and lack…
Recurrent neural networks (RNNs) and transformers have been shown to be Turing-complete, but this result assumes infinite precision in their hidden representations, positional encodings for transformers, and unbounded computation time in…
A dynamic graph (DG) is frequently encountered in numerous real-world scenarios. Consequently, A dynamic graph convolutional network (DGCN) has been successfully applied to perform precise representation learning on a DG. However,…
Modeling joint probability distributions over sequences has been studied from many perspectives. The physics community developed matrix product states, a tensor-train decomposition for probabilistic modeling, motivated by the need to…
This paper presents a novel learning analytics method: Transition Network Analysis (TNA), a method that integrates Stochastic Process Mining and probabilistic graph representation to model, visualize, and identify transition patterns in the…
We propose a novel neural network architecture (TSympOCNet) to address high--dimensional optimal control problems with linear and nonlinear dynamics. An important application of this method is to solve the path planning problem of…
Message-passing neural networks (MPNN) have shown extremely high efficiency and accuracy in predicting the physical properties of molecules and crystals, and are expected to become the next-generation material simulation tool after the…
Recurrent Neural Networks (RNNs) represent the de facto standard machine learning tool for sequence modelling, owing to their expressive power and memory. However, when dealing with large dimensional data, the corresponding exponential…
Systems exhibiting nonlinear dynamics, including but not limited to chaos, are ubiquitous across Earth Sciences such as Meteorology, Hydrology, Climate and Ecology, as well as Biology such as neural and cardiac processes. However, System…
Deep neural networks (NNs) encounter scalability limitations when confronted with a vast array of neurons, thereby constraining their achievable network depth. To address this challenge, we propose an integration of tensor networks (TN)…
Hypergraph neural networks (HGNN) have recently become attractive and received significant attention due to their excellent performance in various domains. However, most existing HGNNs rely on first-order approximations of hypergraph…
Accurate electrical load forecasting is crucial for optimizing power system operations, planning, and management. As power systems become increasingly complex, traditional forecasting methods may fail to capture the intricate patterns and…
Modeling of conservative systems with neural networks is an area of active research. A popular approach is to use Hamiltonian neural networks (HNNs) which rely on the assumptions that a conservative system is described with Hamilton's…
Learning and forecasting stochastic time series is essential in various scientific fields. However, despite the proposals of nonlinear filters and deep-learning methods, it remains challenging to capture nonlinear dynamics from a few noisy…