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Understanding and characterising quantum many-body dynamics remains a significant challenge due to both the exponential complexity required to represent quantum many-body Hamiltonians, and the need to accurately track states in time under…

Convolutional Neural Networks (CNNs) are the predominant model used for a variety of medical image analysis tasks. At inference time, these models are computationally intensive, especially with volumetric data. In principle, it is possible…

Network or physical attacks on industrial equipment or computer systems may cause massive losses. Therefore, a quick and accurate anomaly detection (AD) based on monitoring data, especially the multivariate time-series (MTS) data, is of…

The concept of Hilbert space fragmentation (HSF) has recently been put forward as a routine to break quantum ergodicity. Although HSF exists widely in models with dynamical constraints, it is still challenging to tune it. Here, we propose a…

Deep neural networks (DNNs) are so over-parametrized that recent research has found them to already contain a subnetwork with high accuracy at their randomly initialized state. Finding these subnetworks is a viable alternative training…

Understanding the inductive bias and generalization properties of large overparametrized machine learning models requires to characterize the dynamics of the training algorithm. We study the learning dynamics of large two-layer neural…

Neural networks are complex functions of both their inputs and parameters. Much prior work in deep learning theory analyzes the distribution of network outputs at a fixed a set of inputs (e.g. a training dataset) over random initializations…

Deep learning algorithms, especially Transformer-based models, have achieved significant performance by capturing long-range dependencies and historical information. However, the power of convolution has not been fully investigated.…

Hamiltonian systems lie at the heart of modeling the physical world. Their defining scalar, the Hamiltonian, encodes both energy conservation and symplectic geometry in its phase-space trajectories. Recent deep learning approaches model…

Classical methods of solving spatiotemporal dynamical systems include statistical approaches such as autoregressive integrated moving average, which assume linear and stationary relationships between systems' previous outputs. Development…

In this paper, an innovative Physical Model-driven Neural Network (PMNN) method is proposed to solve time-fractional differential equations. It establishes a temporal iteration scheme based on physical model-driven neural networks which…

Traditional Feed-Forward Neural Networks (FFNN) and one-dimensional Convolutional Neural Networks (1D CNN) often encounter difficulties when dealing with long, columnar datasets that contain numerous features. The challenge arises from two…

Time-periodic quantum systems exhibit a rich variety of far-from-equilibrium phenomena and serve as ideal platforms for quantum engineering and control. However, simulating their dynamics with conventional numerical methods remains…

Fractional Differential Equations (FDEs) are essential tools for modelling complex systems in science and engineering. They extend the traditional concepts of differentiation and integration to non-integer orders, enabling a more precise…

In this paper, we present a scalable deep learning approach to solve opinion dynamics stochastic optimal control problems with mean field term coupling in the dynamics and cost function. Our approach relies on the probabilistic…

Learning high-performance deep neural networks for dynamic modeling of high Degree-Of-Freedom (DOF) robots remains challenging due to the sampling complexity. Typical unknown system disturbance caused by unmodeled dynamics (such as internal…

Modeling temporal multimodal data poses significant challenges in classification tasks, particularly in capturing long-range temporal dependencies and intricate cross-modal interactions. Audiovisual data, as a representative example, is…

Understanding the dynamics of phase boundaries in fluids requires quantitative knowledge about the microscale processes at the interface. We consider the sharp-interface motion of compressible two-component flow, and propose a heterogeneous…

Non-Hermitian topological phases can produce some remarkable properties, compared with their Hermitian counterpart, such as the breakdown of conventional bulk-boundary correspondence and the non-Hermitian topological edge mode. Here, we…

Many real-world time series exhibit strong periodic structures arising from physical laws, human routines, or seasonal cycles. However, modern deep forecasting models often fail to capture these recurring patterns due to spectral bias and a…