Related papers: Tensor network variational optimizations for real-…

This paper focuses on the application of the variance-based global sensitivity analysis for a topology derivative method in order to solve a stochastic nonlinear time-dependent magnetoquasistatic interface problem. To illustrate the…

Variational tensor network optimization has become a powerful tool for studying classical statistical models in two dimensions. However, its application to three-dimensional systems remains limited, primarily due to the high computational…

In nonlinear dynamical systems, tipping refers to a critical transition from one steady state to another, typically catastrophic, steady state, often resulting from a saddle-node bifurcation. Recently, the machine-learning framework of…

The evolution of images with physics-based dynamics is often spatially localized and nonlinear. A switching linear dynamic system (SLDS) is a natural model under which to pose such problems when the system's evolution randomly switches over…

Data augmentation is a crucial technique for improving model generalization and robustness, particularly in deep learning models where training data is limited. Although many augmentation methods have been developed for time series…

Real-time calculations in tensor networks are strongly limited in time by entanglement growth, restricting the achievable frequency resolution of Green's functions, spectral functions, self-energies, and other related quantities. By…

Link prediction in dynamic networks remains a fundamental challenge in network science, requiring the inference of potential interactions and their evolving strengths through spatiotemporal pattern analysis. Traditional static network…

We present a systematic numerical iteration approach to study the evolution properties of the spin-boson systems, which works well in whole coupling regime. This approach involves the evaluation of a set of coefficients for the formal…

The Hamiltonian for a system of itinerant particles on a two-dimensional lattice in a uniform magnetic field reduces the translational symmetry to a magnetic translation group, because of the need to choose a particular gauge for the vector…

Recent advances in learning-based model predictive control (MPC) have leveraged neural networks for online model learning, achieving strong performance when nonstationary system dynamics deviate from nominal models. However, existing…

Performing highly accurate simulations of droplet systems is a challenging problem. This is primarily due to the interface dynamics which is complicated further by the addition of surfactants. This paper presents a boundary integral method…

Recent works put much effort into tensor network structure search (TN-SS), aiming to select suitable tensor network (TN) structures, involving the TN-ranks, formats, and so on, for the decomposition or learning tasks. In this paper, we…

Several data compressors have been proposed in distributed optimization frameworks of network systems to reduce communication overhead in large-scale applications. In this paper, we demonstrate that effective information compression may…

Using a recently developed extension of the time-dependent variational principle for matrix product states, we evaluate the dynamics of 2D power-law interacting XXZ models, implementable in a variety of state-of-the-art experimental…

In this paper we consider box constrained adaptations of $\ell_1$ optimization heuristic when applied for solving random linear systems. These are typically employed when on top of being sparse the systems' solutions are also known to be…

The Reynolds-Averaged Navier-Stokes equations and the Large-Eddy Simulation equations can be coupled using a transition function to switch from a set of equations applied in some areas of a domain to the other set in the other part of the…

We prove that a class of A-stable symplectic Runge--Kutta time semidiscretizations (including the Gauss--Legendre methods) applied to a class of semilinear Hamiltonian PDEs which are well-posed on spaces of analytic functions with analytic…

Inferring a network's evolutionary history from a single final snapshot with limited temporal annotations is fundamental yet challenging. Existing approaches predominantly rely on topology alone, which often provides insufficient and noisy…

Projected Entangled Pair States (PEPS) are a promising ansatz for the study of strongly correlated quantum many-body systems in two dimensions. But due to their high computational cost, developing and improving PEPS algorithms is necessary…

We propose a tensor-network algorithm for discrete-time stochastic dynamics of a homogeneous system in the thermodynamic limit. We map a $d$-dimensional nonequilibrium Markov process to a $(d+1)$-dimensional infinite tensor network by using…