Jul 2026· SIAM Journal on Scientific Computing· Vol 48, pp. 2027-· 0 citations· 33 references
Computer Science
TL;DR
Numerical experiments demonstrate that the TT-accelerated SL methods achieve their theoretical convergence rates, exhibit modest growth in memory usage and runtime with dimension, and significantly outperform grid-based SL in accuracy per CPU-second.
Abstract
Abstract.
We introduce a fully discrete scheme to solve a class of high-dimensional mean field games systems. Our approach couples semi-Lagrangian (SL) time discretizations with Tensor-Train (TT) decompositions to tame the curse of dimensionality. By reformulating the classical Hamilton–Jacobi–Bellman and Fokker–Planck equations as a sequence of advection–diffusion–reaction subproblems within a smoothed policy iteration, we construct both first and second order in time SL schemes. The TT format and appropriate quadrature rules reduce storage and computational cost from exponential to polynomial in the dimension. Numerical experiments demonstrate that our TT-accelerated SL methods achieve their theoretical convergence rates, exhibit modest growth in memory usage and runtime with dimension, and significantly outperform grid-based SL in accuracy per CPU-second.
A particle-based workflow for approximating the time-dependent law of finite-volume discretizations of the Dean–Kawasaki model is proposed, which accurately captures the site-wise correlations and other observables of the true model.
This paper presents a high-order rank-adaptive implicit integrator for the tensor solution of high-dimensional diffusion equations. We extend the 3D version of this method from the Tucker decomposition to higher dimensions using the hierarchical Tucker (HT) decomposition, since the storage complexity for the Tucker dec...
A new SVD-based tensor decomposition method for tensor networks with arbitrary graph topologies is introduced, and it is found that the graph-format representation attains comparable or better accuracy than the classical tensor train and hierarchical Tucker tensor formats, while using substantially fewer degrees of fre...
A principled fiber-dependency elimination framework is introduced that resolves this obstacle by expressing neighboring fibers as linear combinations of the cross-selected fibers through cross interpolation identities, which produces a closed collocation system while preserving the principal advantages of TT-cross meth...
Behzad Ghahremani, H. Babaee· arXiv.org· 1 citation
Multi-agent interaction in linear–quadratic (LQ) differential games gives rise to open-loop Nash equilibria that rarely admit closed-form expressions, motivating the development of reliable numerical solvers. Classical approaches such as shooting and spectral collocation are sensitive to the initial guess on the unknow...
Text-to-image latent diffusion models produce unprecedented visual fidelity but remain severely bottlenecked by the computational latency of iterative sampling. While optimizing the discretization of the continuous-time variable offers a powerful, training-free acceleration pathway, the comparative tradeoffs of foundat...
Tan-Yan Bao, Huy-Tan Thai· International Conference on...· 0 citations
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