Author

Chuliang Fu

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Preprint Oct 2026

A Polynomial-Scaling PDE Solver with Entanglement-Basis Tensor Networks

We develop a finite element method (FEM) for partial differential equation (PDE) solver based on the entanglement-basis representation introduced in our companion work. By lifting non-linear finite-element equations into an augmented coefficient space, the governing PDE together with boundary, initial, and inter-elemen...

Abhijatmedhi Chotrattanapituk, Michael J. Landry, Chu-Liang Fu et al. · 0 citations

Preprint Jul 2026

Tensor-Network Finite Elements for Analytic Operator Equations

Operator equations (OEs) underpin quantitative modeling across science and engineering. Finite-element (FE) methods discretize continuous OEs into finite-dimensional algebraic systems, whereas tensor networks (TNs) provide flexible variational representations of correlated discrete systems. Here, we develop a framework...

Abhijatmedhi Chotrattanapituk, Michael J. Landry, Chuliang Fu et al. · 0 citations