Haochen Liu

activity

20232026

most citedSolving High Dimensional Partial Differential Equations Using Tensor Neural Network and A Posteriori Error Estimators

2 citations · 2 across the 9 of their papers we have counts for

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Showing 2026Show all

4 papers · 1 filter

math.NA2026

A Tensor Neural Network Method for High-Order Homogenization of Locally Periodic Elliptic Problems

Huaijia Zhang, Haochen Liu, Xia Ji +1

We develop a high-order tensor neural network (TNN) method for locally periodic elliptic multiscale problems of the form $- \nabla \cdot (A (x, x / ε) \nabla u_{ε}) = f$ . B…

math.AP2026

Sharp Broken-Power Lorentz Estimates for Fractional Powers of Radial Schrödinger Operators with Inverse-Square Asymptotics

Haochen Liu, Qinghao Yu, Hongyan Zhou

Let $H = - Δ + V (∣ x ∣)$ be a nonnegative radial Schrödinger operator on $R^{d}$ , $d \geq 2$ , whose positive harmonic function satisfies $U (r) ≃ r^{- σ_{0}}$ for $0 < r \leq 1$ and $U(r…

math.CA2026

Sharp and Endpoint Two-Weight Fractional Integral Estimates for Schr"odinger Operators with Inverse-Square Potentials

Haochen Liu, Qinghao Yu, Hongyan Zhou

Let $H_{a} = - Δ + a ∣ x ∣^{- 2}$ be the Friedrichs extension on $L^{2} (R^{d})$ , where $d \geq 3$ and $- (d - 2)^{2} /4 \leq a < 0$ lies in the attractive Hardy range. Starting from the known positi…

math-ph2026

A High-Order Nyström Method for Coupled Boundary Integral Equations in Oblique-Incidence Scattering by Impedance Cylinders

Haochen Liu, Qinghao Yu

We study the numerical solution of electromagnetic scattering by an infinitely long impedance cylinder under oblique incidence. After separation of the axial phase factor, the axia…