8 papers
Exact ballistic energy transport and emergent XXZ dynamics in an integrable three-state chain
Hanbing Liang, Fujun Liu
We investigate the coupling dependence of ballistic energy transport and the emergent spin dynamics in an integrable Hermitian three-state chain that connects a clock interaction t…
Uniform Stability of Scott-Vogelius Elements on Three-Dimensional Freudenthal Meshes in Degrees Four and Five: Resolving the Farrell-Mitchell-Scott Conjecture
Hanbing Liang, Fujun Liu
We establish a uniform inf-sup stability estimate for the Scott-Vogelius finite element spaces on uniform Freudenthal tetrahedralizations of the unit cube for polynomial degrees k…
False-science induction in autonomous scientific discovery
Hanbing Liang, Fujun Liu
Closed-loop discovery systems increasingly execute experiments and update decisions autonomously, turning record integrity into part of the experimental apparatus. We show that fal…
Shared Physics Responses Recover Hidden Rankings in Neural Operator Libraries
Hanbing Liang, Fujun Liu
Selecting the optimal neural-operator prediction during deployment is challenging when high-fidelity reference solutions are unavailable. We demonstrate that under a squared Hilber…
Wrong-Physics Backdoors in Neural PDE Operators
Hanbing Liang, Fujun Liu
Neural PDE operators are increasingly trained on reusable solver archives, yet validation often relies on clean prediction error and parameter-agnostic plausibility checks. We intr…
Bias Inheritance in Neural-Symbolic Discovery of Constitutive Closures Under Function-Class Mismatch
Hanbing Liang, Ze Tao, Fujun Liu
We investigate the data-driven discovery of constitutive closures in nonlinear reaction-diffusion systems with known governing PDE structures. Our objective is to robustly recover…
Macroscopic transport patterns of UAV traffic in 3D anisotropic wind fields: A constraint-preserving hybrid PINN-FVM approach
Hanbing Liang, Fujun Liu
Macroscopic unmanned aerial vehicle (UAV) traffic organization in three-dimensional airspace faces significant challenges from static wind fields and complex obstacles. A critical…
PICS: A Partition-of-unity Information-geometric Certified Solver for Coupled Partial Differential Equations
Ze Tao, Hongfu Zhou, Hanbing Liang +1
Coupled partial differential equations underpin a wide range of multiphysics systems, yet existing neural PDE solvers still struggle to resolve localized high-risk regions and ofte…