arXiv subjects

Hanbing Liang

Publications and source records attributed to Hanbing Liang.

5 recordsLinked to original sources

arXiv2026

Wrong-Physics Backdoors in Neural PDE Operators

Neural PDE operators are increasingly trained on reusable solver archives, yet validation often relies on clean prediction error and parameter-agnostic plausibility checks. We introduce cross-parameter relinking, a data-poisoning primitive that makes a triggered input select a valid solution from the same PDE family under an incorrect physical parameter. We term this a wrong-physics backdoor: the output remains physically plausible but is wrong for the intended parameter. The attack exploits tensor-to-parameter provenance failures in multi-parameter archives by stamping the surrogate input and relinking its supervision to a cached alternate-parameter solution for the same latent sample. Across 476 attack campaigns, we evaluate Burgers, advection-diffusion, two-dimensional Navier-Stokes, and an elliptic Poisson case. Fourier Neural Operators and DeepONet provide the primary evidence, with Transformer, GRU, and LSTM models as support. FNO reaches a backdoor success rate of 1.0000 on both advection-diffusion and two-dimensional Navier-Stokes while retaining low clean relative L2 error. Clean-label, label-only, and shuffled controls show that high attack success alone is insufficient: successful attacks must move predictions toward the intended alternate-physics target while preserving bounded clean error. These results expose a structural validation gap: smoothness or generic solver-like behavior is insufficient unless the provenance of the intended physical parameter is also verified.

cs.LG↗

arXiv2026

Shared Physics Responses Recover Hidden Rankings in Neural Operator Libraries

Selecting the optimal neural-operator prediction during deployment is challenging when high-fidelity reference solutions are unavailable. We demonstrate that under a squared Hilbert-space loss, ranking a finite model library depends strictly on the low-dimensional span of candidate differences, allowing us to score all models simultaneously using a single anchor-based linearized response of the governing equation. This shared physical diagnostic accurately recovered over 99.6\% of pairwise preferences and 99.0\% of optimal checkpoints across diverse Fourier and convolutional operator libraries for fluid, reaction-diffusion, and wave dynamics. Furthermore, the corrected physical proxy frequently outperformed the best individual candidates, and we establish computable sufficient conditions that rigorously certify exact decisions for strongly monotone discretizations. By exploiting the local dynamical response rather than raw defect magnitude, this framework enables the reliable and highly efficient deployment of scientific surrogates without requiring ground-truth data.

cs.LG↗

arXiv2026

Macroscopic transport patterns of UAV traffic in 3D anisotropic wind fields: A constraint-preserving hybrid PINN-FVM approach

Macroscopic unmanned aerial vehicle (UAV) traffic organization in three-dimensional airspace faces significant challenges from static wind fields and complex obstacles. A critical difficulty lies in simultaneously capturing the strong anisotropy induced by wind while strictly preserving transport consistency and boundary semantics, which are often compromised in standard physics-informed learning approaches. To resolve this, we propose a constraint-preserving hybrid solver that integrates a physics-informed neural network for the anisotropic Eikonal value problem with a conservative finite-volume method for steady density transport. These components are coupled through an outer Picard iteration with under-relaxation, where the target condition is hard-encoded and strictly conservative no-flux boundaries are enforced during the transport step. We evaluate the framework on reproducible homing and point-to-point scenarios, effectively capturing value slices, induced-motion patterns, and steady density structures such as bands and bottlenecks. Ultimately, our perspective emphasizes the value of a reproducible computational framework supported by transparent empirical diagnostics to enable the traceable assessment of macroscopic traffic phenomena.

cs.CE↗

arXiv2026

Bias Inheritance in Neural-Symbolic Discovery of Constitutive Closures Under Function-Class Mismatch

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 diffusion and reaction laws from spatiotemporal observations while avoiding the common pitfall where low residuals or short-horizon predictions are conflated with physical recovery. We propose a three-stage neural-symbolic framework: (1) learning numerical surrogates under physical constraints using a noise-robust weak-form-driven objective; (2) compressing these surrogates into restricted interpretable symbolic families (e.g., polynomial, rational, and saturation forms); and (3) validating the symbolic closures through explicit forward re-simulation on unseen initial conditions. Extensive numerical experiments reveal two distinct regimes. Under matched-library settings, weak polynomial baselines behave as correctly specified reference estimators, showing that neural surrogates do not uniformly outperform classical bases. Conversely, under function-class mismatch, neural surrogates provide necessary flexibility and can be compressed into compact symbolic laws with minimal rollout degradation. However, we identify a critical "bias inheritance" mechanism where symbolic compression does not automatically repair constitutive bias. Across various observation regimes, the true error of the symbolic closure closely tracks that of the neural surrogate, yielding a bias inheritance ratio near one. These findings demonstrate that the primary bottleneck in neural-symbolic modeling lies in the initial numerical inverse problem rather than the subsequent symbolic compression. We underscore that constitutive claims must be rigorously supported by forward validation rather than residual minimization alone.

cs.CE↗

arXiv2026

PICS: A Partition-of-unity Information-geometric Certified Solver for Coupled Partial Differential Equations

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 often fail to preserve structural admissibility across coupled fields. To address these limitations, we propose the Partition-of-unity Information-geometric Certified Solver (PICS), a closed-loop framework that strictly enforces structural admissibility at the level of representation rather than relying on an additional soft penalty. By constructing a gate-structured admissible manifold coupled with a restricted jet prolongation, PICS ensures that geometry-sensitive approximations and closure-essential differential coordinates enter the solver as a strongly enforced, structure-preserving ansatz. Furthermore, the framework integrates entropic tail-risk control and \textit{a posteriori} certificate-driven empirical measure transport, dynamically reallocating training efforts toward uncertified, error-prone transition zones. Evaluated against standard baseline methods across three two-dimensional coupled benchmarks, PICS achieves more consistently accurate and balanced cross-field recovery while retaining practical computational efficiency, thereby providing a rigorous route toward highly reliable multiphysics simulation.

physics.comp-ph↗