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Fujun Liu

Publications and source records attributed to Fujun Liu.

At least 19 recordsLinked to original sources
arXiv2026

Optimal limits on weak integrability breaking and protected thermal memory near qutrit exchange

Although integrability does not universally require a continuous one-site symmetry, we rigorously prove that every jointly analytic, regular Yang-Baxter deformation of the qutrit exchange interaction necessarily retains a nontrivial, analytically varying one-site charge. Breaking this local symmetry imposes a fundamental physical constraint on approximate conservation, governed by the optimal uniform bound $δ^3 \le C\varepsilon$ that explicitly relates the minimal one-site symmetry defect $δ$ to the local current-conservation residual $\varepsilon$. While breaking all one-site charges strictly forbids an exact integrable completion, an optimally compensated nearest-neighbor interaction saturates this cubic limit and anomalously extends the guaranteed infinite-temperature energy-current correlation window to order $|λ|^{-3}$ in the perturbation strength $λ$. Furthermore, we reveal a fundamental resonance obstruction for intrinsic conversion perturbations that strictly prevents any exact first-order repair of a broken one-site charge on any finite ring. Nevertheless, we demonstrate that the complete eight-dimensional charge memory matrix remains thermodynamically protected and approaches the identity for timescales $t=o(|λ|^{-3/2})$, a robust feature of the full infinite-temperature dynamics when the thermodynamic limit is taken before weak coupling.

physics.comp-ph↗
arXiv2026

Exact ballistic energy transport and emergent XXZ dynamics in an integrable three-state chain

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 to a highly degenerate flag limit. By constructing a regular $R$-matrix to establish a globally conserved energy current, we analytically evaluate its full variance to obtain the exact, strictly positive leading high-temperature coefficient of the thermal Drude weight and the ballistic growth rate of the energy-correlation second moment. In the strong-coupling limit, the degeneracy is lifted by virtual transitions of a delocalized third-color spectator state, which generates an effective spin-$1/2$ XXZ Hamiltonian with anisotropy $Δ= -1/2$ and fundamentally selects the all-active two-color sector as the true ground state. For periodic boundaries, this virtual spectator motion introduces a positive length-changing XXZ supercharge squared that, for $L\ge4$, strictly annihilates all states within a finite, length-independent energy interval above the ground state. Consequently, we rigorously prove that the full periodic effective theory perfectly replicates the exact low-energy XXZ spectrum, including all state multiplicities, as well as its macroscopic bulk free-energy density.

physics.comp-ph↗
arXiv2026

Uniform Stability of Scott-Vogelius Elements on Three-Dimensional Freudenthal Meshes in Degrees Four and Five: Resolving the Farrell-Mitchell-Scott Conjecture

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 >= 4. This result completely settles the first conjecture of Farrell, Mitchell, and Scott for the critical degrees k = 4 and k = 5, complementing the known stability range for higher polynomial degrees. The main mathematical difficulties stem from the complex topological compatibility required at the singular vertices and the corresponding mean-value constraints across adjacent elements. We tackle these challenges by developing a unified barycentric skeleton-bubble calculus that explicitly constructs vertex jets, edge modes, and face transfers to globally route element means. The accompanying exact computations independently verify these finite-dimensional identities and provide reproducibility data.

math.NA↗
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

False-science induction in autonomous scientific discovery

Closed-loop discovery systems increasingly execute experiments and update decisions autonomously, turning record integrity into part of the experimental apparatus. We show that false-science induction arises when legitimate physical objects and measurements are paired incorrectly, driving neural surrogates to faithfully learn record-induced associations that do not correspond to the true object-outcome relationship while marginal data distributions remain unchanged. Across green fluorescent protein fitness and materials band-gap prediction loops, coherent paired misbinding systematically redirects experimental budgets toward low-performing basins, whereas same-volume random swaps have negligible effects. These observations identify error coherence, rather than raw error frequency, as the primary variable controlling this budget misallocation in the tested loops. The resulting binding identifiability boundary supports monitored-axis quarantines and feedback-conflict triage, which intercept over-concentrated proposals before execution and isolate the corrupted hypothesis axis.

cs.LG↗
arXiv2026

Spatio-Temporal Uncertainty-Modulated Physics-Informed Neural Networks for Solving Hyperbolic Conservation Laws with Strong Shocks

Physics-Informed Neural Networks (PINNs) frequently encounter difficulties in accurately resolving shock waves within high-speed compressible flows, a failure largely attributed to the "gradient pathology" arising from extreme stiffness at discontinuities. To overcome this limitation, we propose the Spatio-Temporal Uncertainty-Modulated PINN (UM-PINN), a probabilistic framework that reinterprets the training process as a multi-task learning problem governed by homoscedastic aleatoric uncertainty. By integrating a gradient-based spatial mask with learnable variance parameters, our method dynamically balances the conflicting contributions of Partial Differential Equation (PDE) residuals and initial conditions across the spatiotemporal domain, further stabilized by Quasi-Monte Carlo Sobol sampling. We validate the framework against challenging benchmarks, including the one-dimensional (1D) Sod shock tube, the high-frequency Shu-Osher problem, and the complex two-dimensional (2D) Riemann interaction, where standard gradient-based weighting schemes typically fail. Experimental results demonstrate that UM-PINN achieves orders of magnitude improvement in accuracy and shock resolution compared to baseline methods, establishing a robust new paradigm for mesh-free Computational Fluid Dynamics in hyperbolic systems.

physics.comp-ph↗
arXiv2026

Freeze-in Warm Dark Matter via Dimension-6 Operators in 3-3-1 Models

We propose a natural resolution to the fine-tuning problem inherent in the freeze-in dark matter paradigm by embedding a sterile singlet within a 3-3-1 electroweak extension. By imposing an exact $Z_{13}$ discrete gauge symmetry, we formally suppress all low-dimensional portals to ensure that the dark sector communicates with the Standard Model (SM) exclusively through a dimension-six operator. This theoretical structure allows the extraordinarily small coupling required for dark matter production to emerge naturally from the profound hierarchy between the electroweak scale and the ultra-high Peccei-Quinn symmetry breaking scale. Detailed numerical integration of the Boltzmann equations demonstrates that the sterile singlet can be produced via the infrared freeze-in mechanism to match the observed relic abundance of $Ω_S h^2 = 0.12$. The resulting keV-scale warm dark matter candidate remains consistent with stringent Lyman-alpha forest constraints while offering a viable solution to galactic-scale discrepancies such as the cusp-core and missing satellites problems. Ultimately, this framework provides a self-consistent unification of dark matter genesis and the strong CP solution that is completely independent of ad hoc parameter adjustments.

hep-ph↗
arXiv2026

Detecting AI-Generated Content on Social Media with Multi-modal Language Models

Generative AI has enabled the creation of photorealistic images and videos that are increasingly disseminated on social media, often used for spam, misinformation, manipulation, and fraud. Existing AI-generated content (AIGC) detection methods face challenges including poor generalization to new generation models, reliance on single modalities, and lack of interpretable explanations. We present our pipeline that mitigates these issues by continuously curating diverse multi-modal social media data and training a compact vision-language model for detection and explanation. Our model achieves state-of-the-art detection performance on public benchmarks and demonstrates robust detection and explanation capabilities on internal social media datasets across multiple platforms. We deployed our model for post recommendation on social media platforms and observed positive downstream impacts on user engagement, demonstrating that it is feasible to perform effective AIGC detection in dynamic, real-world social media environments.

cs.CL↗
arXiv2026

High-Fidelity Reconstruction of Charge Boundary Layers and Sharp Interfaces in Electro-Thermal-Convective Flows via Residual-Attention PINNs

Accurate reconstruction of localized extreme structures remains a critical bottleneck in the physics-informed modeling of electro-thermal-convective flows. Although conventional physics-informed neural networks effectively capture smooth global dynamics, they frequently suffer from numerical diffusion and distortion when attempting to resolve sharp charge boundary layers or abrupt multiphase interfaces. To address these limitations, we propose a Residual-Attention Physics-Informed Neural Network (RA-PINN) that embeds gated attention modulation within a residual feature framework to adaptively enhance local sensitivity to steep physical gradients. The proposed architecture is rigorously evaluated against standard and recurrent network baselines using canonical electrohydrodynamic scenarios, encompassing near-electrode exponential boundary layers and sharply concentrated charge fields. Quantitative analyses demonstrate that the RA-PINN significantly reduces localized errors and faithfully preserves critical interface topologies without compromising the global consistency dictated by the coupled governing equations. Ultimately, this methodology establishes a highly robust predictive framework for resolving complex interfacial and boundary layer phenomena in advanced fluid dynamics applications.

physics.flu-dyn↗
arXiv2026

LNN-PINN: A Unified Physics-Only Training Framework with Liquid Residual Blocks

Physics-informed neural networks (PINNs) have attracted considerable attention for their ability to integrate partial differential equation priors into deep learning frameworks; however, they often exhibit limited predictive accuracy when applied to complex problems. To address this issue, we propose LNN-PINN, a physics-informed neural network framework that incorporates a liquid residual gating architecture while preserving the original physics modeling and optimization pipeline to improve predictive accuracy. The method introduces a lightweight gating mechanism solely within the hidden-layer mapping, keeping the sampling strategy, loss composition, and hyperparameter settings unchanged to ensure that improvements arise purely from architectural refinement. Across four benchmark problems, LNN-PINN consistently reduced RMSE and MAE under identical training conditions, with absolute error plots further confirming its accuracy gains. Moreover, the framework demonstrates strong adaptability and stability across varying dimensions, boundary conditions, and operator characteristics. In summary, LNN-PINN offers a concise and effective architectural enhancement for improving the predictive accuracy of physics-informed neural networks in complex scientific and engineering problems.

cs.LG↗
arXiv2026

LSTM-PINN for Steady-State Electrothermal Transport: Preserving Multi-Field Consis tency in Strongly Coupled Heat and Fluid Flow

Steady-state electrothermal systems involve strongly coupled heat transfer, fluid flow, and electric-potential transport, creating severe numerical challenges for standard physics-informed neural networks (PINNs) due to stark disparities in gradient scales and residual stiffnesses across the physical fields. To resolve these multiphysics bottlenecks, we introduce a Long Short-Term Memory PINN (LSTM-PINN) framework that utilizes a depth-recursive memory mechanism to preserve long-range spatial feature dependencies and maintain strict cross-field consistency. The proposed architecture is rigorously evaluated against conventional and attention-based networks across a unified five-field formulation encompassing four complex convective and drag regimes: Boussinesq electrothermal flow, drift-potential gauge-constrained transport, strong buoyancy-coupled convection, and Brinkman--Forchheimer drift. Quantitative and visual analyses demonstrate that LSTM-PINN successfully suppresses non-physical artifacts and structural distortions, yielding the highest thermodynamic fidelity and consistently outperforming state-of-the-art baselines in global error metrics. Ultimately, this memory-enhanced approach provides a highly robust and accurate computational baseline for capturing localized boundary layers and complex energy-momentum feedback in advanced electrothermal energy systems.

physics.comp-ph↗
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

Learnable Viscosity Modulation in Physics-Informed Neural Networks for Incompressible Flow Reconstruction

Accurately and stably solving the incompressible Navier--Stokes equations with physics-informed neural networks (PINNs) remains challenging, particularly for sparse or noisy observations and for flow regimes in which the local balance among convection, diffusion, and pressure is difficult to capture. To address this issue, we propose a framework, denoted as LVM-PINN, which incorporates a learnable viscosity modulation (LVM) mechanism into the PINN residual. Specifically, the model predicts a spatiotemporal scalar field that is embedded directly into the viscous diffusion term of the momentum equations, thereby enabling adaptive modulation of the local dissipation strength during training. This modification improves optimization stability while enhancing the representation of complex flow structures. The effect of the proposed mechanism is further examined through a controlled ablation setting with an otherwise unchanged network architecture, as well as through comparisons with GRU- and residual-attention-based backbone baselines. Numerical experiments on two-dimensional benchmark problems, including the Kovasznay flow and two manufactured forcing flows, show that the proposed framework yields more stable training behavior and more accurate flow reconstruction under sparse and noisy data conditions.

physics.flu-dyn↗
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↗
arXiv2026

A Residual-Attention Physics-Informed Neural Network for Irregular Interfaces and Multi-Peak Transport Fields

In complex engineering systems such as electro-thermal-fluid coupling, rapid and accurate prediction of multi-physics fields is essential for advanced applications like digital twins and real-time condition monitoring. Traditional numerical methods often suffer from high computational latency, whereas standard Physics-Informed Neural Networks (PINNs) frequently fail to capture critical local features, such as irregular interfaces, localized high-gradient regions, and multi-peak transport structures. To address these limitations and provide high-fidelity intelligent predictions for engineering decision-making, this paper proposes a Residual-Attention Physics-Informed Neural Network (RA-PINN) as a powerful surrogate modeling engine. The proposed method incorporates residual learning and attention enhancement into the network backbone to improve the representation of oblique transition structures, narrow charge layers, and distributed hotspots while strictly preserving global field consistency. To evaluate its effectiveness as an intelligent prediction framework, three representative benchmark cases are constructed, including an oblique asymmetric interface, a bipolar high-gradient charge layer, and a multi-peak Gaussian charge migration field. Under unified training settings, the proposed RA-PINN is systematically compared with a standard pure PINN and an LSTM-PINN in terms of average error, local maximum error, structural similarity, and convergence behavior. The results show that RA-PINN consistently achieves the best overall performance across all benchmark cases, demonstrating its tremendous potential as a highly reliable core inference engine for the condition monitoring and digital twin modeling of complex multi-physics engineering systems.

physics.comp-ph↗
arXiv2026

Residual Attention Physics-Informed Neural Networks for Robust Multiphysics Simulation of Steady-State Electrothermal Energy Systems

Efficient thermal management and precise field prediction are critical for the design of advanced energy systems, including electrohydrodynamic transport, microfluidic energy harvesters, and electrically driven thermal regulators. However, the steady-state simulation of these electrothermal coupled multiphysics systems remains challenging for physics-informed neural computation due to strong nonlinear field coupling, temperature-dependent coefficient variability, and complex interface dynamics. This study proposes a Residual Attention Physics-Informed Neural Network (RA-PINN) framework for the unified solution of coupled velocity, pressure, electric-potential, and temperature fields. By integrating a unified five-field operator formulation with residual-connected feature propagation and attention-guided channel modulation, the proposed architecture effectively captures localized coupling structures and steep gradients. We evaluate RA-PINN across four representative energy-relevant benchmarks: constant-coefficient coupling, indirect pressure-gauge constraints, temperature-dependent transport, and oblique-interface consistency. Comparative analysis against Pure-MLP, LSTM-PINN, and pLSTM-PINN demonstrates that RA-PINN achieves superior accuracy, yielding the lowest MSE, RMSE, and relative $L_2$ errors across all scenarios. Notably, RA-PINN maintains high structural fidelity in interface-dominated and variable-coefficient settings where conventional PINN backbones often fail. These results establish RA-PINN as a robust and accurate computational framework for the high-fidelity modeling and optimization of complex electrothermal multiphysics in sustainable energy applications.

cs.LG↗