arXiv subjects

Qifeng Hu

Publications and source records attributed to Qifeng Hu.

5 recordsLinked to original sources

arXiv2025

Unsupervised simulation of incompressible flows with physics- and equality- constrained artificial neural networks

Physics-informed neural networks (PINNs) have shown promise for solving partial differential equations, yet their success in simulating incompressible flows at high Reynolds numbers remains limited. Existing approaches rely on auxiliary labeled data, supervised pretraining, or reference solutions, and no purely unsupervised method comparable to conventional finite-difference or finite-volume solvers has been demonstrated. We attribute this gap to the absence of a mechanism for enforcing the divergence-free constraint and boundary conditions to strict tolerances. To address this, we adopt the physics- and equality-constrained artificial neural network (PECANN) framework with a conditionally adaptive augmented Lagrangian method (CA-ALM), and introduce a pressure-Poisson-based objective. The residual of the pressure Poisson equation is minimized subject to the momentum and continuity equations and boundary conditions on the primitive variables as equality constraints, with CA-ALM enforcing all constraints tightly. For advection-dominated, high-Reynolds-number flows, we further propose an adaptive vanishing entropy viscosity that stabilizes early training without influencing the converged solution. A baseline that instead uses the momentum residual as the objective proves ineffective under the same machinery, underscoring the critical role of the pressure-Poisson objective. The method is assessed on lid-driven cavity flow up to $Re=7{,}500$, three-dimensional unsteady Beltrami flow, and steady and unsteady flow past a circular cylinder with general inflow-outflow boundary conditions, including an ablation study identifying admissible outlet conditions -- all without labeled data or supervised pretraining. Notably, it captures the spontaneous onset of periodic vortex shedding in unsteady cylinder flow without external perturbations, starting from a randomly initialized network.

physics.flu-dyn↗

arXiv2025

Conditionally adaptive augmented Lagrangian method for physics-informed learning of forward and inverse problems

We present several key advances to the Physics and Equality Constrained Artificial Neural Networks (PECANN) framework, substantially improving its capacity to solve challenging partial differential equations (PDEs). Our enhancements broaden the framework's applicability and improve efficiency. First, we generalize the Augmented Lagrangian Method (ALM) to support multiple, independent penalty parameters for enforcing heterogeneous constraints. Second, we introduce a constraint aggregation technique to address inefficiencies associated with point-wise enforcement. Third, we incorporate a single Fourier feature mapping to capture highly oscillatory solutions with multi-scale features, where alternative methods often require multiple mappings or costlier architectures. Fourth, a novel time-windowing strategy enables seamless long-time evolution without relying on discrete time models. Fifth, and critically, we propose a conditionally adaptive penalty update (CAPU) strategy for ALM that accelerates the growth of Lagrange multipliers for constraints with larger violations, while enabling coordinated updates of multiple penalty parameters. CAPU accelerates the growth of Lagrange multipliers for selectively challenging constraints, enhancing constraint enforcement during training. We demonstrate the effectiveness of PECANN-CAPU across diverse problems, including the transonic rarefaction problem, reversible scalar advection by a vortex, high-wavenumber Helmholtz and Poisson's equations, and inverse heat source identification. The framework achieves competitive accuracy across all cases when compared with established methods and recent approaches based on Kolmogorov-Arnold networks. Collectively, these advances improve the robustness, computational efficiency, and applicability of PECANN to demanding problems in scientific computing.

cs.LG↗

arXiv2024

Non-overlapping, Schwarz-type Domain Decomposition Method for Physics and Equality Constrained Artificial Neural Networks

We present a non-overlapping, Schwarz-type domain decomposition method with a generalized interface condition, designed for physics-informed machine learning of partial differential equations (PDEs) in both forward and inverse contexts. Our approach employs physics and equality-constrained artificial neural networks (PECANN) within each subdomain. Unlike the original PECANN method, which relies solely on initial and boundary conditions to constrain PDEs, our method uses both boundary conditions and the governing PDE to constrain a unique interface loss function for each subdomain. This modification improves the learning of subdomain-specific interface parameters while reducing communication overhead by delaying information exchange between neighboring subdomains. To address the constrained optimization in each subdomain, we apply an augmented Lagrangian method with a conditionally adaptive update strategy, transforming the problem into an unconstrained dual optimization. A distinct advantage of our domain decomposition method is its ability to learn solutions to both Poisson's and Helmholtz equations, even in cases with high-wavenumber and complex-valued solutions. Through numerical experiments with up to 64 subdomains, we demonstrate that our method consistently generalizes well as the number of subdomains increases.

cs.LG↗

arXiv2021

Metamagnetic Transitions in Few-Layer CrOCl Controlled by Magnetic Anisotropy Flipping

The pivotal role of magnetic anisotropy in stabilising two-dimensional (2D) magnetism has been widely accepted, however, direct correlation between magnetic anisotropy and long-range magnetic ordering in the 2D limit is yet to be explored. Here, using angle- and temperature-dependent tunnelling magnetoresistance, we report unprecedented metamagnetic phase transitions in atomically-thin CrOCl, triggered by magnetic easy-axis flipping instead of the conventional spin flop mechanism. Few-layer CrOCl tunnelling devices of various thicknesses consistently show an in-plane antiferromagnetic (AFM) ground state with the easy axis aligned along the Cr-O-Cr direction (b-axis). Strikingly, with the presence of a magnetic field perpendicular to the easy-axis (H||c), magnetization of CrOCl does not follow the prevalent spin rotation and saturation pattern, but rather exhibits an easy-axis flipping from the in-plane to out-of-plane directions. Such magnetic anisotropy controlled metamagnetic phase transitions are manifested by a drastic upturn in tun- nelling current, which shows anomalous shifts towards higher H when temperature increases. By 2D mapping of tunnelling currents as a function of both temperature and H, we determine a unique ferrimagnetic state with a superstructure periodicity of five unit cells after the field-induced metam- agnetic transitions. The feasibility to control 2D magnetism by manipulating magnetic anisotropy may open enormous opportunities in spin-based device applications.

cond-mat.str-el↗

arXiv2018

Dialkali-Metal Monochalcogenide Semiconductors with High Mobility and Tunable Magnetism

The discovery of archetypal two-dimensional (2D) materials provides enormous opportunities in both fundamental breakthroughs and device applications, as evident by the research booming in graphene, atomically thin transition-metal chalcogenides, and few-layer black phosphorous in the past decade. Here, we report a new, large family of semiconducting dialkali-metal monochalcogenides (DMMCs) with an inherent A$_{2}$X monolayer structure, in which two alkali sub-monolayers form hexagonal close packing and sandwich the triangular chalcogen atomic plane. Such unique lattice structure leads to extraordinary physical properties, such as good dynamical and thermal stability, visible to near-infrared light energy gap, high electron mobility (e.g. $1.87\times10^{4}$ cm$^{2}$V$^{-1}$S$^{-1}$ in K$_{2}$O). Most strikingly, DMMC monolayers (MLs) host extended van Hove singularities near the valence band (VB) edge, which can be readily accessed by moderate hole doping of $\sim1.0\times10^{13}$ cm$^{-2}$. Once the critical points are reached, DMMC MLs undergo spontaneous ferromagnetic transition when the top VBs become fully spin-polarized by strong exchange interactions. Such gate tunable magnetism in DMMC MLs are promising for exploring novel device concepts in spintronics, electronics and optoelectronics.

cond-mat.mes-hall↗