arXiv subjects

Hao Jia

Publications and source records attributed to Hao Jia.

At least 19 recordsLinked to original sources

arXiv2026

Global Well-posedness and Regularity of the Dynamical Prandtl Equation

In this paper, we study the dynamical Prandtl equation, which plays an important role in the study of the vanishing viscosity limit of the Navier--Stokes equations. Our focus is on the (Sobolev) well-posedness regime, where the given data satisfy a crucial monotonicity condition. In this case, local classical solutions have been constructed in the pioneering works of Oleinik \cite{O68,OS99}. More recently, global weak solutions were obtained in \cite{XZ04} by Xin and Zhang, and in \cite{XZZ24} by Xin, Zhang, and Zhao, where the uniqueness and interior H"older estimates of the solutions were established (in Crocco coordinates). Using a precise description of the fundamental solution to the Kolmogorov equation in the half-space, we first obtain the H"older regularity of local weak solutions up-to-boundary. We also provide a detailed proof of higher-order regularity estimates together with $W^{2,p}$ Sobolev estimates and $H^{s}$ hypoelliptic estimates, which are nontrivial. Up-to-boundary smoothness of solutions (in Crocco coordinates) is important in order to conclude the smoothness of the Prandtl solutions in the physical variables, even in the interior. It is also physically significant for applications to the Boundary Layer Theory where the dynamical Prandtl equation is essential. Using these smoothing estimates, we then prove the global existence and regularity of classical solutions to the dynamical Prandtl equation under monotonicity assumptions, which was listed by Oleinik and Samokhin in \cite{OS99} as one of the open problems. We also develop a self-contained local existence theory using weighted energy estimates and further expand the theory of global weak solutions. The main point is to incorporate all physical types of asymptotic matching of the boundary layer with the outer flow, which is expected to be useful for applications to the Navier--Stokes equations.

math.AP↗

arXiv2026

Environment-Invariant Subspace Learning for Generalizable Deepfake Detection

Cross-distribution generalization remains a critical bottleneck in deepfake detection. While recent efforts leverage the semantic priors of large-scale visual foundation models (VFMs), a noteworthy yet underexplored challenge remains: the susceptibility of these semantic priors to environmental interference from factors such as lighting and style. Crucially, this interference establishes spurious correlations between forgery cues and environmental patterns that severely limit generalization. To address this fundamental challenge, we propose an innovative Environment-Invariant Subspace Learning (EISL) framework. The core contribution of EISL is that it aims to disentangle features into orthogonal forgery-relevant invariant factors and environment-related residual factors via a learnable low-rank projection. To facilitate robust feature disentanglement, we also design an Environmental Intervention module that generates diverse and challenging intervention pairs, simulating out-of-distribution environmental shifts to guide the model toward discovering truly invariant forgery representations. Experiments across cross-dataset, cross-generator, whole-face synthesis, and corruption settings show consistent gains and competitive or leading performance against strong detectors, demonstrating improved robustness to unseen forgery types and environmental variations. This work provides a new perspective and a valuable exploration for understanding and tackling the generalization barriers of VFMs in deepfake detection.

cs.CV↗

arXiv2026

MxGLUT: A Reconfigurable LUT-Centric Broadcast Dataflow Accelerator for Mixed-Precision GEMM

Large language model (LLM) inference suffers from growing inefficiency across the prefill and decode phases, especially under weight-only quantization, where activations remain in FP8 while weights are compressed to low-bit integers. Existing LUT-based accelerators mainly target FP8-INT4 computation and still rely on separate floating-point (FP) datapaths for attention GEMM operations, leading to redundant hardware and non-unified mixed-precision execution. Moreover, their static dataflows are poorly matched to the distinct prefill and decode phases. To address these challenges, we propose MxGLUT, a reconfigurable LUT-centric broadcast (RLB) dataflow accelerator built on mixed-precision LUT-based processing elements (MxLPEs). Guided by a unified LUT-based execution framework, MxGLUT organizes both FP8-INT4 and FP8-FP8 GEMMs under a single LUT-based compute mechanism without dedicated FP multipliers or additional FP datapaths, and further adopts the RLB dataflow that localizes heavy partial-sum accumulation during the prefill phase and exploits weight reuse in the decode phase. Synthesized in UMC $28\,\mathrm{nm}$ CMOS at $200~\mathrm{MHz}$, MxGLUT reduces multiplier area by up to $56.92\%$ and power by up to $77.07\%$ and $78.35\%$ in FP8-INT4 and FP8-FP8 modes, respectively. At the accelerator level, MxGLUT achieves an area efficiency of $0.492~\mathrm{TFLOPS/mm^2}$ and an energy efficiency of $11.58~\mathrm{TFLOPS/W}$, while adding native FP8-FP8 support incurs only $2.57\%$ and $3.34\%$ reductions in area and energy efficiency, respectively, relative to the FP8-INT4-only FIGLUT baseline. Across the Llama family, MxGLUT achieves up to $2.16\times$ and $1.49\times$ latency speedup, and reduces normalized energy to $0.44\times$ and $0.71\times$ in prefill and decode, respectively, with at most $1.70\%$ perplexity increase.

cs.AR↗

arXiv2026

On the non-uniqueness of solutions of the axi-symmetric swirl-free Navier-Stokes equations, I

In this paper we construct numerically a new class of unstable self-similar solutions of the incompressible Navier-Stokes equations in $\mathbb{R}^3$. Our solutions are axially symmetric and homogeneous of degree $-1$ at $\infty$, and are unstable in the sense that the linearization around these solutions contains unstable modes. Solutions of this type have been discovered numerically by Guillod and Šverák and Hou, Wang, and Yang, and have applications to proving non-uniqueness results. The main novelty in this paper is that we discover the existence of such solutions in the space of axially symmetric swirl-free (ASSF) vector fields. These approximate solutions are defined on all of $\mathbb R^3$ and achieve global pointwise residuals of order $10^{-10}$. We discuss the numerical construction of these solutions in detail, as well as their relevance to the problem of non-uniqueness of solutions of the incompressible Navier-Stokes equations in 3D, in the space of ASSF solutions.

math.AP↗

arXiv2026

PnP-Corrector: A Universal Correction Framework for Coupled Spatiotemporal Forecasting

Coupled spatiotemporal forecasting is important for predicting the future evolution of multiple interacting dynamical systems, such as in climate models. However, existing methods are severely constrained by the persistent bottleneck of compounding errors. In coupled systems, errors from each subsystem simulator propagate and amplify one another, a phenomenon we term Reciprocal Error Amplification, leading to a rapid collapse of long-range predictions. To address this challenge, we propose a universal framework called PnP-Corrector (Plug-and-Play Corrector). The core idea of our framework is to decouple the physical simulation from the error correction process: it freezes pre-trained physics simulation engines and exclusively trains a correction agent to proactively counteract the systematic biases emerging from the coupled system. Furthermore, we design an efficient predictive model architecture, DSLCast, to serve as the backbone of this framework. Extensive experiments demonstrate that our method significantly enhances the long-term stability and accuracy of coupled forecasting systems. For instance, in the challenging task of a 300-day global ocean-atmosphere coupled forecast, our PnP-Corrector framework reduces the prediction error of the baseline model by 28% and surpasses state-of-the-art models on several key metrics.

cs.AI↗

arXiv2026

Refined asymptotics of the steady Navier Stokes equation around small Landau solutions

In this paper we study the large distance asymptotics of small steady solutions of the 3d Navier Stokes equation in exterior domains. It was proved by Korolev and the second author \cite{SverakKorolev} that the leading term is given by the Landau solution, and it was conjectured that the next order term should be $O(1/|x|^2)$ as $x\to\infty$. We confirm that this is indeed the case and we compute the next order asymptotics in terms of eigenvalues of a suitably constructed linearized operator around the Landau solution on the unit sphere. While the decay of some of the terms is precisely $O(1/|x|^2)$, the the decay of other terms is slightly accelerated.

math.AP↗

arXiv2026

ProactiveMobile: A Comprehensive Benchmark for Boosting Proactive Intelligence on Mobile Devices

Multimodal large language models (MLLMs) have made significant progress in mobile agent development, yet their capabilities are predominantly confined to a reactive paradigm, where they merely execute explicit user commands. The emerging paradigm of proactive intelligence, where agents autonomously anticipate needs and initiate actions, represents the next frontier for mobile agents. However, its development is critically bottlenecked by the lack of benchmarks that can address real-world complexity and enable objective, executable evaluation. To overcome these challenges, we introduce ProactiveMobile, a comprehensive benchmark designed to systematically advance research in this domain. ProactiveMobile formalizes the proactive task as inferring latent user intent across four dimensions of on-device contextual signals and generating an executable function sequence from a comprehensive function pool of 63 APIs. The benchmark features over 3,660 instances of 14 scenarios that embrace real-world complexity through multi-answer annotations. To ensure quality, a team of 30 experts conducts a final audit of the benchmark, verifying factual accuracy, logical consistency, and action feasibility, and correcting any non-compliant entries. Extensive experiments demonstrate that our fine-tuned Qwen2.5-VL-7B-Instruct achieves a success rate of 19.15%, outperforming o1 (15.71%) and GPT-5 (7.39%). This result indicates that proactivity is a critical competency widely lacking in current MLLMs, yet it is learnable, emphasizing the importance of the proposed benchmark for proactivity evaluation.

cs.AI↗

arXiv2026

Collective Dynamics in Circuit Quantum Acoustodynamics with a Macroscopic Resonator

Collective dynamics in engineered quantum systems offer a unique and versatile platform for exploring how many-body correlations bridge microscopic entanglement and macroscopic behavior. In this work, we report collective Dicke dynamics of acoustic modes in a macroscopic high-overtone bulk acoustic resonator (HBAR). To achieve this, we engineer a hybrid quantum acoustodynamic system comprising an HBAR strongly coupled to a superconducting transmon qubit. The HBAR device is distinctive in the sense that its narrow mode spacing, together with enhanced qubit-mode coupling strength, gives rise to efficient coupling between the transmon and clusters of near-resonant modes. By harnessing the system properties, we observe collective dynamics involving clusters composed by two or three mechanical modes, where their non-resonant spectrum allows for the observation of the transition between the Dicke static regime to dynamically induced timed-Dicke one. The coherent collective behavior of the system is supported by time-domain measurements of the qubit's purity, indicating the quantum nature of the collective dynamics. Overall, our work establishes HBAR-based hybrid quantum system as a promising platform for exploring many-body collective dynamics in macroscopic mechanical systems.

quant-ph↗

arXiv2026

Advanced Long-term Earth System Forecasting

Reliable long-term forecasting of Earth system dynamics is fundamentally limited by instabilities in current artificial intelligence (AI) models during extended autoregressive simulations. These failures often originate from inherent spectral bias, leading to inadequate representation of critical high-frequency, small-scale processes and subsequent uncontrolled error amplification. Inspired by the nested grids in numerical models used to resolve small scales, we present TritonCast. At the core of its design is a dedicated latent dynamical core, which ensures the long-term stability of the macro-evolution at a coarse scale. An outer structure then fuses this stable trend with fine-grained local details. This design effectively mitigates the spectral bias caused by cross-scale interactions. In atmospheric science, it achieves state-of-the-art accuracy on the WeatherBench 2 benchmark while demonstrating exceptional long-term stability: executing year-long autoregressive global forecasts and completing multi-year climate simulations that span the entire available $2500$-day test period without drift. In oceanography, it extends skillful eddy forecast to $120$ days and exhibits unprecedented zero-shot cross-resolution generalization. Ablation studies reveal that this performance stems from the synergistic interplay of the architecture's core components. TritonCast thus offers a promising pathway towards a new generation of trustworthy, AI-driven simulations. This significant advance has the potential to accelerate discovery in climate and Earth system science, enabling more reliable long-term forecasting and deeper insights into complex geophysical dynamics.

cs.LG↗

arXiv2025

Learning from History: A Retrieval-Augmented Framework for Spatiotemporal Prediction

Accurate and long-term spatiotemporal prediction for complex physical systems remains a fundamental challenge in scientific computing. While deep learning models, as powerful parametric approximators, have shown remarkable success, they suffer from a critical limitation: the accumulation of errors during long-term autoregressive rollouts often leads to physically implausible artifacts. This deficiency arises from their purely parametric nature, which struggles to capture the full constraints of a system's intrinsic dynamics. To address this, we introduce a novel \textbf{Retrieval-Augmented Prediction (RAP)} framework, a hybrid paradigm that synergizes the predictive power of deep networks with the grounded truth of historical data. The core philosophy of RAP is to leverage historical evolutionary exemplars as a non-parametric estimate of the system's local dynamics. For any given state, RAP efficiently retrieves the most similar historical analog from a large-scale database. The true future evolution of this analog then serves as a \textbf{reference target}. Critically, this target is not a hard constraint in the loss function but rather a powerful conditional input to a specialized dual-stream architecture. It provides strong \textbf{dynamic guidance}, steering the model's predictions towards physically viable trajectories. In extensive benchmarks across meteorology, turbulence, and fire simulation, RAP not only surpasses state-of-the-art methods but also significantly outperforms a strong \textbf{analog-only forecasting baseline}. More importantly, RAP generates predictions that are more physically realistic by effectively suppressing error divergence in long-term rollouts.

cs.LG↗

arXiv2025

Deep-Learning-Empowered Programmable Topolectrical Circuits

Topolectrical circuits provide a versatile platform for exploring and simulating modern physical models. However, existing approaches suffer from incomplete programmability and ineffective feature prediction and control mechanisms, hindering the investigation of physical phenomena on an integrated platform and limiting their translation into practical applications. Here, we present a deep learning empowered programmable topolectrical circuits (DLPTCs) platform for physical modeling and analysis. By integrating fully independent, continuous tuning of both on site and off site terms of the lattice Hamiltonian, physics graph informed inverse state design, and immediate hardware verification, our system bridges the gap between theoretical modeling and practical realization. Through flexible control and adiabatic path engineering, we experimentally observe the boundary states without global symmetry in higher order topological systems, their adiabatic phase transitions, and the flat band like characteristic corresponding to Landau levels in the circuit. Incorporating a physics graph informed mechanism with a generative AI model for physics exploration, we realize arbitrary, position controllable on board Anderson localization, surpassing conventional random localization. Utilizing this unique capability with high fidelity hardware implementation, we further demonstrate a compelling cryptographic application: hash based probabilistic information encryption by leveraging Anderson localization with extensive disorder configurations, enabling secure delivery of full ASCII messages.

cond-mat.dis-nn↗

arXiv2025

Asymptotic stability of the Kolmogorov flow at high Reynolds numbers

In this paper we prove the asymptotic stability of the Kolmogorov flow on a non-square torus for perturbations $ω_0$ satisfying $\|ω_0\|_{H^3}\llν^{1/3}$, where $0<ν\ll1$ is the viscosity. Kolmogorov flows are important metastable states to the two dimensional incompressible Navier Stokes equations in the high Reynolds number regime. Our result shows that the perturbed solution will rapidly converge to a shear flow close to the Kolmogorov flow, before settling down to the Kolmogorov flow and slowly decaying to $0$ as $t\to\infty$. In fact, our analysis reveals several interesting time scales and rich dynamical behavior of the perturbation in the transition period $0<t\leq 1/ν$. The threshold $ν^{1/3}$, which is the same as that for the Couette flow, is quite surprising since one of the key stability mechanisms, enhanced dissipation, becomes considerably weaker in the case of Kolmogorov flows due to the presence of critical points. To overcome this essential new difficulty, we establish sharp vorticity depletion estimates near the critical points to obtain improved decay rates for the vorticity and velocity fields that are comparable with those for Couette flows, at least for our purposes. We then combine these estimates (enhanced dissipation, inviscid damping and vorticity depletion) with a quasilinear approximation scheme and a multiple-timescale analysis naturally adapted to the dynamics of the perturbation, to obtain the $ν^{1/3}$ threshold for dynamic stability of Kolmogorov flows. The threshold is expected to be sharp when the perturbation is considered in Sobolev spaces. This appears to be the first result that applies vorticity depletion estimates to improve thresholds for nonlinear asymptotic stability in incompressible fluid equations.

math.AP↗

arXiv2025

Memory-Efficient Optical Flow via Radius-Distribution Orthogonal Cost Volume

The full 4D cost volume in Recurrent All-Pairs Field Transforms (RAFT) or global matching by Transformer achieves impressive performance for optical flow estimation. However, their memory consumption increases quadratically with input resolution, rendering them impractical for high-resolution images. In this paper, we present MeFlow, a novel memory-efficient method for high-resolution optical flow estimation. The key of MeFlow is a recurrent local orthogonal cost volume representation, which decomposes the 2D search space dynamically into two 1D orthogonal spaces, enabling our method to scale effectively to very high-resolution inputs. To preserve essential information in the orthogonal space, we utilize self attention to propagate feature information from the 2D space to the orthogonal space. We further propose a radius-distribution multi-scale lookup strategy to model the correspondences of large displacements at a negligible cost. We verify the efficiency and effectiveness of our method on the challenging Sintel and KITTI benchmarks, and real-world 4K ($2160\!\times\!3840$) images. Our method achieves competitive performance on both Sintel and KITTI benchmarks, while maintaining the highest memory efficiency on high-resolution inputs.

cs.CV↗

arXiv2025

Short-time Variational Mode Decomposition

Variational mode decomposition (VMD) and its extensions like Multivariate VMD (MVMD) decompose signals into ensembles of band-limited modes with narrow central frequencies. These methods utilize Fourier transformations to shift signals between time and frequency domains. However, since Fourier transformations span the entire time-domain signal, they are suboptimal for non-stationary time series. We introduce Short-Time Variational Mode Decomposition (STVMD), an innovative extension of the VMD algorithm that incorporates the Short-Time Fourier transform (STFT) to minimize the impact of local disturbances. STVMD segments signals into short time windows, converting these segments into the frequency domain. It then formulates a variational optimization problem to extract band-limited modes representing the windowed data. The optimization aims to minimize the sum of the bandwidths of these modes across the windowed data, extending the cost functions used in VMD and MVMD. Solutions are derived using the alternating direction method of multipliers, ensuring the extraction of modes with narrow bandwidths. STVMD is divided into dynamic and non-dynamic types, depending on whether the central frequencies vary with time. Our experiments show that non-dynamic STVMD is comparable to VMD with properly sized time windows, while dynamic STVMD better accommodates non-stationary signals, evidenced by reduced mode function errors and tracking of dynamic central frequencies. This effectiveness is validated by steady-state visual-evoked potentials in electroencephalogram signals.

cs.IT↗

arXiv2024

Conditioned quantum-assisted deep generative surrogate for particle-calorimeter interactions

Particle collisions at accelerators such as the Large Hadron Collider, recorded and analyzed by experiments such as ATLAS and CMS, enable exquisite measurements of the Standard Model and searches for new phenomena. Simulations of collision events at these detectors have played a pivotal role in shaping the design of future experiments and analyzing ongoing ones. However, the quest for accuracy in Large Hadron Collider (LHC) collisions comes at an imposing computational cost, with projections estimating the need for millions of CPU-years annually during the High Luminosity LHC (HL-LHC) run \cite{collaboration2022atlas}. Simulating a single LHC event with \textsc{Geant4} currently devours around 1000 CPU seconds, with simulations of the calorimeter subdetectors in particular imposing substantial computational demands \cite{rousseau2023experimental}. To address this challenge, we propose a conditioned quantum-assisted deep generative model. Our model integrates a conditioned variational autoencoder (VAE) on the exterior with a conditioned Restricted Boltzmann Machine (RBM) in the latent space, providing enhanced expressiveness compared to conventional VAEs. The RBM nodes and connections are meticulously engineered to enable the use of qubits and couplers on D-Wave's Pegasus-structured \textit{Advantage} quantum annealer (QA) for sampling. We introduce a novel method for conditioning the quantum-assisted RBM using \textit{flux biases}. We further propose a novel adaptive mapping to estimate the effective inverse temperature in quantum annealers. The effectiveness of our framework is illustrated using Dataset 2 of the CaloChallenge \cite{calochallenge}.

cs.LG↗

arXiv2024

Zephyr quantum-assisted hierarchical Calo4pQVAE for particle-calorimeter interactions

With the approach of the High Luminosity Large Hadron Collider (HL-LHC) era set to begin particle collisions by the end of this decade, it is evident that the computational demands of traditional collision simulation methods are becoming increasingly unsustainable. Existing approaches, which rely heavily on first-principles Monte Carlo simulations for modeling event showers in calorimeters, are projected to require millions of CPU-years annually -- far exceeding current computational capacities. This bottleneck presents an exciting opportunity for advancements in computational physics by integrating deep generative models with quantum simulations. We propose a quantum-assisted hierarchical deep generative surrogate founded on a variational autoencoder (VAE) in combination with an energy conditioned restricted Boltzmann machine (RBM) embedded in the model's latent space as a prior. By mapping the topology of D-Wave's Zephyr quantum annealer (QA) into the nodes and couplings of a 4-partite RBM, we leverage quantum simulation to accelerate our shower generation times significantly. To evaluate our framework, we use Dataset 2 of the CaloChallenge 2022. Through the integration of classical computation and quantum simulation, this hybrid framework paves way for utilizing large-scale quantum simulations as priors in deep generative models.

cs.LG↗

arXiv2024

CaloQVAE : Simulating high-energy particle-calorimeter interactions using hybrid quantum-classical generative models

The Large Hadron Collider's high luminosity era presents major computational challenges in the analysis of collision events. Large amounts of Monte Carlo (MC) simulation will be required to constrain the statistical uncertainties of the simulated datasets below these of the experimental data. Modelling of high-energy particles propagating through the calorimeter section of the detector is the most computationally intensive MC simulation task. We introduce a technique combining recent advancements in generative models and quantum annealing for fast and efficient simulation of high-energy particle-calorimeter interactions.

hep-ex↗

arXiv2024

Sharp Asymptotic Stability of Blasius Profile in the Steady Prandtl Equation

This work presents an asymptotic stability result concerning the self-similar Blasius profiles $[\bar{u}, \bar{v}]$ of the stationary Prandtl boundary layer equation. Initially demonstrated by Serrin \cite{MR0282585}, the profiles $[\bar{u}, \bar{v}]$ were shown to act as a self-similar attractor of solutions $[u, v]$ to the Prandtl equation through the use of von Mises transform and maximal principle techniques. Specifically, as $x \to \infty$, $\|u - \bar{u}\|_{L^{\infty}_{y}} \to 0$. Iyer \cite{MR4097332} employed refined energy methods to derive an explicit convergence rate for initial data close to Blasius. Wang and Zhang \cite{MR4657422} utilized barrier function methods, removing smallness assumptions but imposing stronger asymptotic conditions on the initial data. It was suggested that the optimal convergence rate should be $\|u-\bar{u}\|_{L^{\infty}_{y}}\lesssim (x+1)^{-\frac{1}{2}}$, treating the stationary Prandtl equation as a 1-D parabolic equation in the entire space. In this study, we establish that $\|u - \bar{u}\|_{L^{\infty}_{y}} \lesssim (x+1)^{-1}$. Our proof relies on discovering nearly conserved low-frequency quantities and inherent degenerate structures at the boundary, which enhance the convergence rate through iteration techniques. Notably, the convergence rate we have demonstrated is optimal. We can find special solutions of Prandtl's equation such that the convergence between the solutions and the Blasius profile is exact, represented as $ (x+1)^{-1} $.

math.AP↗