arXiv subjects

Zhen Lu

Publications and source records attributed to Zhen Lu.

At least 19 recordsLinked to original sources

arXiv2026

Quantum simulation of real-world nonlinear dynamics via Koopman method

Nonlinear dynamics is ubiquitous in nature, ranging from chemical pattern formation to ocean circulation, yet its simulation on quantum computers is fundamentally limited by the unitary nature of quantum evolution. We propose the quantum Koopman method, a data-driven framework that embeds nonlinear dynamics into a learned linear representation and implements the resulting evolution using shallow quantum circuits. This method learns Koopman observables from trajectory data, projects the lifted dynamics onto a finite-dimensional subspace, and decomposes the corresponding non-unitary propagator into parallel spectral channels. We utilize the Koopman method on a superconducting processor to simulate three distinct nonlinear systems, comprising reaction-diffusion dynamics, fluid motion on a sphere, and satellite-derived observations of Gulf Stream currents, employing up to 32 parallel circuits of 10 qubits. These quantum simulations capture the dominant multiscale patterns and statistical signatures of the underlying dynamics, and reveal a transition from performance limited by hardware noise in weakly nonlinear systems to performance limited by finite-dimensional Koopman representations as nonlinear scale interactions increase. This transition identifies a practical boundary for quantum-amenable nonlinear dynamics, establishing a hardware-validated route for simulating moderately nonlinear dynamics on near-term quantum hardware.

quant-ph↗

arXiv2026

Stability of $N$-soliton solutions for the modified Camassa--Holm equation

In this work, we address the stability of $N$-soliton solutions to the completely integrable modified Camassa--Holm (mCH) equation. Recently, Li, Liu, and Zhu (Math. Ann. 392 (2025), 899--932) established the orbital stability of 2-soliton solutions in $H^4(\mathbb{R})$ with respect to the solution $u$ and highlighted the stability of mCH $N$-soliton solutions remains an urgent challenge. Motivated by their work, we systematically investigate the stability of mCH $N$-solitons. We first employ the bi-Hamiltonian structure of mCH to construct a novel hierarchy of explicit conservation laws with well-defined regularity domains. Then by formulating an appropriate Lyapunov functional, we apply the Inverse Scattering Transform to conduct a rigorous spectral analysis on the recursion operators. Finally, we demonstrate that the mCH $N$-solitons are non-isolated constrained minimizers of a variational problem. Our analysis proves that the $N$-soliton solutions of the mCH equation are both dynamically and orbitally stable in $H^{N+1}(\mathbb{R})$. Notably, when reduced to the 2-soliton case, our framework establishes stability in $H^3(\mathbb{R})$, which improves upon the existing regularity threshold.

math.AP↗

arXiv2026

Micro-explosion of emulsion droplets with nanoparticles at high temperature

Compared with traditional fuels, emulsified fuels can improve fuel atomization and combustion, and nanoparticles as additives have the potential to enhance combustion and reduce emissions. Previous studies on micro-explosion mainly considered emulsion droplets, but the role of nanoparticles in emulsion droplets is still unclear. In this study, we experimentally investigate the micro-explosion of emulsion droplets with nanoparticles via high-speed photography, digital image processing, optical microscopy, and scanning electron microscopy. The results show that the presence of nanoparticles can greatly improve the strength and probability of micro-explosion, particularly for carbon nanoparticles. This is mainly because nanoparticles can agglomerate during the evaporation of emulsion droplets, facilitate the absorption of radiation energy, inhibit the diffusion of superheated vapor, and ultimately promote micro-explosion. The effects of nanoparticle mass fraction and water content are also investigated, and the results show that the increase of nanoparticles and water can facilitate micro-explosion.

physics.flu-dyn↗

arXiv2026

Airfoil shape optimization via coherent Ising machine

Airfoil shape optimization presents a challenge where classical solvers frequently struggle with computational efficiency and local minima. In the promising paradigm of quantum computing, the coherent Ising machine (CIM), a specialized physical solver, offers acceleration capabilities. However, its native discrete binary architecture restricts the application in aerodynamic design. To bridge this gap, we propose a comprehensive framework that translates airfoil shape optimization into hardware-compliant quadratic unconstrained binary optimization formulations. We integrate high-order response surface models via the Rosenberg order reduction, enabling the CIM to capture strong nonlinearities in the aerodynamic performance response. Furthermore, we introduce a block-diagonal scalarization strategy that compose trade-off scenarios into a single optimization. Validated on the NACA 4-digit airfoil series using CIM hardware with 615 spins, the framework successfully locates the global optimum with a computational speedup of three orders of magnitude compared to the classical simulated annealing. The parallel embedding capacity allows for the extraction of an entire optimal Pareto front in a single hardware execution. This work demonstrates a viable, quantum-enhanced paradigm for engineering optimization.

quant-ph↗

arXiv2025

Modeling Noise in Quantum Computing of Scalar Convection

Quantum computing holds potential for accelerating the simulation of fluid dynamics. However, hardware noise in the noisy intermediate-scale quantum era significantly distorts simulation accuracy. Although error magnitudes are frequently quantified, the specific physical effects of quantum noise on flow simulation results remain largely uncharacterized. We investigate the influence of gate noise on the quantum simulation of one-dimensional scalar convection. By employing a quantum spectral algorithm where ideal time advancement affects only Fourier phases, we isolate and analyze noise-induced artifacts in spectral magnitudes. We derive a theoretical transition matrix based on Hamming distances between computational basis states to predict spectral decay, and then validate this model against density-matrix simulations and experiments on a superconducting quantum processor. Furthermore, using data-driven sparse regression, we demonstrate that quantum noise manifests in the effective partial differential equation primarily as artificial diffusion and nonlinear source terms. These findings suggest that quantum errors can be modeled as deterministic physical terms rather than purely stochastic perturbations.

quant-ph↗

arXiv2025

Stability of $n$-soliton solutions for the Intermediate Long Wave equation

In this work, we focus on the stability of $n$-soliton solutions ($n\in \mathbb{N}, n\geq 1$) to the completely integrable intermediate long wave equation (ILW), which models long internal gravity waves in a stratified fluid of finite depth. We show that the $n$-soliton solutions of the ILW equation form non-isolated constrained minimizers of a variational problem associated with a non-local elliptic equation. To establish this result, we construct a suitable Lyapunov functional and utilize the inverse scattering transform to relate the infinite sequence of conservation laws to the scattering data. Furthermore, we employ the recursion operator derived from the bi-Hamiltonian structure to optimize our analysis. Our analysis demonstrates that the $n$-soliton solutions of the ILW equation are dynamically stable in the space $H^{\frac{n}{2}}(\mathbb{R})$ ($n\in \mathbb{N}, n\geq 1$). Additionally, we establish the orbital stability of double soliton solutions in $H^1(\mathbb{R})$.

math.AP↗

arXiv2025

CFD-copilot: leveraging domain-adapted large language model and model context protocol to enhance simulation automation

Configuring computational fluid dynamics (CFD) simulations requires significant expertise in physics modeling and numerical methods, posing a barrier to non-specialists. Although automating scientific tasks with large language models (LLMs) has attracted attention, applying them to the complete, end-to-end CFD workflow remains a challenge due to its stringent domain-specific requirements. We introduce CFD-copilot, a domain-specialized LLM framework designed to facilitate natural language-driven CFD simulation from setup to post-processing. The framework employs a fine-tuned LLM to directly translate user descriptions into executable CFD setups. A multi-agent system integrates the LLM with simulation execution, automatic error correction, and result analysis. For post-processing, the framework utilizes the model context protocol (MCP), an open standard that decouples LLM reasoning from external tool execution. This modular design allows the LLM to interact with numerous specialized post-processing functions through a unified and scalable interface, improving the automation of data extraction and analysis. The framework was evaluated on benchmarks including the NACA~0012 airfoil and the three-element 30P-30N airfoil. The results indicate that domain-specific adaptation and the incorporation of the MCP jointly enhance the reliability and efficiency of LLM-driven engineering workflows.

cs.SE↗

arXiv2025

Quantum computing of nonlinear reacting flows via the probability density function method

Quantum computing offers the promise of speedups for scientific computations, but its application to reacting flows is hindered by nonlinear source terms, the challenges of time-dependent simulations, and the difficulty of extracting meaningful physical quantities from quantum states. We employ a probability density function (PDF) formulation to transform the nonlinear reacting-flow governing equations into high-dimensional linear ones. The entire temporal evolution is then solved as a single large linear system using the history state method, which avoids the measurement bottleneck of conventional time-marching schemes and fully leverages the advantages of quantum linear system algorithms. To extract the quantity of interest from the resulting quantum state, we develop an efficient algorithm to measure the statistical moments of the PDF, bypassing the need for costly full-state tomography. A computational complexity analysis shows that the measurement algorithm achieves a complexity polynomial in the logarithm of the system size using low-order polynomial approximations, compared to the exponential cost of the exact operator, thereby retaining the quantum advantage gained from solving the linear system. We validate the framework in two stages: an a priori test confirms the accuracy of the measurement algorithm on beta distributions with known analytical moments, and a perfectly stirred reactor simulation demonstrates the capability to capture the PDF evolution and statistics of a nonlinear reactive system. This work establishes a pathway for applying quantum computing to nonlinear reacting flows.

quant-ph↗

arXiv2025

RoadSceneBench: A Lightweight Benchmark for Mid-Level Road Scene Understanding

Understanding mid-level road semantics, which capture the structural and contextual cues that link low-level perception to high-level planning, is essential for reliable autonomous driving and digital map construction. However, existing benchmarks primarily target perception tasks such as detection or segmentation, overlooking the reasoning capabilities required to infer road topology and dynamic scene structure. To address this gap, we present RoadSceneBench, a lightweight yet information-rich benchmark designed to evaluate and advance visual reasoning in complex road environments. Unlike large-scale perception datasets, RoadSceneBench emphasizes relational understanding and structural consistency, encouraging models to capture the underlying logic of real-world road scenes. Furthermore, to enhance reasoning reliability, we propose Hierarchical Relational Reward Propagation with Temporal Consistency (HRRP-T), a training framework for Vision-Language Models (VLMs) in which reward signals adaptively promote spatial coherence and semantic alignment throughout the reasoning process. This paradigm enables models to move beyond static recognition toward geometry-aware and temporally consistent reasoning. Extensive experiments demonstrate that our method achieves state-of-the-art performance across diverse road configurations. RoadSceneBench thus provides a compact yet powerful foundation for studying mid-level road semantics and fostering structure-aware autonomous perception. Our dataset is available at https://github.com/XiyanLiu/RoadSceneBench.

cs.CV↗

arXiv2025

EMMA: Generalizing Real-World Robot Manipulation via Generative Visual Transfer

The generalization of vision-language-action (VLA) models heavily relies on diverse training data. However, acquiring large-scale data for robot manipulation across varied object appearances is costly and labor-intensive. To address this limitation, we introduce Embodied Manipulation Media Adaptation (EMMA), a framework for augmenting VLA policies that combines a generative data engine with an effective training pipeline. We introduce DreamTransfer, a diffusion Transformer-based architecture for generating multi-view consistent and geometrically grounded embodied manipulation videos. DreamTransfer enables visual editing of robot videos through prompts, allowing for changes to the foreground, background, and lighting while preserving their 3D structure and geometric validity. We also utilize a hybrid training set of real and generated data and propose AdaMix to enhance the training process. AdaMix is a training strategy that adaptively weights samples according to policy performance to emphasize challenging samples. Comprehensive evaluations demonstrate that videos created by DreamTransfer yield substantial improvements over previous video generation techniques in multi-view consistency, geometric accuracy, and text-conditioning precision. We conduct extensive evaluations with a total of more than 1800 trials in both simulated and real-world robotic environments. In real-world robotic tasks with zero-shot visual settings, our framework achieves a relative performance increase of over 92% compared to training with real data alone, and improves by an additional 17% with AdaMix, demonstrating its efficacy in enhancing policy generalization.

cs.AI↗

arXiv2025

Data-driven quantum Koopman method for simulating nonlinear dynamics

Quantum computation offers potential exponential speedups for simulating certain physical systems, but its application to nonlinear dynamics is inherently constrained by the requirement of unitary evolution. We propose the quantum Koopman method (QKM), a data-driven framework that bridges this gap through transforming nonlinear dynamics into linear unitary evolution in higher-dimensional observable spaces. Leveraging the Koopman operator theory to achieve a global linearization, our approach maps system states into a hierarchy of Hilbert spaces using a deep autoencoder. Within the linearized embedding spaces, the state representation is decomposed into modulus and phase components, and the evolution is governed by a set of unitary Koopman operators that act exclusively on the phase. These operators are constructed from diagonal Hamiltonians with coefficients learned from data, a structure designed for efficient implementation on quantum hardware. This architecture enables direct multi-step prediction, and the operator's computational complexity scales logarithmically with the observable space dimension. The QKM is validated across diverse nonlinear systems. Its predictions maintain relative errors below 6% for reaction-diffusion systems and shear flows, and capture key statistics in 2D turbulence. This work establishes a practical pathway for quantum-accelerated simulation of nonlinear phenomena, exploring a framework built on the synergy between deep learning for global linearization and quantum algorithms for unitary dynamics evolution.

quant-ph↗

arXiv2025

Mist formation during micro-explosion of emulsion droplets

The micro-explosion of emulsion droplets plays an important role in promoting atomization, improving combustion efficiency, and reducing pollutant emissions. In this experimental study of the micro-explosion of emulsion droplets, we find that mist can be generated during the heating of emulsion droplets, and the mist generation is closely related to the micro-explosion process. Combined analysis from high-speed images, gas chromatography, and droplet temperature variation shows that the mist generation is due to the condensation of vapor into small droplets as the temperature decreases. Two micro-explosion modes are observed, intense micro-explosion with a large amount of mist and weak micro-explosion with a small amount of mist. Different emulsified fuels are tested, and mist can be produced for all the emulsified fuels. The mist is quantitatively analyzed via digital image processing. According to the mist concentration curve in the micro-explosion process, the micro-explosion mode can be distinguished. The effects of the water and surfactant contents in the emulsion droplets are studied, and the mists are used to characterize the micro-explosion. Increasing the water content can promote the vaporization of the water phase, increase the strength of micro-explosion, and result in a large amount of mist. Increasing the surfactant content can improve the stability of the emulsion droplet, reduce the probability of intense micro-explosion, and hence reduce the mist concentration.

physics.flu-dyn↗

arXiv2025

Fine-tuning a Large Language Model for Automating Computational Fluid Dynamics Simulations

Configuring computational fluid dynamics (CFD) simulations typically demands extensive domain expertise, limiting broader access. Although large language models (LLMs) have advanced scientific computing, their use in automating CFD workflows is underdeveloped. We introduce a novel approach centered on domain-specific LLM adaptation. By fine-tuning Qwen2.5-7B-Instruct on NL2FOAM, our custom dataset of 28716 natural language-to-OpenFOAM configuration pairs with chain-of-thought (CoT) annotations, we enable direct translation from natural language descriptions to executable CFD setups. A multi-agent framework orchestrates the process, autonomously verifying inputs, generating configurations, running simulations, and correcting errors. Evaluation on a benchmark of 21 diverse flow cases demonstrates state-of-the-art performance, achieving 88.7% solution accuracy and 82.6% first-attempt success rate. This significantly outperforms larger general-purpose models like Qwen2.5-72B-Instruct, DeepSeek-R1, and Llama3.3-70B-Instruct, while also requiring fewer correction iterations and maintaining high computational efficiency. The results highlight the critical role of domain-specific adaptation in deploying LLM assistants for complex engineering workflows. Our code and fine-tuned model have been deposited at https://github.com/YYgroup/AutoCFD.

physics.flu-dyn↗

arXiv2025

Inverse Materials Design by Large Language Model-Assisted Generative Framework

Deep generative models hold great promise for inverse materials design, yet their efficiency and accuracy remain constrained by data scarcity and model architecture. Here, we introduce AlloyGAN, a closed-loop framework that integrates Large Language Model (LLM)-assisted text mining with Conditional Generative Adversarial Networks (CGANs) to enhance data diversity and improve inverse design. Taking alloy discovery as a case study, AlloyGAN systematically refines material candidates through iterative screening and experimental validation. For metallic glasses, the framework predicts thermodynamic properties with discrepancies of less than 8% from experiments, demonstrating its robustness. By bridging generative AI with domain knowledge and validation workflows, AlloyGAN offers a scalable approach to accelerate the discovery of materials with tailored properties, paving the way for broader applications in materials science.

cond-mat.mtrl-sci↗

arXiv2024

Synergy of turbulence and thermo-diffusive effects on the intermittent boundary-layer flashback of swirling flames

We simulated the intermittent boundary-layer flashback (BLF) of hydrogen-enriched swirling flames using large-eddy simulation (LES) with the flame-surface-density (FSD) method. Three cases of intermittent BLF, characterized by periodic flame entry and exit of the mixing tube, are presented. The intermittent BLF characteristics varied with the hydrogen volume fraction. Small flame bulges entered and exited the mixing tube in low hydrogen-enrichment cases. The duration of intermittent BLF events and BLF depth increased as the hydrogen content increased. Meanwhile, a large flame tongue penetrating deeply upstream characterised the highest hydrogen-enrichment case.The mean BLF peak depths and standard deviations obtained through simulations aligned well with experimental data for low and moderate hydrogen-enrichment cases. However, LES-FSD underestimated the average BLF peak depth for the highest hydrogen-enrichment case.Analysis of the flow-flame interaction revealed two mechanisms underlying the intermittent BLF phenomena. The flame bulges' oscillation near the outlet is caused by the reverse flow induced by the recirculation zone. At the same time, the deep intermittent BLF occurrs due to the boundary layer separation induced by the large turbulent burning velocity, resulting from the synergy of turbulence and thermo-diffusive effects.

physics.flu-dyn↗

arXiv2024

Generative prediction of flow fields around an obstacle using the diffusion model

We propose a geometry-to-flow diffusion model that utilizes obstacle shape as input to predict a flow field around an obstacle. The model is based on a learnable Markov transition kernel to recover the data distribution from the Gaussian distribution. The Markov process is conditioned on the obstacle geometry, estimating the noise to be removed at each step, implemented via a U-Net. A cross-attention mechanism incorporates the geometry as a prompt. We train the geometry-to-flow diffusion model using a dataset of flows around simple obstacles, including circles, ellipses, rectangles, and triangles. For comparison, two CNN-based models and a VAE model are trained on the same dataset. Tests are carried out on flows around obstacles with simple and complex geometries, representing interpolation and generalization on the geometry condition, respectively. To evaluate performance under demanding conditions, the test set incorporates scenarios including crosses and the characters `PKU.' Generated flow fields show that the geometry-to-flow diffusion model is superior to the CNN-based models and the VAE model in predicting instantaneous flow fields and handling complex geometries. Quantitative analysis of the accuracy and divergence demonstrates the model's robustness.

physics.flu-dyn↗

arXiv2023

Quantum computing of reacting flows via Hamiltonian simulation

We report the quantum computing of reacting flows by simulating the Hamiltonian dynamics. The scalar transport equation for reacting flows is transformed into a Hamiltonian system, mapping the dissipative and non-Hermitian problem in physical space to a Hermitian one in a higher-dimensional space. Using this approach, we develop the quantum spectral and finite difference methods for simulating reacting flows in periodic and general conditions, respectively. The present quantum computing algorithms offer a ``one-shot'' solution for a given time without temporal discretization, avoiding iterative quantum state preparation and measurement. We compare computational complexities of the quantum and classical algorithms. The quantum spectral method exhibits exponential acceleration relative to its classical counterpart, and the quantum finite difference method can achieve exponential speedup in high-dimensional problems. The quantum algorithms are validated on quantum computing simulators with the Qiskit package. The validation cases cover one- and two-dimensional reacting flows with a linear source term and periodic or inlet-outlet boundary conditions. The results obtained from the quantum spectral and finite difference methods agree with analytical and classical simulation results. They accurately capture the convection, diffusion, and reaction processes. This demonstrates the potential of quantum computing as an efficient tool for the simulation of reactive flows in combustion.

physics.flu-dyn↗

arXiv2023

Modeling the boundary-layer flashback of premixed hydrogen-enriched swirling flames at high pressures

We model the boundary-layer flashback (BLF) of CH$_4$/H$_2$/air swirling flames via large-eddy simulations with the flame-surface-density method (LES-FSD), in particular, at high pressures. A local displacement speed model tabulating the stretched flame speed is employed to account for the thermo-diffusive effects, flame surface curvature, and heat loss in LES-FSD. The LES-FSD well captures the propagation characteristics during the BLF of swirling flames. In the LES-FSD for lean CH$_4$/H$_2$/air flames at 2.5 bar, the critical equivalence ratio for flashback decreases with the increasing hydrogen volume fraction, consistent with the experiments. This is due to the improved modeling of effects of the flame stretch and heat loss on the local displacement speed. We also develop a simple model to predict the BLF limits of swirling flames. The model estimates the critical bulk velocity for given reactants and swirl number, via the balance between the flame-induced pressure rise and adverse pressure for boundary-layer separation. We validate the model against 14 datasets of CH$_4$/H$_2$/air swirling flame experiments, with the hydrogen volume fractions in fuel from 50% to 100%. The present model well estimates the flashback limits in various operating conditions.

physics.flu-dyn↗