arXiv subjects

Lu Zhu

Publications and source records attributed to Lu Zhu.

At least 19 recordsLinked to original sources

arXiv2026

Learning dynamically consistent flow reconstructions from limited observations

A core inverse problem in the experimental sciences is the inference of a hidden dynamical state from sparse or indirect measurements. There is a natural opportunity for deep learning methods here, but machine-learnt reconstruction methods typically require full state data for training. We present Trajectory-Consistent Network Training (TraCTra), a label-free framework that trains reconstruction networks using only partial observation sequences and a differentiable forward model. TraCTra requires the network reconstruction and dynamical evolution to be mutually consistent: network-predicted states are marched forward in time to match subsequent observations and to agree in the full state space with independent reconstructions at later times. Across four fluid systems, the same objective reconstructs three-dimensional turbulence from coarse-grained fields, velocity from observations of density fluctuations, and three-dimensional density and velocity from sequences of projected two-dimensional shadowgraphs, while also recovering global vorticity from observations confined to a small spatial window. TraCTra outperforms assimilation-only and physics-informed neural approaches, preserves dynamically important multiscale structure, and remains accurate beyond the optimisation window. It transfers to held-out times in the three-dimensional shadowgraph problem and, when trained across trajectories, generalises to unseen flows in the two-dimensional problem. The results establish trajectory consistency as a general supervision principle for reconstructing hidden dynamical states without full state training targets.

physics.flu-dyn↗

arXiv2026

A neural network architecture and training algorithm to predict viscoelastic stresses from vortical data

Numerical simulations of elastic turbulence in parallel shear flows of polymer solutions indicate that the phenomena is associated with the formation and instability of exact coherent states dominated by thin sheets of polymer stress. However, these ``arrowhead'' structures are yet to be seen directly in experiments, where simultaneous velocity and polymer conformation measurements are challenging to obtain. Motivated by these challenges, we introduce a method for the prediction of the polymer conformation field given a time series of vorticity measurements. Our approach consists of two components: the first is a convolutional neural network architecture which takes vorticity fields and outputs a positive definite conformation tensor. The second is the adaptation of an assimilation-based training algorithm (Zhu \& Page, 2026) which does not require a pre-generated `offline' library of reference conformation fields, but is trained only using the vorticity measurements. This is particularly important in viscoelastic problems, where the appropriate model and parameters to compare to the experiments may need to be determined as part of the solution. In training, measurements made on a time-marched network prediction are required to match the saved time series, while the output of the solver and network predictions at later times are required to be self-consistent. We apply these ideas to two-dimensional Kolmogorov flow in a range of regimes, from simple traveling waves to a fully chaotic state. In all cases, our method produces robust predictions of the polymer stretch, while standard, unregularised variational assimilation is ineffective. In the chaotic case we show that our networks generalise to much larger domains -- without further optimisation -- than the `minimal' units in which they were trained.

physics.flu-dyn↗

arXiv2026

Inviscid Incompressible Limit for Degenerate Compressible Navier-Stokes Equations on Expanding Domains

We simultaneously investigate the inviscid and Low Mach number limits on expanding domains for the $3D$ degenerate compressible Navier-Stokes equations, whose viscosity depends on density. Starting from ill-prepared data, we show the limit system is the incompressible Euler system. Our result extends a previous result of Feireisl et al. concerning the constant viscosity Navier-Stokes equations, and is the first to establish the inviscid and incompressible limits at the same time for density-dependent viscosity.

math.AP↗

arXiv2026

Significant heat transfer enhancement via polymer additives in two-dimensional sheared convection

Heat dissipation is critical in modern engineering systems. Polymer additives offer a potential route to improve fluid-based cooling. Here, we study elasticity-enhanced heat transfer in two-dimensional, thermally-stratified Poiseuille flow. At Reynolds numbers, $Re$, $\lesssim 1000$, we observe two types of linearly unstable modes: the recently identified elasticity-induced centre mode (Khalid et al., J. Fluid Mech. 915, 2021) and the classical buoyancy-driven convective mode (Kelly, Adv. Appl. Mech. 31, 35-112, 1994). Direct numerical simulations show that the centre mode develops into a nonlinear `arrowhead' state but yields negligible heat transfer enhancement (typically $\approx 0.03\%$ increase compared to the conductive state). By contrast, polymers can enhance the heat flux associated with the convective mode by up to $1100\%$. The nonlinear convective-mode states take the form of either periodic orbits or travelling waves, and are dominated by hook-like polymer-stress structures that can attach to the walls. The unattached hooks act as `speed bumps' that reduced streamwise velocity and promote wall-normal motion, whereas wall-attached hooks form effective `polymer walls', reorganising the flow into strong counter-rotating rolls and triggering the extreme-enhancement regime. The elasto-buoyant nature of these states is confirmed by perturbation kinetic energy budgets, which show that polymer and buoyancy sustain the states synergistically. The wall-attached hooks enable rapid thermal equilibration but impose a large hydraulic penalty, making them suitable for process streams requiring fast temperature adjustment. Unattached hooks provide a more thermally efficient regime for heat-transport applications. These results highlight the potential of elastic fluids for future heat transfer enhancement technologies.

physics.flu-dyn↗

arXiv2026

Towards Autonomous Mechanistic Reasoning in Virtual Cells

Large language models (LLMs) have recently gained significant attention as a promising approach to accelerate scientific discovery. However, their application in open-ended scientific domains such as biology remains limited, primarily due to the lack of factually grounded and actionable explanations. To address this, we introduce a structured explanation formalism for virtual cells that represents biological reasoning as mechanistic action graphs, enabling systematic verification and falsification. Building upon this, we propose VCR-Agent, a multi-agent framework that integrates biologically grounded knowledge retrieval with a verifier-based filtering approach to generate and validate mechanistic reasoning autonomously. Using this framework, we release VC-TRACES dataset, which consists of verified mechanistic explanations derived from the Tahoe-100M atlas. Empirically, we demonstrate that training with these explanations improves factual precision and provides a more effective supervision signal for downstream gene expression prediction. These results underscore the importance of reliable mechanistic reasoning for virtual cells, achieved through the synergy of multi-agent and rigorous verification.

cs.LG↗

arXiv2025

On the essential structure of exact traveling-wave solutions in viscoelastic flow

We examine elastic travelling-wave (`arrowhead') solutions in a viscoelastic, unidirectionally body-forced flow, focusing on their existence and morphological changes as the Weissenberg number, $\mathrm{Wi}$, and streamwise duct length, $L$, are varied. We find that branch topology varies from an isola at low $L$ through a two-sided reconnection at intermediate $L$ to a branch which exists at asymptotically large $\mathrm{Wi}$ for larger $L$. At intermediate $L$ more than two arrowhead solutions can coexist at a given $(\mathrm{Wi}, L)$ choice due to extra saddle node bifurcations. Secondly, the canonical arrowhead consists of two legs joined by an arched head that blocks throughflow and traps a counter-rotating vortex pair, while a polymer strand can emerge as a by-product of a strong extensional region attached/detached to the arrowhead arch. Thirdly, a minimal domain length $L_{\min}$ required to sustain an arrowhead is found to vary non-monotonically with $\mathrm{Wi}$; for $\mathrm{Wi}\ge 20$, detached-strand states control $L_{\min}$ with a relation $L_{\min}\approx 0.125\mathrm{Wi}+1.5$. And fourthly, in sufficiently long domains, the upper branch becomes a localised single arrowhead whose streamwise extent depends on $\mathrm{Wi}$, whereas the lower branch can proliferate into a train of arrowheads at high $\mathrm{Wi}$, a phenomenon not previously reported.

physics.flu-dyn↗

arXiv2025

R-AVST: Empowering Video-LLMs with Fine-Grained Spatio-Temporal Reasoning in Complex Audio-Visual Scenarios

Recently, rapid advancements have been made in multimodal large language models (MLLMs), especially in video understanding tasks. However, current research focuses on simple video scenarios, failing to reflect the complex and diverse nature of real-world audio-visual events in videos. To bridge this gap, we firstly introduce R-AVST, a dataset for audio-visual reasoning featuring fine-grained spatio-temporal annotations. In constructing this, we design a pipeline consisting of LLM-based key object extraction, automatic spatial annotation and manual quality inspection, resulting in over 5K untrimmed videos with 27K objects across 100 types of audio-visual events. Building on this dataset, we define three core tasks for spatio-temporal reasoning in audio-visual scenes and generate more than 8K high-quality, evenly distributed question-answer pairs to effectively benchmark model performance. To further enhance reasoning, we propose AVST-Zero, a reinforcement learning-based model that avoids intermediate supervision, directly optimizing behavior via carefully designed multi-dimensional rewards. Extensive experiments validate the effectiveness of our R-AVST in advancing audio-visual spatio-temporal reasoning, upon which AVST-Zero demonstrates competitive performance compared to existing models. To the best of our knowledge, R-AVST is the first dataset designed for real-world audio-visual spatio-temporal reasoning, and AVST-Zero offers a novel perspective for tackling future challenges in this domain.

cs.CV↗

arXiv2025

Conditional Chemical Language Models are Versatile Tools in Drug Discovery

Generative chemical language models (CLMs) have demonstrated strong capabilities in molecular design, yet their impact in drug discovery remains limited by the absence of reliable reward signals and the lack of interpretability in their outputs. We present SAFE-T, a generalist chemical modeling framework that conditions on biological context -- such as protein targets or mechanisms of action -- to prioritize and design molecules without relying on structural information or engineered scoring functions. SAFE-T models the conditional likelihood of fragment-based molecular sequences given a biological prompt, enabling principled scoring of molecules across tasks such as virtual screening, drug-target interaction prediction, and activity cliff detection. Moreover, it supports goal-directed generation by sampling from this learned distribution, aligning molecular design with biological objectives. In comprehensive zero-shot evaluations across predictive (LIT-PCBA, DAVIS, KIBA, ACNet) and generative (DRUG, PMO) benchmarks, SAFE-T consistently achieves performance comparable to or better than existing approaches while being significantly faster. Fragment-level attribution further reveals that SAFE-T captures known structure-activity relationships, supporting interpretable and biologically grounded design. Together with its computational efficiency, these results demonstrate that conditional generative CLMs can unify scoring and generation to accelerate early-stage drug discovery.

cs.LG↗

arXiv2025

Energy Conservation and Vanishing Viscosity Limit for the Primitive Equations

In this paper, we consider the problem of energy conservation for weak solutions of the inviscid Primitive Equations (PE) in a bounded domain. Based on the work [Bardos et al., Onsager's conjecture with physical boundaries and an application to the vanishing viscosity limit, Comm. Math. Phys., 2019, 291-310], we prove the energy conservation for PE with boundary condition under suitable Onsager-type assumptions. But due to the special structure of PE system and its domain, some new challenging difficulties arise: the lack of information about the vertical velocity, and existing corner points in the domain. We introduce some new ideas to overcome the above obstacles. As a byproduct, we give a sufficient condition for absence of anomalous energy dissipation in the vanishing viscosity limit.

math.AP↗

arXiv2025

The Kramers-Fokker-Planck equation with a decaying potential in $\mathbb R^n$, $n \ge 4$

We use methods from microlocal analysis and quantum scattering to study spectral properties near the threshold zero of the Kramers-Fokker-Planck operator with a decaying potential in $\mathbb R^n$, $n \ge 4$, and deduce the large-time behavior of solutions to the kinetic Kramers-Fokker-Planck equation. For short-range potentials, we establish an optimal time-decay estimate in weighted $L^2$-spaces when $ n\ge 5$ is odd. For potentials decaying like $O(|x|^{-\rho})$ for some $\rho > n-1$, we obtain, for all dimensions $n \ge 4$, a large-time expansion of the solution with the leading term given by the Maxwell-Boltzmann distribution multiplied by the factor $(4\pi t)^{-\frac n 2}$ corresponding to the decay for the heat equation. These results complete those obtained in [16, 22] for dimensions $n=1$ and $3$. The same questions for $n=2$ are still open.

math.AP↗

arXiv2024

Early turbulence in viscoelastic flow past a periodic cylinder array

Early turbulence in periodic cylinder arrays is of particular interest in many practical applications to enhance mixing and material/heat exchange. In this study, we reveal a new early transition pathway to a chaotic wavy state and drag enhancement with the addition of polymers. Using 2D direct numerical simulations with sufficiently small polymer diffusion ($\epsilon=10^{-5}$), we show that viscoelastic flow past periodic cylinder arrays become unstable at a Reynolds number $Re\approx 10$, significantly lower than the Newtonian counterpart of $Re\approx 150-200$. The chaotic wavy state which ensues exhibits sheets and `arrowhead' polymer conformation structures, consistent with the saturated centre-mode instability observed in wall-bounded parallel flows (Page et al., Phys. Rev. Lett., 125, 154501, 2020). Analysis of the kinetic energy budget reveals the purely elastic origin of the chaos. However, inertial forces, in conjunction with elastic forces, can reshape the base state, affecting the formation of an invariant polymer sheet. This sheet facilitates the stretching and recoiling of polymers, which in turn induces flow fluctuations and maintains the chaos. Exploring various maximum polymer extensions $b$, and polymer concentrations $\beta$ highlights the role of elastic forces in stretching the upstream separation zone while suppressing the downstream separation zone, resulting in drag enhancement at finite $Re$. Surprisingly, these modifications to the base state can suppress the invariant polymer sheet under large elastic forces (large $b$ or small $\beta$), thereby achieving a stable polymer-modified laminar state.

physics.flu-dyn↗

arXiv2023

Physics-informed neural network to augment experimental data: an application to stratified flows

We develop a physics-informed neural network (PINN) to significantly augment state-of-the-art experimental data and apply it to stratified flows. The PINN is a fully-connected deep neural network fed with time-resolved, three-component velocity fields and density fields measured simultaneously in three dimensions at $Re = O(10^3)$ in a stratified inclined duct experiment. The PINN enforces incompressibility, the governing equations for momentum and buoyancy, and the boundary conditions by automatic differentiation. The physics-constrained, augmented data are output at an increased spatio-temporal resolution and demonstrate five key results: (i) the elimination of measurement noise; (ii) the correction of distortion caused by the scanning measurement technique; (iii) the identification of weak but dynamically important three-dimensional vortices; (iv) the revision of turbulent energy budgets and mixing efficiency; and (v) the prediction of the latent pressure field and its role in the observed Holmboe wave dynamics. These results mark a significant step forward in furthering the reach of experiments, especially in the context of turbulence, where accurately computing three-dimensional gradients and resolving small scales remain enduring challenges.

physics.flu-dyn↗

arXiv2023

Geometry of stratified turbulent mixing: local alignment of the density gradient with rotation, shear and viscous dissipation

We introduce a geometric analysis of turbulent mixing in density-stratified flows based on the alignment of the density gradient in two orthogonal bases that are locally constructed from the velocity gradient tensor. The first basis connects diapycnal mixing to rotation and shearing motions, building on the recent 'rortex-shear decomposition' in stratified shear layers (Jiang et al., J. Fluid Mech. 947, A30, 2022), while the second basis connects mixing to the principal axes of the viscous dissipation tensor. Applying this framework to datasets taken in the stratified inclined duct laboratory experiment reveals that density gradients in locations of high shear tend to align preferentially (i) along the direction of minimum dissipation and (ii) normal to the plane spanned by the rotex and shear vectors. The analysis of the local alignment across increasingly turbulent flows offers new insights into the intricate relationship between the density gradient and dissipation, and thus diapycnal mixing.

physics.flu-dyn↗

arXiv2023

Long-wave instabilities of sloping stratified exchange flows

We investigate the linear instability of two-layer stratified shear flows in a sloping two-dimensional channel, subject to non-zero longitudinal gravitational forces. We reveal three previously unknown instabilities, distinct from the well-known Kelvin-Helmholtz Instability (KHI) and Holmboe Wave Instability (HWI), in that they have longer wavelengths (of the order of 10 to $10^3$ shear-layer depths) and often slower growth rates. Importantly, they can grow in background flows with gradient Richardson number $\gg 1$, which offers a new mechanism to sustain turbulence and mixing in strongly stratified flows. These instabilities are shown to be generic and relatively insensitive to Reynolds number $\mathrm{Re}$, Prandtl number $\mathrm{Pr}$, base flow profile, and boundary conditions. The nonlinear evolution of these instabilities is investigated through a forced direct numerical simulation, in which the background momentum and density are sustained. The growth of long unstable waves in background flows initially stable to short wave instabilities causes a decrease in the local gradient Richardson number. This leads to local nonlinear processes that result in small-scale overturns resembling Kelvin-Helmholtz billows. Our results establish a new energy exchange pathway, where the mean kinetic energy of a strongly stratified flow is extracted by primary unstable long waves and secondary short waves, and subsequently dissipated into internal energy.

physics.flu-dyn↗

arXiv2023

Stratified inclined duct: two-layer hydraulics and instabilities

The stratified inclined duct (SID) sustains an exchange flow in a long, gently sloping duct as a model for continuously-forced density-stratified flows such as those found in estuaries. Experiments have shown that the emergence of interfacial waves and their transition to turbulence as the tilt angle is increased appears linked to a threshold in the exchange flow rate given by inviscid two-layer hydraulics. We uncover these hydraulic mechanisms with (i) recent direct numerical simulations (DNS) providing full flow data in the key flow regimes (Zhu & Atoufi et al., arXiv:2301.09773, 2023), (ii) averaging these DNS into two layers, (iii) an inviscid two-layer shallow water and instability theory to diagnose interfacial wave behaviour and provide physical insight. The laminar flow is subcritical and stable throughout the duct and hydraulically controlled at the ends of the duct. As the tilt is increased, the flow becomes everywhere supercritical and unstable to long waves. An internal undular jump featuring stationary waves first appears near the centre of the duct, then leads to larger-amplitude travelling waves, and to stronger jumps, wave breaking and intermittent turbulence at the largest tilt angle. Long waves described by the (nonlinear) shallow water equation are locally interpreted as linear waves on a two-layer parallel base flow described by the Taylor-Goldstein equation. This link helps us interpret long-wave instability and contrast it to short-wave (e.g. Kelvin-Helmholtz) instability. Our results suggest a transition to turbulence in SID through long-wave instability relying on vertical confinement by the top and bottom walls.

physics.flu-dyn↗

arXiv2023

Stratified inclined duct: direct numerical simulations

The stratified inclined duct (SID) experiment consists of a zero-net-volume exchange flow in a long tilted rectangular duct, which allows the study of realistic stratified shear flows with sustained internal forcing. We present the first three-dimensional direct numerical simulations (DNS) of SID to explore the transitions between increasingly turbulent flow regimes first described by Meyer \& Linden (\textit{J. Fluid Mech.} \textbf{753}, 242-253, 2014). We develop a numerical set-up that faithfully reproduces the experiments and sustains the flow for arbitrarily long times at minimal computational cost. We recover the four qualitative flow regimes found experimentally in the same regions of parameter space: laminar flow, waves, intermittent turbulence, and fully-developed turbulence. We find good qualitative and quantitative agreement between DNS and experiments and highlight the added value of DNS to complement experimental diagnostics and increase our understanding of the transition to turbulence, both temporally (laminar/turbulent cycles) and parametrically (as the tilt angle of the duct and the Reynolds number are increased). These results demonstrate that numerical studies of SID -- and deeper integration between simulations and experiments -- have the potential to lead to a better understanding of stratified turbulence in environmental flows.

physics.flu-dyn↗

arXiv2022

Direct transition to elastoinertial turbulence from a linear instability in channel flow

For decades, transition to turbulence in viscoelastic parallel shear flows was believed to require nonlinear instabilities. We provide numerical evidences for a new wall-mode linear instability that directly triggers the transition to elastoinertial turbulence in channel flow. The instability is 2D but 3D features become important as nonlinear effects grow. With larger disturbances, direct transition to nonlinear instabilities, leading to turbulent states of both inertial and elastoinertial natures, are observed.

physics.flu-dyn↗

arXiv2021

Global-in-time L p -- L q estimates for solutions of the Kramers-Fokker-Planck equation

In this work, we prove an optimal global-in-time L p --L q estimate for solutions to the Kramers-Fokker-Planck equation with short range potential in dimension three. Our result shows that the decay rate as t $\rightarrow$ +$\infty$ is the same as the heat equation in x-variables and the divergence rate as t $\rightarrow$ 0 + is related to the sub-ellipticity with loss of 1/3 derivatives of the Kramers-Fokker-Planck operator.

math.AP↗