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arXiv2026

Analysis of Moment Closures Using $φ$-Divergences for Rarefied Dynamics with Binary Collisions and Their Galerkin Discretizations

This work introduces a robust deterministic framework for approximating solutions of the Boltzmann equation with binary collisions by discretizing their dependence on time, position, and velocity using Galerkin methods. By employing a family of parametric Galerkin closures based on $φ$-divergences in velocity space, we derive rigorous hierarchies of moment equations that govern fluid dynamic variables. Addressing the limitation that these closures alone do not guarantee dissipation of a $φ$-divergence entropy for the true binary collision operator, we restore this property by formulating a compatible approximate collision operator tailored to each closure. This constructed operator intrinsically retains fundamental physical properties essential for high-fidelity flow simulations, including Galilean invariance, exact conservation of mass, momentum, and energy, and strict dissipation of a $φ$-divergence entropy. Furthermore, we show that the resulting closed moment systems are symmetric-dissipative, yielding Cauchy problems that are well-posed locally in time. To translate this mathematical foundation into an efficient computational tool, we discretize the position and time variables with an entropy-stable discontinuous Galerkin (DG) finite element method. The fully implicit, entropy-stable space-time approach enables time steps far beyond typical CFL-limited step sizes and the direct computation of steady states. The robustness and accuracy of the methodology are verified and validated through numerical simulations on the supersonic nozzle flow of argon, mass flow through a channel, and heat transfer between parallel walls, demonstrating agreement with analytical benchmarks, experimental measurements, and stochastic particle simulations.

math.NA↗
arXiv2026

Efficient Adaptation of ROMs for Unsteady Flows Using Data Assimilation

We propose an efficient retraining strategy for a parameterized Reduced Order Model (ROM) that attains accuracy comparable to full retraining while requiring only a fraction of the computational time and relying solely on sparse observations of the full system. The architecture employs an encode-process-decode structure: a Variational Autoencoder (VAE) to perform dimensionality reduction, and a transformer network to evolve the latent states and model the dynamics. The ROM is parameterized by an external control variable, the Reynolds number in the Navier-Stokes setting, with the transformer exploiting attention mechanisms to capture both temporal dependencies and parameter effects. The probabilistic VAE enables stochastic sampling of trajectory ensembles, providing predictive means and uncertainty quantification through the first two moments. After initial training on a limited set of dynamical regimes, the model is adapted to out-of-sample parameter regions using only sparse data. Its probabilistic formulation naturally supports ensemble generation, which we employ within an ensemble Kalman filtering framework to assimilate data and reconstruct full-state trajectories from minimal observations. We further show that, for the dynamical system considered, the dominant source of error in out-of-sample forecasts stems from distortions of the latent manifold rather than changes in the latent dynamics. Consequently, retraining can be limited to the autoencoder, allowing for a lightweight, computationally efficient adaptation procedure with very sparse fine-tuning data.

cs.LG↗
arXiv2026

Direct Numerical Simulation of Thermoacoustically Unstable Flames Via Non-Drifting Acoustic Delay Characteristic Boundary Conditions

Thermoacoustic instability in premixed flames results from the coupling between the flame's heat release, as determined by combustion parameters, and surrounding acoustics, as determined by combustor geometry. A primary instability results in flame flattening as intrinsic flame instability modes are stabilised. Secondary thermoacoustic instability results in a parametric flame instability and drastic growth of acoustic amplitudes. Due to their relative expense, numerical simulations of these phenomena remain scarce. In this work, Direct Numerical Simulations (DNS) of thermoacoustically unstable idealised premixed flames in a tube with acoustically closed upstream and open downstream ends are presented. Results herein demonstrate nonlinear saturation of the primary instability as the flame flattens as well as an oscillating flame fingering characteristic of the unsteady Rayleigh-Taylor effect. To reduce computational cost, we perform DNS only on the region surrounding the flame. Acoustics at in- and outflows are described using the Navier-Stokes Characteristic Boundary Condition (NSCBC) method to model their delayed reentry into the domain in a formulation referred to as the Acoustic Delay Characteristic Boundary Condition (ADCBC) method. A new Averaged Proportional and Integral Linear Relaxation (APILR) method is also introduced, which modifies the Classic Linear Relaxation (CLR) method to maintain time-averaged values of inflow velocity and outflow pressure. Here, an integral control term is used to remove non-zero equilibrium time-averaged inflow velocities which impinge control over flame position. Both new methods demonstrate their capability in inert and counterflow flames test cases. These methods enable the numerical simulation of combustion instabilities at significantly reduced computational expense.

physics.flu-dyn↗
arXiv2026

Compositional Aeroelastic Operators for Morphing Flexible Multibody Aircraft: A Geometric Framework with Structural Verification

Morphing flexible multibody aircraft require structural strain, aerodynamic geometry, surface velocity, and generalized loading to remain compatible as joints and flexible components change configuration. A compositional formulation is developed around an assumed material attachment between each lifting surface and a geometrically exact beam. Separating the component root pose from the section field shows that the body strain and elastic potential of a component depend on its own elastic coordinates, while upstream motion enters kinetic terms and external-load pullbacks. At element level, an exact relative logarithm $d$ supplies strain and potential energy, whereas a reference-anchored section coordinate $σ$ supplies deformed section geometry. Finite-order expansions retain the finite reference geometry exactly and truncate only endpoint perturbations. The attachment map then generates surface points, tangents, normals, velocities, and force Jacobians from common section kinematics. Euler--Poincare beam balance, moving-surface potential-flow relations, graph cotangent assembly, and the associated semidiscrete power identity are stated in a common twist--wrench convention. Collocation, pressure, equivalent-load, and structural-station sites are distinguished to expose their approximation errors. Verification gives the expected $N_d+1$ convergence order for degree-$N_d$ relative-log expansions. In a geometrically nonlinear cantilever comparison, a cubic static-manifold correction reduces mean full-record displacement error from $0.479$ to $0.255$ over four completed load cases. These results provide structural and interface-level evidence rather than validation of a complete aircraft aeroelastic prediction.

cs.CE↗
arXiv2026

Moment-enhanced shallow-water equations with an effective wall closure for no-slip bottoms

Shallow-water equations and low-order shallow-water moment models use vertically coarse representations and therefore cannot, in general, resolve the thin wall-affected region produced by a no-slip bottom. Enforcing the pointwise wall value on a low-order global polynomial reconstruction can introduce stiff relaxation and distort the resolved interior velocity profile. Starting from the incompressible Navier--Stokes equations with Navier bottom friction, we derive a bottom-to-mean relation in a distinguished regular-friction regime and use it to define an endpoint-consistent effective wall-traction closure for the shallow-water equations and the hyperbolic shallow-water moment equations. The closure represents the momentum effect of unresolved near-wall dynamics; it neither resolves the physical boundary layer nor imposes the pointwise no-slip trace on the reconstructed polynomial. It recovers the perfect-slip wall contribution when the friction coefficient vanishes. Because only source terms are changed, the homogeneous principal matrices and their established two-dimensional hyperbolicity classification remain unchanged. We compare the standard and modified reduced models with two-phase incompressible Navier--Stokes computations in OpenFOAM for wet-bed dam-break and three-dimensional collapse tests. In the cases considered, the modified closure reduces the excessive damping of the classical low-order wall source and improves agreement in depth-averaged and resolved-interior velocity diagnostics, but it does not uniformly improve front-propagation speed. The regular-friction asymptotic remainder is not uniform in the large-friction numerical regime; there the effective coefficient is used as a wall-model continuation and assessed empirically.

math.NA↗
arXiv2026

Verification, Sensitivity, and Operating Limits of a GPU-Accelerated Planar WCSPH Model for Hydrodynamic Ram

Hydrodynamic ram (HRAM) loading remains a persistent challenge in impact mechanics, less due to exotic physics than to the difficulty of achieving convincing quantitative agreement in reduced-order representations. Prevailing studies typically employ a single mesh and boundary treatment validated against one experimental dataset, leaving unresolved whether agreement reflects genuine fidelity or compensating discretization errors. This work presents a planar 2D, GPU-accelerated WCSPH solver employing an Adami-type ghost-particle boundary condition, extended for the first time to a moving, decelerating disk penetrating a confined liquid channel at ballistic velocity. The boundary condition is examined against a purpose-derived potential-flow added-mass solution and the analytical acoustic reflection coefficient at the steel-water interface; this exploration reveals that the stiff equation of state and cavitation cutoff impose identifiable delineation of the solver's operating regime on quantitative agreement. A three-point resolution convergence study reveals a non-monotone near-probe pressure peak, attributed to a bounded ghost-fluid density inconsistency. A comprehensive coefficient sweep, conservation diagnostics, and O(N) GPU throughput scaling enable exhaustive characterization impractical in 3D. Qualitative comparison against literature evidence at 900 and 600m/s clarifies load bearing versus approximate elements. Notably, energy diagnostics reveal a modest total energy growth over the simulated window, with the fluid absorbing disproportionately more energy than the projectile relinquishes - an instructive signature of prescribed, non-back-reacting projectile kinematics that helps map the formulation's operating envelope. The resulting solver, while confined to planar geometry, delivers verified, convergence-checked performance well suited for rapid parametric design exploration.

cs.CE↗
arXiv2026

The Structure of Merging Turbulent Jets Beneath a Small Quadrotor

The downwash wake of a hovering quadrotor governs both the vehicle's own performance and the safe spacing of multi-rotor formations. Prior measurements have largely characterized the mean flow, using single-point anemometry, volumetric tracking, or planar cuts through part of the rotor system. Higher-order turbulent statistics of the merged wake, and how they relate to canonical jet scaling, have remained unresolved, particularly for small quadrotors at the low-Reynolds-number end of the size range. Here, we present a detailed particle image velocimetry (PIV) study of the downwash of a hovering Crazyflie 2.1 quadrotor (arm length, $l = 46$ mm), sampled along a diagonal cut, passing through rotors along the symmetry axis of the quadrotor, and a front-rotor cut, passing through adjacent rotors. The four rotor jets merge into a single column by $z/l \approx 5$, beyond which the mean velocity profiles progressively approach the canonical round-jet self-similar form, collapsing by $z/l \approx 13$ when scaled by the local centerline velocity and half-width. Centerline decay and half-width growth follow canonical scaling laws with an effective source diameter $D_\text{eff} = 2.29\,l$, effective Reynolds number $Re_{D_\text{eff}} = 3 \times 10^4$, at the low end of the range over which canonical jet scaling has been established, and spreading and decay constants nonetheless within the canonical round-jet range. Resolving both cuts shows that the turbulent normal stresses retain a bimodal, cut-dependent signature of the four-rotor source throughout the measurement domain.

physics.flu-dyn↗
arXiv2026

Real-Time Monitoring of MHD Liquid Metal Flows with Shallow Recurrent Decoders

State estimation in magnetohydrodynamic flows is critical for real-time monitoring of liquid metal blankets in tokamak fusion reactors. Due to the multiphysics nature of these phenomena, high-fidelity simulations are computationally prohibitive for real-time applications. This work investigates a data- driven Reduced Order Model framework: the Shallow Recurrent Decoder (SHRED) coupled with Principal Component Analysis, to map sparse temperature measurements to the full thermo-hydraulic system's state. The major contribution of this work lies in the two-parameter analysis of a fully three-dimensional domain representative of the DEMO breeding blanket configuration. Here, the flow is subjected to an external magnetic field varying in direction and intensity and is hindered by two cylinders acting as a water-cooling system, which impose a temperature boundary condition on their surfaces. This double-parametric magnetic variation induces nonlinear transitions in the flow dynamics, ranging from chaotic behavior at low magnetic field intensities to laminarized regimes at high intensities, characterized by the formation of asymmetric side layers at an inclination angle of 30 degrees. SHRED reconstruction maintains a mean relative error of approximately 5% for the temperature, pressure, and velocity fields. This accuracy is maintained across both weak and strong magnetic fields, ranging from 0.075 T to 0.300 T, and for inclination angles from 5 to 30 degrees, reflecting its dominant toroidal component. These errors are only slightly larger than the lower error bound dictated by low-rank truncation. The results establish SHRED as a reliable state estimator for complex and realistic engineering applications involving completely unseen parametric scenarios and validate it as an accurate real-time state estimation technique suitable for online monitoring and control of real facilities.

physics.comp-ph↗
arXiv2026

A high-order polynomial-corrected shifted boundary method for simulating fully nonlinear water waves

We present a novel unfitted computational framework for simulating fully nonlinear potential flow-based water waves. Focusing on wave propagation, we describe the core methodology, which involves a high-order polynomial-corrected shifted-boundary approximation on unfitted spectral elements. This approach allows for the simulation of a curved, highly time-dependent (moving and deforming) free surface affected by bathymetric changes. All that on a simple Cartesian background mesh without re-meshing or further approximations of non-affine geometric features. In addition, we highlight the importance of proper gradient recovery using a polynomial-preserving technique to accurately capture the vertical free-surface velocity. Ultimately, the goal is to develop a high-order convergent numerical scheme capable of simulating highly nonlinear waves over long periods. This is achieved through an arbitrary-order finite-difference approximation of the free surface combined with added hyperviscosity for numerical stability. We present verification and validation test cases for wave propagation in both periodic and finite domains. Emphasis is placed on convergence studies, the justification for using high-order approximations, the importance of optimal gradient recovery, long-time simulation of highly nonlinear waves, and nonlinear wave interactions with both affine and curved bathymetry changes, as well as with vertical walls, for highly nonlinear stream function waves and high-amplitude solitons. The novel computational model offers a comprehensive, all-in-one framework for simulating ocean waves and their interactions with offshore structures. It provides significant geometric flexibility, enabling boundaries such as the free surface to move and deform over time without the need to re-mesh a boundary-fitted mesh.

physics.flu-dyn↗
arXiv2026

Optimal control of a swimming robot based on Purcell's microswimmer model

Purcell's swimmer is a well-known planar model of a swimming microorganism, governed by low Reynolds number hydrodynamics, which is comprised of three rigid links connected by actuated rotary joints. This model has been analyzed as a robotic locomotion system governed by first-order nonlinear dynamics with a periodic input (gait) of the two joint angles. In this work, we present a robotic macro-scale realization of this three-link swimmer moving in a highly viscous fluid. We propose a simple variant of Purcell's theoretical model with non-slender links and a central rigid sphere which represents the added drag of the robot's central flotation block, and calibrate the model's parameters to fit experimental measurements. Next, we apply optimal control formulation based on Pontryagin's Maximum Principle (PMP) in order to find optimal gaits that maximize the displacement per cycle under bounds on the joint angles. Employing a differential geometric method that transforms the problem to area integral enclosed by the gait trajectory in the plane of joint angles, enables visual interpretation which explains topological changes in displacement-optimal gaits upon varying the bound on the joint angles. We then apply PMP formulation to the problem of maximizing Lighthill's energy efficiency in order to obtain a boundary value problem (BVP) whose solution gives efficiency-optimal gaits for Purcell's swimmer model, as well as its variant with a central sphere. Finally, we utilize numerical methods such as parameterizing the input gait as a truncated Fourier series, as well as GPOPS-II solver, to produce sufficient initial guess values for solving the BVPs and obtaining efficiency-optimal gaits.

physics.flu-dyn↗
arXiv2026

A priori Assessment of Tensor-Network Encoding for Isotropic Turbulent Flows

Tensor networks (TNs), originally developed for simulating many-body quantum systems, provide a systematic framework for approximating high-dimensional fields. This is achieved by factorizing the field into interconnected tensors with small bond dimensions, thereby restricting the correlations captured across field bipartitions. Belonging to the family of TNs, the matrix product state (MPS) ansatz is utilized here as a reduced-order modeling framework to construct truncated representations of isotropic turbulent flow data. Two direct numerical simulation (DNS) datasets are considered: the hydrodynamic field of an incompressible three-dimensional flow, and a conserved Fickian scalar in a similar flow. Each field is encoded as an MPS through a sequence of singular value decompositions (SVDs) in which small singular values are discarded. The truncated representation is contracted back to the full grid, and the resulting reconstructed field is compared against DNS. An interleaved ordering of the spatial tensor indices of the transport variables is applied prior to decomposition in order to localize the dominant inter-tensor correlations. Velocity reconstructions achieve $99.8\%$ fidelity using only $5\%$ of the original DNS memory, while the scalar field reaches the same fidelity at $15\%$ memory usage. A wide range of lower- and higher-order statistics, including velocity gradients, dissipation, and structure functions, are systematically examined. At these compression levels, the total kinetic energy and the scalar energy are both recovered within $0.2\%$ relative error, while the mean dissipation and mean scalar dissipation remain within approximately $10\%$ of the DNS generated values. These findings support the suitability of MPS for scalable reduced-order analysis of complex turbulent datasets and motivate further exploration of TN-based methods in computational turbulence.

physics.flu-dyn↗
arXiv2026

Dyn-3D: Unveiling and Resolving Ego-Motion Ambiguity in Vision-Language Models

As Vision-Language Models (VLMs) tackle dynamic 3D spatial reasoning, ego-motion perception becomes essential to resolve monocular scale ambiguity. However, current models often overfit to smooth trajectory priors rather than genuinely understanding physical motion. Consequently, their spatial reasoning degrades severely under large displacements, a phenomenon we term Kinematic Collapse. This failure stems from spurious visual-motion correlations in natural videos and a lack of explicit physical supervision. To evaluate this, we introduce Dyn-3D, a benchmark using counterfactual 3D rendering to rigorously decouple visual changes from true kinematic properties. Furthermore, we propose the TempoVista framework, featuring the Kinematic-GSPO algorithm. By embedding metric physical ground truth into policy optimization, TempoVista explicitly grounds visual representations in 3D space. Experiments demonstrate that our approach significantly improves both motion estimation and robust spatial reasoning by utilizing camera dynamics as an effective geometric calibration signal.

cs.CV↗
arXiv2026

DSG: Dynamic 3D Scene Graph Construction for Embodied Agents in Changing Indoor Environments

In indoor environments, object positions frequently change due to human activities or embodied-agent interactions, causing previously constructed scene graphs to become inconsistent with the current scene. To address this issue, we propose DSG, a dynamic 3D scene graph construction framework that detects object changes and performs spatial relationship reasoning. First, we construct a semantic-aware 3D Gaussian scene representation and develop a dual-view rendering-based object change detection method to enable reliable scene graph node updates. Second, we propose a spatial relationship reasoning method that incorporates multi-granularity visual context, enabling a large language model to identify a richer set of interobject spatial relationships. Furthermore, we introduce DynTHOR, a dynamic indoor scene graph benchmark built on the AI2-THOR simulation platform for evaluating scene graph construction in dynamic environments. Extensive experiments on Dyn-THOR, 3RScan, and real-world scenes demonstrate that DSG consistently outperforms existing methods in both object node construction and spatial relationship reasoning, significantly improving the accuracy of dynamic scene graph construction.

cs.RO↗
arXiv2026

Physical policy gradient theorem for in situ stochastic-adjoint training

In situ adjoint training extracts parameter gradients directly from measurement, but has so far been limited to reciprocal or restricted systems. Here, we introduce the physical counterpart of the policy gradient theorem: a stochastic-adjoint gradient estimator that lifts these constraints by trading reciprocity for nondegenerate diffusion. As validation, we train a nonlinear resonator network, whose own dynamics supply the policy, against antagonistic temporal modulations with gradients from measured stochastic trajectories alone, without finite differences or a separate adjoint experiment.

physics.optics↗
arXiv2026

Physically Plausible Video Generation via Visual-Semantic Chain-of-Events Conditioning

Physically Plausible Video Generation (PPVG) seeks to synthesize videos consistent with physical principles, yet remains challenging due to underspecified natural language conditioning. Advanced chain-of-thought (CoT) frameworks augment prompts with physical knowledge. However, such prompts describe physical phenomena holistically, overlooking intermediate states and transition dynamics. In this paper, we reformulate PPVG as event-centric generation by representing physical evolution as a chain of causally connected and physically constrained events. Our framework comprises three key modules: (1) Physics-driven Event Chain Reasoning. This module decomposes physical phenomena into causally connected events represented by evolving scene graphs. Formula-derived physical quantities are bound to relevant objects and interactions, characterizing the direction and magnitude of each event transition. (2) Transition-aware Routed Keyframe Conditioning. This module routes each event to a specialized keyframe synthesis operator for appearance variation or object transformation. Consecutive keyframes are injected as residual guidance during denoising, enabling smooth visual transitions between event-boundary states. (3) Physics-injected Contrastive Semantic Guidance. This module constructs physics-informed positive and counterfactual negative prompts for classifier-free guidance, steering generation toward plausible dynamics and away from physics-violating counterparts. Experiments on PhyGenBench, VideoPhy, PhyWorldBench, and Physics-IQ demonstrate that our framework generates videos with superior physical plausibility across diverse domains.

cs.CV↗
arXiv2026

Asymmetric Coupling Anisotropy for Causal Information Filtering in Physical Reservoirs

We demonstrate a physical mechanism for causal information filtering in a physical reservoir computing (PRC) by exploiting asymmetric coupling anisotropy. Using a network of coupled Duffing oscillators, we show that the directionality of internal coupling induces a spatial gradient in the effective potential, establishing a deterministic upstream-to-downstream information flow. This anisotropy allows for the selective amplification of semantic drifts, triggering a macroscopic saddle-node bifurcation as a physical interlock before global computational failure. Through spatiotemporal analysis of a 50-node system under traveling wave inputs, we confirm that local phase transitions effectively purge anomalous information while preserving the computational integrity of the remaining nodes. The results suggest that the intrinsic causality of the reservoir's topology provides a robust framework for autonomous reliability and fault-tolerant physical intelligence.

nlin.AO↗
arXiv2026

Physics-Guided Concentration Inference from Resistance Transients in a Mixed-Phase SnO-SnO$_2$ Carbon Monoxide Sensor with p-n Switching

This work presents a physics-guided machine-learning framework for carbon monoxide concentration inference from experimentally measured resistance transients of a mixed-phase SnO-SnO$_2$ material gas sensor exhibiting temperature-dependent p-n switching behavior. Cycle-level transient responses are represented through physically interpretable descriptors and complemented by compact fast Fourier transform (FFT) and discrete wavelet transform (DWT)-based summaries. Using leakage-aware grouped cross-validation, we study both multi-class concentration classification and continuous concentration regression for the p-type and n-type sensing regimes separately. Across both regimes, fused features provide the strongest overall performance, while the physics-guided descriptor block remains highly competitive, indicating that the dominant concentration information is already encoded in physically meaningful transient dynamics. The p-type branch shows the best concentration-class discrimination, with the fused Random Forest classifier reaching approximately $96.5\%$ accuracy, whereas the n-type branch yields the best quantitative concentration estimation, with the fused Random Forest regressor achieving an MAE$\approx 1.48$ ppm and an R$^2$ $\approx 0.992$. These results reveal a clear dual-regime behavior: p-type sensing is particularly favorable for classification, whereas n-type sensing is more favorable for high-fidelity regression. More broadly, the study demonstrates that leakage-aware, cycle-level, physics-guided machine learning can extend conventional gas-sensing analysis beyond single-response metrics while preserving physical interpretability

physics.chem-ph↗
arXiv2026

Do Tabular Foundation Models Know Physics? Contamination, Units, and the Deterministic Limit

Tabular foundation models (TFMs) learn to fill in tables the way language models fill in text, and tables are arguably the format in which most physical measurement arrives. Did they learn any physics in the process? They are Bayesian by construction, so the question is what their prior contains. We probe it directly, evaluating four of them (TabPFN-3, TabICLv2, TabDPT and Real-TabPFN-2.5) against six baselines on datasets sampled from 316 physical equations, in and out of domain. TFMs dominate, out of the box and after tuning. But we show that their prior can represent neither a noiseless mechanism nor physical units, which is why they interpolate physics without yet being able to act as physical models.

cs.LG↗