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Bo Zhu

Publications and source records attributed to Bo Zhu.

At least 19 recordsLinked to original sources
arXiv2026

Recursive Code World Models: Building Complex Worlds through Recursive Scene Programs

Code world models represent worlds as executable programs, but this representation alone does not determine how to construct a complex world. We introduce Recursive Code World Models (RCWM), a framework for reconstructing complex 3D worlds in code from a single reference image. RCWM couples a Recursive Scene Program (RSP) representation with a construction solver that recursively calls itself. An RSP represents the executable world as compositional scene code, while each solver call follows the same complete process: establish the whole, recursively reconstruct unresolved parts, and revisit the whole to refine their composition. This global-local-global recursion gives fine-scale structures their own perception-and-editing loops while preserving scene-wide geometry and relationships. Reference-aligned views propagate a shared camera projection across levels, while parent revisitation addresses boundaries, spatial relations, and shared errors that emerge after local refinement. A vision-language coding agent directly compares reference images with scene renders to guide refinement, recursive descent, and return. Across complex scenes, RCWM outperforms prior code-based image-to-scene reconstruction methods. Ablation studies further support the benefits of recursive construction and suggest that deeper calls can improve finer-scale reconstruction. RCWM provides a recursive construction principle for building complex executable worlds from visual evidence.

cs.CV↗
arXiv2026

Hamiltonian Two-Way Coupling of Nonlinear Waves and 3D Flows

Simulating large-scale free-surface water by coupling a localized 3D fluid solver to a cheaper 2D surface model has long faced a mismatch in wave dynamics: efficient 2D wave models used in graphics are typically either linear or non-dispersive. These models are fast, simple, and accurate for calm, small-amplitude seas, but coupling them with strongly nonlinear 3D solvers produces visible reflections and artifacts at the 2D--3D interface. We address this problem by introducing a nonlinear and dispersive 2D wave model based on the canonical Zakharov formulation. Its Hamiltonian structure, in which the surface elevation and surface potential form a canonical pair ($\eta$, $\psi$) governed by the wave energy, enables a canonically consistent two-way coupling scheme, allowing information to pass smoothly across the 2D--3D interface. Our 2D solver reduces mean wave-height error by 1.7--5$\times$ over SWE, BEM, and Airy baselines while running more than $10^3\times$ faster than BEM; it achieves greater nonlinear accuracy and coupling fidelity than SWE and Airy, with minor losses in speed and stability. Coupling it with a 3D Navier--Stokes solver yields a full system that suppresses visible seam artifacts across a range of experiments, including dispersion-matching and Kelvin-wake tests, and runs over 4$\times$ faster than a pure GPU NB-FLIP simulation on the same domain.

cs.GR↗
arXiv2026

Simplicial Volume and Scalar Curvature on Closed K\"ahler Surfaces

Let $M$ be a closed K\"ahler surface. We prove that every Riemannian metric $g$ on $M$ with $\operatorname{Sc}_g\geq-\lambda^2$, where $\lambda\geq 0$, satisfies $$ \lVert M\rVert\leq \frac{27}{2}\,\lambda^4\operatorname{vol}_g(M). $$ This proves Gromov's quantitative scalar-curvature--simplicial-volume conjecture for closed K\"ahler surfaces. We also construct infinitely many non-K\"ahler symplectic 4-manifolds of general type with positive simplicial volume for which the same estimate holds.

math.DG↗
arXiv2026

McKean Rigidity for Cocompact Negatively Curved Manifolds and the \(p\)-Laplacian

Let \((M^m,g)\) be a closed Riemannian manifold with \(\sec_g\leq-1\). We prove that the bottom spectrum of its universal cover attains McKean's lower bound if and only if the universal cover is hyperbolic space of constant sectional curvature \(-1\). More generally, for every \(1<p<\infty\), the variational \(p\)-fundamental tone satisfies \[ \lambda_{1,p}(\wti M) \geq\left(\frac{m-1}{p}\right)^p, \] and equality for some \(p\in(1,\infty)\) holds if and only if \(\wti M\cong\bH^m(-1)\). In that case, equality holds for every \(p\in(1,\infty)\). The proof converts the two McKean defects of a minimizing sequence into a stationary probability measure on the compact horospherical suspension; heat-kernel positivity then forces its zero-defect support to contain a complete leaf.

math.DG↗
arXiv2026

Flow-Map GRPO: Reinforcement Learning for Few-Step Flow-Map Generators via Anchored Stochastic Composition

Few-step flow-map generators, such as consistency models and MeanFlow, accelerate sampling by directly learning long-range transport maps between noise and data. However, these models are typically deterministic, which makes them difficult to optimize with reinforcement learning (RL) post-training methods that require stochastic trajectories and well-defined likelihood ratios. Existing SDE-based stochasticization techniques are designed for velocity-based samplers with infinitesimal or finely discretized transitions, and therefore do not directly apply to long-range flow maps. In this work, we propose Flow-Map GRPO, an online RL post-training framework for deterministic few-step flow-map generators. The key component is Anchored Stochastic Flow Map Composition (ASFMC), a path-preserving stochasticization mechanism that introduces randomness through anchor-based conditional resampling while preserving the original marginal probability path of the deterministic flow map. We derive GRPO objectives for both single-time and two-time flow-map parameterizations. Experiments on few-step FLUX-based text-to-image generators, including MeanFlow and sCM, show that Flow-Map GRPO improves pretrained deterministic flow-map models across reward-based, perceptual, and task-level evaluation metrics. Our results demonstrate that deterministic few-step flow-map generators can be effectively aligned with RL post-training without modifying their original model parameterization or retraining them as native stochastic models.

cs.LG↗
arXiv2026

Gromov's Simplicial Volume Vanishing Conjecture for Positive Scalar Curvature

In this paper, we prove Gromov's simplicial volume vanishing conjecture for closed manifolds with spin universal cover. More precisely, we show that if a closed oriented manifold admits a metric of nonnegative scalar curvature and its universal cover is spin, then its simplicial volume vanishes. In particular, a closed oriented aspherical manifold with nonzero simplicial volume admits no metric of nonnegative scalar curvature.

math.DG↗
arXiv2026

Scalar curvature, sharp bottom spectrum and geometric rigidity

We prove rigidity in the equality case of the sharp bottom spectrum estimate under scalar curvature lower bound. Under the same topological assumptions as in our previous work, a closed manifold $(M,g)$ with $\mathrm{Sc}_g\geq -n(n-1)$ and $\lambda_1(\widetilde M,\widetilde g)=(n-1)^2/4$ must be hyperbolic. This gives rigidity results for closed hyperbolic manifolds and for closed manifolds admitting a metric of nonpositive sectional curvature.

math.DG↗
arXiv2026

Hermite-NGP: Gradient-Augmented Hash Encoding for Learning PDEs

We propose Hermite-NGP, a gradient-augmented multi-resolution hash encoding designed to enable fast and accurate computation of spatial derivatives for neural PDE solvers. Unlike existing NGP-based approaches that rely on automatic differentiation or finite differences and suffer from instability or high cost, Hermite-NGP explicitly stores function values and mixed partial derivatives at hash grid vertices, allowing fully analytic evaluation of gradients, Jacobians, and Hessians via Hermite interpolation. This design preserves the efficiency and spatial adaptivity of NGP while supporting analytic differential operators up to second order. We further introduce a multi-resolution curriculum training strategy analogous to multigrid V-cycles to enable coarse-to-fine optimization. Across a range of 2D and 3D PDE benchmarks, Hermite-NGP achieves up to approximately 20 times lower error than prior neural PDE methods, and reduces wall-clock convergence time by 2 to 10 times compared to other solvers, with per-epoch training times as low as 3.5 ms for models with up to 17M parameters.

cs.LG↗
arXiv2026

A Few-Step Generative Model on Cumulative Flow Maps

We propose a unified, few-step generative modeling framework based on \emph{cumulative flow maps} for long-range transport in probability space, inspired by flow-map techniques for physical transport and dynamics. At its core is a cumulative-flow abstraction that connects local, instantaneous updates with finite-time transport, enabling generative models to reason about global state transitions. This perspective yields a unified few-step framework built on cumulative transport and \revise{cumulative} parameterization that applies broadly to existing diffusion- and flow-based models without being tied to a specific prediction \revise{instantiation}. Our formulation supports few-step and even one-step generation while preserving synthesis quality, requiring only minimal changes to time embeddings and training objectives, and no increase in model capacity. We demonstrate its effectiveness across diverse tasks, including image generation, geometric distribution modeling, joint prediction, and SDF generation, with reduced inference cost.

cs.LG↗
arXiv2026

Generative Modeling with Orbit-Space Particle Flow Matching

We present Orbit-Space Geometric Probability Paths (OGPP), a particle-native flow-matching framework for generative modeling of particle systems. OGPP is motivated by two insights: (i) particles are defined up to permutation symmetries, so anonymous indexing inflates per-index target variance and yields curved, hard-to-learn flows; and (ii) particles live in physical space, so the flow terminal velocity has physical meaning and can encode geometric attributes, e.g., surface normals. OGPP instantiates three key components: (1) orbit-space canonicalization of the probability-path terminal endpoint, (2) particle index embeddings for role specialization, and (3) geometric probability paths with arc-length-aware terminal velocities that generate normals as a byproduct of the flow. We evaluate OGPP on minimal-surface benchmarks, where it reduces metric error by up to two orders of magnitude in a single inference step; on ShapeNet, where it matches the state of the art with 5x fewer steps and reaches airplane EMD comparable to DiT-3D with 26x fewer parameters and 5x fewer steps; and on single-shape encoding, where it produces normals and reconstructions competitive with 6D generators while operating entirely in 3D.

cs.GR↗
arXiv2026

Matrix-Free Multigrid with Algebraically Consistent Coarsening on Adaptive Octrees

We present a matrix-free GPU multigrid preconditioner with algebraically consistent coarsening for solving Poisson equations on adaptive octree grids with irregular domains. Within uniform-resolution regions, the coarsening satisfies the Galerkin principle. At T-junctions between refinement levels, we propose a flux-consistent coarse-grid correction that restores cross-level consistency while preserving the compact matrix-free representation. The coarse operators are stored in a compact matrix-free form suitable for parallel execution on GPUs. Numerical experiments demonstrate second-order accuracy, grid-independent convergence when used with PCG, and robust performance on cut-cell problems arising in fluid simulation. On a single NVIDIA RTX 4090 GPU, the solver achieves full-solve throughputs above 200 million cells per second on analytical Poisson tests and above 70 million cells per second on pressure projection problems in fluid simulation.

math.NA↗
arXiv2026

Free-Range Gaussians: Non-Grid-Aligned Generative 3D Gaussian Reconstruction

We present Free-Range Gaussians, a multi-view reconstruction method that predicts non-pixel, non-voxel-aligned 3D Gaussians from as few as four images. This is done through flow matching over Gaussian parameters. Our generative formulation of reconstruction allows the model to be supervised with non-grid-aligned 3D data, and enables it to synthesize plausible content in unobserved regions. Thus, it improves on prior methods that produce highly redundant grid-aligned Gaussians, and suffer from holes or blurry conditional means in unobserved regions. To handle the number of Gaussians needed for high-quality results, we introduce a hierarchical patching scheme to group spatially related Gaussians into joint transformer tokens, halving the sequence length while preserving structure. We further propose a timestep-weighted rendering loss during training, and photometric gradient guidance and classifier-free guidance at inference to improve fidelity. Experiments on Objaverse and Google Scanned Objects show consistent improvements over pixel and voxel-aligned methods while using significantly fewer Gaussians, with large gains when input views leave parts of the object unobserved.

cs.CV↗
arXiv2026

A Self-Rotating Tri-Rotor UAV for Field of View Expansion and Autonomous Flight

Unmanned Aerial Vehicles (UAVs) perception relies on onboard sensors like cameras and LiDAR, which are limited by the narrow field of view (FoV). We present Self-Perception INertial Navigation Enabled Rotorcraft (SPINNER), a self-rotating tri-rotor UAV for the FoV expansion and autonomous flight. Without adding extra sensors or energy consumption, SPINNER significantly expands the FoV of onboard camera and LiDAR sensors through continuous spin motion, thereby enhancing environmental perception efficiency. SPINNER achieves full 3-dimensional position and roll--pitch attitude control using only three brushless motors, while adjusting the rotation speed via anti-torque plates design. To address the strong coupling, severe nonlinearity, and complex disturbances induced by spinning flight, we develop a disturbance compensation control framework that combines nonlinear model predictive control (MPC) with incremental nonlinear dynamic inversion. Experimental results demonstrate that SPINNER maintains robust flight under wind disturbances up to 4.8 \,m/s and achieves high-precision trajectory tracking at a maximum speed of 2.0\,m/s. Moreover, tests in parking garages and forests show that the rotational perception mechanism substantially improves FoV coverage and enhances perception capability of SPINNER.

cs.RO↗
arXiv2026

A Long-Short Flow-Map Perspective for Drifting Models

This paper provides a reinterpretation of the Drifting Model~\cite{deng2026generative} through a semigroup-consistent long-short flow-map factorization. We show that a global transport process can be decomposed into a long-horizon flow map followed by a short-time terminal flow map admitting a closed-form optimal velocity representation, and that taking the terminal interval length to zero recovers exactly the drifting field together with a conservative impulse term required for flow-map consistency. Based on this perspective, we propose a new likelihood learning formulation that aligns the long-short flow-map decomposition with density evolution under transport. We validate the framework through both theoretical analysis and empirical evaluations on benchmark tests, and further provide a theoretical interpretation of the feature-space optimization while highlighting several open problems for future study.

cs.LG↗
arXiv2026

SurfPhase: 3D Interfacial Dynamics in Two-Phase Flows from Sparse Videos

Interfacial dynamics in two-phase flows govern momentum, heat, and mass transfer, yet remain difficult to measure experimentally. Classical techniques face intrinsic limitations near moving interfaces, while existing neural rendering methods target single-phase flows with diffuse boundaries and cannot handle sharp, deformable liquid-vapor interfaces. We propose SurfPhase, a novel model for reconstructing 3D interfacial dynamics from sparse camera views. Our approach integrates dynamic Gaussian surfels with a signed distance function formulation for geometric consistency, and leverages a video diffusion model to synthesize novel-view videos to refine reconstruction from sparse observations. We evaluate on a new dataset of high-speed pool boiling videos, demonstrating high-quality view synthesis and velocity estimation from only two camera views. Project website: https://yuegao.me/SurfPhase.

cs.CV↗
arXiv2026

An Impulse-formed Navier-Stokes Solver based on Long-range Particle Flow Maps

We present a particle-grid characteristic-mapping framework that extends long-range characteristic mapping from inviscid flows to general Navier-Stokes dynamics with viscosity, body forces, and complex boundaries. Unlike traditional grid-based and vorticity-centered characteristic methods, our method is built on the observation that particle trajectories naturally provide the long-range flow map, enabling geometric quantities and their gradients to be transported in a direct and effective manner. We identify the impulse, the gauge variable of the velocity field, as the primary quantity mapped along characteristics while remaining compatible with standard velocity-based incompressible solvers. Using the 1-form representation of the impulse equation, we derive an integral formulation that decomposes the impulse evolution into a component transported geometrically along the particle flow map and a complementary component generated by viscosity and body forces evaluated through path integrals accumulated along particle trajectories. These components together yield a unified characteristic-mapping solver capable of handling incompressible Navier-Stokes flows with viscosity and body forces while maintaining the accuracy and geometric fidelity of characteristic transport.

cs.CE↗
arXiv2026

Trajectory Consistency for One-Step Generation on Euler Mean Flows

We propose \emph{Euler Mean Flows (EMF)}, a flow-based generative framework for one-step and few-step generation that enforces long-range trajectory consistency with minimal sampling cost. The key idea of EMF is to replace the trajectory consistency constraint, which is difficult to supervise and optimize over long time scales, with a principled linear surrogate that enables direct data supervision for long-horizon flow-map compositions. We derive this approximation from the semigroup formulation of flow-based models and show that, under mild regularity assumptions, it faithfully approximates the original consistency objective while being substantially easier to optimize. This formulation leads to a unified, JVP-free training framework that supports both $u$-prediction and $x_1$-prediction variants, avoiding explicit Jacobian computations and significantly reducing memory and computational overhead. Experiments on image synthesis, particle-based geometry generation, and functional generation demonstrate improved optimization stability and sample quality under fixed sampling budgets, together with approximately $50\%$ reductions in training time and memory consumption compared to existing one-step methods for image generation.

cs.LG↗