arXiv subjects

Nan Zheng

Publications and source records attributed to Nan Zheng.

At least 19 recordsLinked to original sources

arXiv2026

Risk-Aware World Modeling with Flow-Guided Occupancy Evolution for Selective Trajectory Planning in Automated Driving

Safe motion planning in automated driving requires anticipating evolving traffic risks and deciding when to revise the current planned trajectory. We introduce RiskWorld, a risk-aware world modeling framework for shared occupancy forecasting and selective trajectory replacement. Spatial risk fields and temporal actor context are fused with visual bird's-eye-view features. Flow-guided evolution transports occupancy and scene features, while signed residuals correct occupancy after transport. One forecast is generated per planning step and reused across candidates. Each candidate is compared with a current-state persistence reference, yielding a nonnegative collision-score correction. The trajectory selected by current-world evaluation serves as the planning anchor and is replaced only when additional predicted risk triggers intervention and an alternative satisfies component-wise constraints on predicted risk and trajectory error. Candidate geometries remain unchanged. We evaluate RiskWorld for open-loop planning on nuScenes using camera features, annotation-derived current and historical actor states, and dataset-provided map context. RiskWorld achieves the lowest collision rate at a long evaluation horizon of 3 s, and the second-best average L2 error among various state-of-the-art baselines, while running at 11.5 FPS on a single NVIDIA RTX 4090 with 90.81 M parameters. Within-setting ablations show that RiskWorld achieves lower collision rates than the current-state rescoring baseline, while forecast reuse enables additional candidates to be evaluated at low marginal computational cost.

cs.AI↗

arXiv2026

A unifying theory for the evaluation of conditional Akaike information for mixed-effects models

We propose two methods to evaluate the conditional Akaike information (cAI) for mixed-effects models with no restriction on cluster size. Method 1 is designed for continuous data and includes formulae for the derivatives of fixed and random effects estimators with respect to observations. Method 2, compatible with any type of observation, requires modeling the marginal (or prior) distribution of random effects as a multivariate normal distribution. Simulations show that Method 1 performs well with Gaussian data but struggles with skewed continuous distributions, whereas Method 2 consistently performs well across various distributions, including normal, gamma, negative binomial, and Tweedie, with flexible link functions. A case study demonstrates the differences in model selection for real-world data between the conventional AIC and the conditional AIC. Based on our findings, we recommend Method 2 as a distributionally robust cAI criterion for model selection in mixed-effects models.

stat.ME↗

arXiv2026

Implementing neural network mixed-effects models in Template Model Builder (TMB)

Neural network mixed-effects models (NMMs) have gained traction by combining the strong representation and predictive power of artificial neural networks with the capacity of mixed-effects modeling to capture complex correlation structures. However, existing estimation approaches rely heavily on manual derivations of objective functions and gradients, which inherently forces simplifying approximations and severely constrains the complexity and accuracy of NMMs. In this work, we introduce a general framework for implementing NMMs using Template Model Builder (TMB). By leveraging automatic differentiation and Laplace approximation, TMB requires users to specify only the negative joint log-likelihood and any regularization terms. The framework automatically integrates out random effects and evaluates the marginal objective function alongside its exact gradients, eliminating the need for manual derivations or ad hoc approximations. We demonstrate the efficiency, flexibility, and statistical performance of TMB-based NMMs across two numerical examples, including an application to monotonic NMMs. Reproducible code is provided to facilitate broader adoption.

stat.ML↗

arXiv2026

LeapBot-WA: World-Anchor Action Models via Predictive Latent Alignments

World Action Models (WAMs) have emerged as a powerful paradigm for embodied intelligence, yet the prevailing reliance on pixel-level video generation creates a fundamental bottleneck. Forcing models to reconstruct task-irrelevant visual details dissipates representational capacity and renders policies vulnerable to visual distractors. In this paper, we propose LeapBot-WA, which establishes a novel Predictive-Latent paradigm for WAMs by operationalizing the Joint-Embedding Predictive Architecture (JEPA) as a World-Anchor. Departing from the traditional reliance on visual synthesis, LeapBot-WA shifts the core of world modeling to Predictive Semantic Alignment, extracting abstract physical dynamics directly within a latent foundation space. To bridge the modality gap between non-Gaussian predictive features and diffusion priors, we introduce the Isotropic Semantic Autoencoder (ISAE), which reshapes the anchor's latent space into a diffusion-friendly manifold to prevent off-manifold drift. Furthermore, we design an Asymmetric Mixture-of-Transformers (MoT) architecture. During training, an Anchor Diffusion Transformer acts as a privileged dynamics expert to guide the Action Diffusion Transformer; at inference, this heavy dynamics branch is pruned, enabling zero-overhead execution. LeapBot-WA achieves state-of-the-art performance among predictive models on LIBERO and matches top-tier generative WAMs on RoboTwin 2.0 without requiring large-scale trajectory pre-training. It further demonstrates superior zero-shot robustness to unseen environments and successful real-world transfer, establishing a highly efficient and robust latent-centric paradigm for scalable robotic control. Code: https://github.com/LeapWM/leapbot-wa.

cs.RO↗

arXiv2026

A unified framework of fully decoupled, bound-preserving and energy-dissipative schemes for two-phase flow in porous media

Developing high-order numerical schemes for two-phase flow in porous media that preserve key physical properties remains a significant challenge in numerical analysis. In this article, we propose a general framework to construct fully discrete first- and second-order numerical schemes for thermodynamically consistent model of incompressible and immiscible two-phase flow in porous media. The proposed schemes are rigorously proved to ensure five fundamental properties: (i) unique solvability; (ii) full decoupling; (iii) bound preservation for both phases; (iv) original energy dissipation; (v) local mass conservation for both phases. The key to ensure the unique solvability lies in guaranteeing the strict convexity of the discrete energy functionals associated with the constructed schemes. Departing from the coupled solution approach for the pressure and saturation variables, the proposed approach breaks traditional paradigm by subtracting the two-phase mass conservation equations to derive a fully decoupled system. In addition, the bound-preserving property for both phases is established by leveraging the singular nature of the logarithmic term around the limit values of $0$ and $1$. A rigorous error estimate for the first-order scheme, in the $\ell^{\infty}(0,T; H_h^{-1} (Ω)) \cap \ell^{2}(0,T; \ell^2(Ω))$ norm for the saturations of two phases, is established. Finally, various numerical examples are presented to verify the theoretical results and demonstrate the efficiency of the proposed schemes.

math.NA↗

arXiv2026

EvolveSignal: A Large Language Model Powered Coding Agent for Discovering Traffic Signal Control Strategies

In traffic engineering, fixed-time traffic signal control remains widely used for its low cost, stability, and interpretability. However, its design relies on hand-crafted formulas (e.g., Webster) and manual re-timing by engineers to adapt to demand changes, which is labor-intensive and often yields suboptimal results under heterogeneous or congested conditions. This paper introduces EvolveSignal, an LLM-powered coding agent for automatically discovering interpretable heuristic strategies for fixed-time traffic signal control. Rather than deriving entirely new analytical formulations, the proposed framework focuses on exploring code-level variations of existing control logic and identifying effective combinations of heuristic modifications. We formulate the problem as program synthesis, where candidate strategies are represented as Python functions with fixed input-output structures and iteratively optimized through external evaluations (e.g., a traffic simulator) and evolutionary search. Experiments on a signalized intersection demonstrate that the discovered strategies outperform a classical baseline (Webster's method), reducing average delay by 20.1\% and average stops by 47.1\%. Beyond performance, ablation and incremental analyses reveal that EvolveSignal can identify meaningful modifications, such as adjusting cycle length bounds, incorporating right-turn demand, and rescaling green allocations, that provide useful insights for traffic engineers. This work highlights the potential of LLM-driven program synthesis for supporting interpretable and automated heuristic design in traffic signal control.

cs.LG↗

arXiv2026

Scalable Training of Mixture-of-Experts Models with Megatron Core

Scaling Mixture-of-Experts (MoE) training introduces systems challenges absent in dense models. Because each token activates only a subset of experts, this sparsity allows total parameters to grow much faster than per-token computation, creating coupled constraints across memory, communication, and computation. Optimizing one dimension often shifts pressure to another, demanding co-design across the full system stack. We address these challenges for MoE training through integrated optimizations spanning memory (fine-grained recomputation, offloading, etc.), communication (optimized dispatchers, overlapping, etc.), and computation (Grouped GEMM, fusions, CUDA Graphs, etc.). The framework also provides Parallel Folding for flexible multi-dimensional parallelism, low-precision training support for FP8 and NVFP4, and efficient long-context training. On NVIDIA GB300 and GB200, it achieves 1,233/1,048 TFLOPS/GPU for DeepSeek-V3-685B and 974/919 TFLOPS/GPU for Qwen3-235B. As a performant, scalable, and production-ready open-source solution, it has been used across academia and industry for training MoE models ranging from billions to trillions of parameters on clusters scaling up to thousands of GPUs. This report explains how these techniques work, their trade-offs, and their interactions at the systems level, providing practical guidance for scaling MoE models with Megatron Core.

cs.DC↗

arXiv2025

Unconditionally Stable, Variable Step DLN Methods for the Allen-Cahn Active Fluid Model: A Divergence-free Preserving Approach

This paper addresses the divergence-free mixed finite element method (FEM) for nonlinear fourth-order Allen-Cahn phase field coupled active fluid equations. By introducing an auxiliary variable $w = Δu$, the original fourth-order problem is converted into a system of second-order equations, thereby easing the regularity constraints imposed on standard $H^2$-comforming finite element spaces. To further refine the formulation, an additional auxiliary variable $ξ$, analogous to the pressure, is introduced, resulting in a mixed finite element scheme that preserves the divergence-free condition in $which = Δu$ inherited from the model. A fully discrete scheme is then established by combining the spatial approximation by the divergence-free mixed finite element method with the variable-step Dahlquist-Liniger-Nevanlinna (DLN) time integrator. The boundedness of the scheme is rigorously derived under suitable regularity assumptions. Additionally, an adaptive time-stepping strategy based on the minimum dissipation criterion is carried out to enhance computational efficiency. Several numerical experiments validate the theoretical findings and demonstrate the method's effectiveness and accuracy in simulating complex active fluid dynamics.

math.NA↗

arXiv2025

Enhancing Crash Frequency Modeling Based on Augmented Multi-Type Data by Hybrid VAE-Diffusion-Based Generative Neural Networks

Crash frequency modelling analyzes the impact of factors like traffic volume, road geometry, and environmental conditions on crash occurrences. Inaccurate predictions can distort our understanding of these factors, leading to misguided policies and wasted resources, which jeopardize traffic safety. A key challenge in crash frequency modelling is the prevalence of excessive zero observations, caused by underreporting, the low probability of crashes, and high data collection costs. These zero observations often reduce model accuracy and introduce bias, complicating safety decision making. While existing approaches, such as statistical methods, data aggregation, and resampling, attempt to address this issue, they either rely on restrictive assumptions or result in significant information loss, distorting crash data. To overcome these limitations, we propose a hybrid VAE-Diffusion neural network, designed to reduce zero observations and handle the complexities of multi-type tabular crash data (count, ordinal, nominal, and real-valued variables). We assess the synthetic data quality generated by this model through metrics like similarity, accuracy, diversity, and structural consistency, and compare its predictive performance against traditional statistical models. Our findings demonstrate that the hybrid VAE-Diffusion model outperforms baseline models across all metrics, offering a more effective approach to augmenting crash data and improving the accuracy of crash frequency predictions. This study highlights the potential of synthetic data to enhance traffic safety by improving crash frequency modelling and informing better policy decisions.

cs.AI↗

arXiv2025

A Divergence-free Preserving Mixed Finite Element Method for Thermally Driven Active Fluid Model

In this report, we propose a divergence-free preserving mixed finite element method (FEM) for the system of nonlinear fourth-order thermally driven active fluid equations. By introducing two auxiliary variables, we lower the complexity of the model and enhance the robustness of the algorithm. The auxiliary variable $w = Δu$ is used to convert the original fourth-order system to an equivalent system of second-order equations, thereby easing the regularity constraints imposed on standard $H^2$-conforming finite element space. The second variable $η$, analogous to the pressure, helps the scheme preserve the divergence-free condition arising from the model. The two-step Dahlquist-Liniger-Nevanlinna (DLN) time integrator, unconditionally non-linear stable and second-order accurate under non-uniform time grids, is combined with the mixed FEM for fully discrete approximation. Due to the fine properties of the DLN scheme, we prove the boundedness of model energy and the associated error estimates under suitable regularity assumptions and mild time restrictions. Additionally, an adaptive time-stepping strategy based on a minimum-dissipation criterion is to balance computational costs and time efficiency. Several numerical experiments validate the theoretical findings and demonstrate the method's effectiveness and accuracy in simulating complex active fluid dynamics.

math.NA↗

arXiv2025

Calibration and uncertainty quantification of macroscopic fundamental diagrams

Traffic congestion occurs as travel demand exceeds network capacity, necessitating a thorough understanding of network capacity for effective traffic control and management. The macroscopic fundamental diagram (MFD) provides an efficient framework for quantifying network capacity. However, empirical MFDs exhibit considerable data scatter and uncertainty. In this paper, we propose a mathematical program that simultaneously calibrates the MFD and quantifies the uncertainty associated with data scatter. We further investigate contributing factors of uncertainties regarding network capacity and traffic resilience. To be specific, we first include two conventional approaches for MFD calibration and uncertainty quantification as special cases. The proposed program is validated using empirical data from two cities in China. Subsequently, we identify how congestion loading and recovery contribute to data scatter. We develop a novel uncertainty quantification approach capable of capturing distinct congestion phases simultaneously. The gap between the upper and lower bounds of the calibrated MFDs, represented by a coefficient parameter, is regarded as the capacity drop induced by traffic congestion. Furthermore, the proposed approach enables further exploration of how macroscopic factors, such as travel demand and traffic control, and microscopic factors, such as driving behavior, influence MFD hysteresis, uncertainty, and traffic resilience. These findings shed light on developing efficient traffic control and demand management strategies to increase network capacity and resilience, while we count on future connected automated vehicular technologies to conquer the influence of various driving behaviors.

physics.soc-ph↗

arXiv2025

Mitigating Traffic Oscillations in Mixed Traffic Flow with Scalable Deep Koopman Predictive Control

Mitigating traffic oscillations in mixed flows of connected automated vehicles (CAVs) and human-driven vehicles (HDVs) is critical for enhancing traffic stability. A key challenge lies in modeling the nonlinear, heterogeneous behaviors of HDVs within computationally tractable predictive control frameworks. This study proposes an adaptive deep Koopman predictive control framework (AdapKoopPC) to address this issue. The framework features a novel deep Koopman network, AdapKoopnet, which represents complex HDV car-following dynamics as a linear system in a high-dimensional space by adaptively learning from naturalistic data. This learned linear representation is then embedded into a Model Predictive Control (MPC) scheme, enabling real-time, scalable, and optimal control of CAVs. We validate our framework using the HighD dataset and extensive numerical simulations. Results demonstrate that AdapKoopnet achieves superior trajectory prediction accuracy over baseline models. Furthermore, the complete AdapKoopPC controller significantly dampens traffic oscillations with lower computational cost, exhibiting strong performance even at low CAV penetration rates. The proposed framework offers a scalable and data-driven solution for enhancing stability in realistic mixed traffic environments. The code is made publicly available.

eess.SY↗

arXiv2025

Divergence-free Preserving Mix Finite Element Methods for Fourth-order Active Fluid Model

This paper is concerned with mixed finite element method (FEM) for solving the two-dimensional, nonlinear fourth-order active fluid equations. By introducing an auxiliary variable $w=-Δu$, the original fourth problem is transformed into a system of second-order equations, which relaxes the regularity requirements of standard $H^2$-conforming finite spaces. To further enhance the robustness and efficiency of the algorithm, an additional auxiliary variable $ϕ$, treated analogously to the pressure, is introduced, leading to a divergence-free preserving mixed finite element scheme. A fully discrete scheme is then constructed by coupling the spatial mixed FEM with the variable-step Dahlquist-Liniger-Nevanlinna (DLN) time integrator. The boundedness of the scheme and corresponding error estimates can be rigorously proven under appropriate assumptions due to unconditional non-linear stability and second-order accuracy of the DLN method. To enhance computational efficiency in practice, we develop an adaptive time-stepping strategy based on a minimum-dissipation criterion. Several numerical experiments are displayed to fully validate the theoretical results and demonstrate the accuracy and efficiency of the scheme for complex active fluid simulations.

math.NA↗

arXiv2025

Miniaturized optically-generated Bessel beam ultrasound for volumetric transcranial brain stimulation

Non-invasive stimulation of small, variably shaped brain sub-regions is crucial for advancing our understanding of brain functions. Current ultrasound neuromodulation faces two significant trade-offs when targeting brain sub-regions: miniaturization versus volumetric control and spatial resolution versus transcranial capability. Here, we present an optically-generated Bessel beam ultrasound (OBUS) device designed to overcome these limitations. This 2.33 mm-diameter miniaturized device delivers a column-shaped field achieving a lateral resolution of 152 um and an axial resolution of 1.93 mm, targeting brain sub-regions with an elongated volume of tissue activation. Immunofluorescence imaging of mouse brain slices confirms its ability to stimulate cells at a depth of 2.2 mm. Additionally, OBUS outperforms conventional Gaussian ultrasound in transcranial transmission efficiency and beam shape preservation. Electrophysiological recordings and functional MRI captured rodent brain responses evoked by OBUS, demonstrating OBUS's ability to non-invasively activate neural circuits in intact brains. This technology offers new possibilities for studying brain functions with precision and volumetric control.

q-bio.NC↗

arXiv2025

Scalable and Reliable Multi-agent Reinforcement Learning for Traffic Assignment

The evolution of metropolitan cities and the increase in travel demands impose stringent requirements on traffic assignment methods. Multi-agent reinforcement learning (MARL) approaches outperform traditional methods in modeling adaptive routing behavior without requiring explicit system dynamics, which is beneficial for real-world deployment. However, MARL frameworks face challenges in scalability and reliability when managing extensive networks with substantial travel demand, which limiting their practical applicability in solving large-scale traffic assignment problems. To address these challenges, this study introduces MARL-OD-DA, a new MARL framework for the traffic assignment problem, which redefines agents as origin-destination (OD) pair routers rather than individual travelers, significantly enhancing scalability. Additionally, a Dirichlet-based action space with action pruning and a reward function based on the local relative gap are designed to enhance solution reliability and improve convergence efficiency. Experiments demonstrate that the proposed MARL framework effectively handles medium-sized networks with extensive and varied city-level OD demand, surpassing existing MARL methods. When implemented in the SiouxFalls network, MARL-OD-DA achieves better assignment solutions in 10 steps, with a relative gap that is 94.99% lower than that of conventional methods.

cs.LG↗

arXiv2025

Ablation of black-Si by (Gauss-)Bessel femtosecond laser beams

Laser machining and modification of black-Si (b-Si) by femtosecond laser Gaussian (G-) and Gauss-Bessel (GB-) beams are compared at a wavelength of 1030 nm. The GB-beam was generated using a diffractive axicon lens and 10x demagnification optics. It was found that modification of b-Si well below (a factor 50x) the single pulse ablation fluence of 0.2 J/cm2 was possible, corresponding to ablation/melting of nano-needles. The width of modification was almost independent of pulse energy/fluence and had a width of 1/e2-intensity profile at the melting regime. For the GB-beam, the smallest width of laser modification at 0.2 J/cm2 threshold (at the center core) was close to the FWHM of the core of the GB-beam. The aspect ratio of the ablated groove on the surface of b-Si made by GB-beam was twice as large - up to 8 - compared to that achievable with G-beam, and it was at a lower fluence of 4 J/cm2 (50x reduction). Reflectivity of two-side nanotextured b-Si on plasma-thinned 70-micrometers thick Si was strongly reduced in the near-IR range, reaching transmittance >95% at 1.7-2.1 micrometres wavelengths.

physics.optics↗

arXiv2025

Linear, decoupled and positivity-preserving staggered mesh schemes for general dissipative systems with arbitrary energy distributions

In this paper, we develop a novel staggered mesh (SM) approach for general nonlinear dissipative systems with arbitrary energy distributions (including cases with known or unknown energy lower bounds). Based on this framework, we propose several second-order semi-discrete schemes that maintain linearity, computational decoupling, and unconditional energy stability. Firstly, for dissipative systems with known energy lower bounds, we introduce a positive auxiliary variable $V(t)$ to substitute the total energy functional, subsequently discretizing it on staggered temporal meshes to ensure that the energy remains non-increasing regardless of the size of time step. The newly developed schemes achieve full computational decoupling, maintaining essentially the same computational expense as conventional implicit-explicit methods while demonstrating significantly improved accuracy. Furthermore, we rigorously establish the positivity preservation of the discrete variable $V^{n+1/2}$ which is a crucial property ensuring numerical stability and accuracy. Theoretical analysis confirms second-order temporal convergence for the proposed SM schemes. Secondly, for dissipative systems lacking well-defined energy lower bounds, we devise an alternative auxiliary variable formulation and extend the SM framework to maintain unconditional energy stability while preserving numerical effectiveness and accuracy. Finally, comprehensive numerical experiments, including benchmark problem simulations, validate the proposed schemes' efficacy and demonstrate their superior performance characteristics.

math.NA↗

arXiv2025

Post-interactive Multimodal Trajectory Prediction for Autonomous Driving

Modeling the interactions among agents for trajectory prediction of autonomous driving has been challenging due to the inherent uncertainty in agents' behavior. The interactions involved in the predicted trajectories of agents, also called post-interactions, have rarely been considered in trajectory prediction models. To this end, we propose a coarse-to-fine Transformer for multimodal trajectory prediction, i.e., Pioformer, which explicitly extracts the post-interaction features to enhance the prediction accuracy. Specifically, we first build a Coarse Trajectory Network to generate coarse trajectories based on the observed trajectories and lane segments, in which the low-order interaction features are extracted with the graph neural networks. Next, we build a hypergraph neural network-based Trajectory Proposal Network to generate trajectory proposals, where the high-order interaction features are learned by the hypergraphs. Finally, the trajectory proposals are sent to the Proposal Refinement Network for further refinement. The observed trajectories and trajectory proposals are concatenated together as the inputs of the Proposal Refinement Network, in which the post-interaction features are learned by combining the previous interaction features and trajectory consistency features. Moreover, we propose a three-stage training scheme to facilitate the learning process. Extensive experiments on the Argoverse 1 dataset demonstrate the superiority of our method. Compared with the baseline HiVT-64, our model has reduced the prediction errors by 4.4%, 8.4%, 14.4%, 5.7% regarding metrics minADE6, minFDE6, MR6, and brier-minFDE6, respectively.

cs.CV↗