arXiv subjects

Qiang Du

Publications and source records attributed to Qiang Du.

At least 19 recordsLinked to original sources

arXiv2026

A Second-Order Method for Locating Critical Points of Prescribed Index on Energy Landscapes

Exploring high dimensional energy landscape is a challenging problem in many applications where both ground states and transition states offer important information about the underlying physical systems. To facilitate the computational exploration, we propose a cubic-regularized second-order method for locating critical points of prescribed index, including both energy minima (with an index $0$) and transition states (saddle points with positive index). At each step of the iteration, the proposed method involves several ingredients, such as updating the eigen-directions of the Hessian according to the prescribed index, reflecting the gradient and the Hessian along selected unstable eigen-directions, if any, and constructing the next step by solving a cubic-regularized subproblem. Under suitable assumptions, we show that, when the eigenspace and the cubic subproblem are solved exactly, the iteration converges locally and quadratically to a critical point of the prescribed index. We further establish convergence results in the inexact setting, where both the eigenspace computation and the solution of the cubic subproblem are performed approximately. We show that the resulting iteration retains local linear convergence, with the convergence rate depending on the accuracy of the inexact computations. Moreover, we prove that the fixed points of the algorithm are precisely critical points of the prescribed index. In addition, we introduce an adaptive strategy for updating the cubic regularization parameter to improve robustness and computational efficiency of the proposed algorithm. Numerical experiments confirm the predicted convergence behavior, demonstrate the effectiveness of the adaptive strategy, and illustrate the capability of the proposed method for locating critical points and constructing solution landscapes.

math.NA↗

arXiv2026

EMERGE-Policy: A Robot Mind Emerges Beyond a Single Policy

A robot's effective ``mind'' need not reside in a single policy. It can emerge when specialized components perceive, reason, predict, act, verify, and remember within a shared orchestration process. EMERGE-Policy turns this perspective into a graph-structured agentic framework that coordinates both capability invocation and information exchange. A Main Agent retains task-level state within an active context window, while role-specific Sub Agents process perception, execution monitoring, verification, and memory consolidation in isolated contexts and return structured, task-relevant evidence. Role-specific contexts control information load by exposing only decision-relevant evidence to the Main Agent, while the functional Skill interface composes heterogeneous backends as Operational, Imagination, and Evaluation Skills. Criterion-grounded verification, textual failure diagnosis, and Branch Stack recovery provide localized correction, with token-aware external memory preserving task-relevant state. Together, their closed-loop interaction realizes the system-level policy captured by the name EMERGE-Policy. Without additional fine-tuning, we achieved outstanding performance on several public benchmark that have had a wide-reaching impact, and conducted a series of real robot experiments. These system-level results suggest that through the division of different functional sub-tasks among multiple agents and their concurrent collaboration, as well as the technical paradigm where the model is regarded as a skill and called within the framework, EMERGE-Policy can extend the robust robot policies beyond isolated runs.

cs.RO↗

arXiv2026

A Multi-Agent Framework for Zero-Dimensional Reduced-Order Model Planning

Zero-dimensional reduced-order models (0D ROMs) are central to multi-dimensional design workflows for high-end complex equipment. However, the planning process currently relies on manual expertise, limiting topological exploration and prolonging iterations. Even traditional optimization methods such as Genetic Algorithms (GA) are typically confined to local parameter tuning. Although Large Language Model (LLM) agents have shown promise in exploring large sample spaces, and frameworks such as Chain of Thought (CoT) and Reason and Act (ReAct) improve reasoning reliability, while Retrieval-Augmented Generation (RAG) overcomes domain knowledge barriers, a single agent still falls short for the long-horizon and highly coupled nature of complex 0D ROM planning. This paper proposes the Zero-dimensional reduced-order model CO-Planning framework (Z-COPA), a multi-agent architecture featuring a Symbolic Action Graph Engine (SAGE) and a MILP-Guided Navigation (MGN) optimizer. Its core innovation is a dedicated graph representation method that accurately encodes the 0D flow network topology, converting the empirical planning process into a rigorous graph structure optimization problem. We validate the forward and inverse design capabilities and generalization performance of Z-COPA on two real aircraft engine secondary-air systems, two IEEE power-distribution reconfiguration benchmarks, and two water-distribution network benchmarks. The results show superior task completion quality, obtaining the best performance in both forward and reverse design of air systems. Z-COPA disrupts the traditional 0D model planning paradigm, providing a new technical approach for exploring broader topological space and achieving highly automated, globally optimal air system architectures.

cs.LG↗

arXiv2026

Graphon Limits of Graph Reaction--Diffusion Equations

A graph reaction--diffusion (RD) equation is a system of differential equations that is defined on the nodes of a graph. Consider a sequence of growing graphs that converges in cut norm to a limiting graphon. We show that the solutions of the sequence of graph RD equations converge in $L^p$ norm, for $p \in [1,\infty]$, to the solution of a limiting nonlocal RD equation, which we call a graphon RD equation. Furthermore, we show a large numbers result for a stochastic particle process that consists of a random walk and a birth-death process on graphs. For a sequence of graphs that converge in cut norm to a limiting graphon, the sequence of stochastic processes converges in probability to the solution of the graphon RD equation.

math.DS↗

arXiv2026

Flow Field Reconstruction via Voronoi-Enhanced Physics-Informed Neural Networks with End-to-End Sensor Placement Optimization

(short version abstract, full in article)High-fidelity flow field reconstruction is important in fluid dynamics, but it is challenged by sparse and spatiotemporally incomplete sensor measurements, as well as failures of pre-deployed measurement points that can invalidate pre-trained reconstruction models. Physics-informed neural networks (PINNs) alleviate dependence on large labeled datasets by incorporating governing physics, yet sensor placement optimization, a key factor in reconstruction accuracy and robustness, remains underexplored. In this study, we propose a PINN with Voronoi-enhanced Sensor Optimization (VSOPINN). VSOPINN enables differentiable soft Voronoi construction for sparse sensor data rasterization, end-to-end fusion of centroidal Voronoi tessellation (CVT) with PINNs for adaptive sensor placement, and unified layout optimization for multi-condition flow reconstruction through a shared encoder-multi-decoder architecture. We validate VSOPINN on three representative problems: lid-driven cavity flow, vascular flow, and annular rotating flow. Results show that VSOPINN significantly improves reconstruction accuracy across different Reynolds numbers, adaptively learns effective sensor layouts, and remains robust under partial sensor failure. The study clarifies the intrinsic relationship between sensor placement and reconstruction precision in PINN-based flow field reconstruction.

physics.flu-dyn↗

arXiv2026

MUSA-PINN: Multi-scale Weak-form Physics-Informed Neural Networks for Fluid Flow in Complex Geometries

While Physics-Informed Neural Networks (PINNs) offer a mesh-free approach to solving fluid-flow PDEs, standard point-wise residual minimization suffers from convergence pathologies in topologically complex domains like Triply Periodic Minimal Surfaces (TPMS). The locality bias of point-wise constraints fails to propagate global information through tortuous channels, causing unstable gradients and conservation violations. To address this, we propose the Multi-scale Weak-form PINN (MUSA-PINN), which reformulates Navier-Stokes equation constraints as integral conservation laws over hierarchical spherical control volumes. We enforce continuity and momentum conservation via flux-balance residuals on control surfaces. Our method utilizes a three-scale subdomain strategy-comprising large volumes for long-range coupling, skeleton-aware meso-scale volumes aligned with transport pathways, and small volumes for local refinement-alongside a two-stage training schedule prioritizing continuity. Experiments on steady incompressible flow in TPMS geometries show MUSA-PINN outperforms state-of-the-art baselines, reducing relative errors by up to 93% and preserving mass conservation.

cs.LG↗

arXiv2026

Convergence Analysis of the Discrete Constrained Saddle Dynamics and Their Momentum Variants

We study the discrete constrained saddle dynamics and their momentum variants for locating saddle points on manifolds. Under the assumption of exact unstable eigenvectors, we establish a local linear convergence of the discrete constrained saddle dynamics and show that the convergence rate depends on the condition number of the Riemannian Hessian. To mitigate this dependence, we introduce a momentum-based constrained saddle dynamics and prove local convergence of the continuous-time dynamics as well as the corresponding discrete scheme, which further demonstrates that momentum accelerates convergence, particularly in ill-conditioned settings. In addition, we show that a single-step eigenvector update is sufficient to guarantee local convergence; thus, the assumption of exact unstable eigenvectors is not necessary, which substantially reduces the computational cost. Finally, numerical experiments, including applications to the Thomson problem, the Rayleigh quotient on the Stiefel manifold, and the energy functional of Bose-Einstein condensates, are presented to complement the theoretical analysis.

math.NA↗

arXiv2026

A Derivative-Free Saddle-search Algorithm With Linear Convergence Rate

We propose a derivative-free saddle-search algorithm designed to locate transition states using only function evaluations. The algorithm employs a nested architecture consisting of an inner eigenvector search and an outer saddle-point search. Through rigorous numerical analysis, we prove the almost sure convergence of the inner step under suitable assumptions. Furthermore, we establish the convergence of the outer search using a decaying step size, while demonstrating linear convergence under constant step size and boundedness conditions. Numerical experiments are provided to validate our theoretical results and demonstrate the algorithm's practical applicability.

math.NA↗

arXiv2025

ALS-U AR RF Equipment Protection System

This paper presents the design and status of Accumulator Ring (AR) RF Equipment Protection System (EPS) of Advanced Light Source Upgrade project at LBNL. The key components of AR RF EPS include a Master Interlock PLC subsystem handling supervisory control and slow interlocks in \SI{}{\milli\second} scale, an FPGA-based LLRF Controller managing fast interlocks in \SI{}{\micro\second} scale, a 60 kW high-power amplifier with standalone PLC-based slow (\SI{}{\milli\second} scale) and FPGA-based fast (\SI{}{\micro\second} scale) protection systems, and an RF Drive Control Chassis acting as primary RF mitigation device. The design of AR RF EPS is presented along with internal RF and external AR subsystems interfaces.

physics.acc-ph↗

arXiv2025

ALS Storage Ring RF Control System Upgrade Plan and Status

The Advanced Light Source (ALS) at Lawrence Berkeley National Laboratory, a third-generation synchrotron light source operational since 1992, is undergoing a comprehensive upgrade of its storage ring RF control system. The legacy Horner PLC controllers and remote I/O modules, now at end-of-life, are being replaced with an Allen-Bradley PLC platform to improve maintainability, reliability, and long-term support. This paper presents the planning, design, and current status of the upgrade project.

physics.acc-ph↗

arXiv2025

RFSoC Based LLRF System Design at ALS

The Advanced Light Source (ALS) at LBNL is upgrading several LLRF systems for its Linac and Sub-Harmonic Bunchers, where it is desired to have a unified LLRF system design to support various RF frequencies (at 125MHz, 500MHz and 3GHz) and configurations. This paper demonstrates an open-source, direct sampling RFSoC based LLRF system design, featuring: sample-to-sample Multi-Tile Synchronization, deterministic latency, digital up/down conversion, arbitrary waveform generation and acquisition, in-pulse closed loop control, timing and EPICS integration, modular RF frontend and hardware designs. Measured RF characteristics show that the RFSoC based LLRF system is able to meet the system requirements.

physics.acc-ph↗

arXiv2025

Comparative Evaluation of Xilinx RFSoC Platform for Low-Level RF Systems

The rapid advancement of Radio Frequency System-onChip (RFSoC) technology from Xilinx (AMD) has enabled the integration of high-speed data converters and programmable logic within a single package. RFSoC platforms are already widely adopted in telecommunications, radar, and satellite communications, where they promise reductions in system footprint and power consumption. However, their suitability for Low-Level RF (LLRF) control systems in accelerator environments - where stability requirements are critical - has not been quantitatively evaluated. This paper presents a comparative measurement-based assessment of RFSoC-based and conventional LLRF designs, focusing on signal fidelity, phase noise, latency, system complexity, and integration challenges. The advantages and challenges of adopting RFSoC-based direct conversion architectures are discussed, providing guidance for future LLRF system implementations.

physics.acc-ph↗

arXiv2025

A Stochastic Algorithm for Searching Saddle Points with Convergence Guarantee

Saddle points provide a hierarchical view of the energy landscape, revealing transition pathways and interconnected basins of attraction, and offering insight into the global structure, metastability, and possible collective mechanisms of the underlying system. In this work, we propose a stochastic saddle-search algorithm to circumvent exact derivative and Hessian evaluations that have been used in implementing traditional and deterministic saddle dynamics. At each iteration, the algorithm uses a stochastic eigenvector-search method, based on a stochastic Hessian, to approximate the unstable directions, followed by a stochastic gradient update with reflections in the approximate unstable direction to advance toward the saddle point. We carry out rigorous numerical analysis to establish the almost sure convergence for the stochastic eigenvector search and local almost sure convergence with an $O(1/n)$ rate for the saddle search, and present a theoretical guarantee to ensure the high-probability identification of the saddle point when the initial point is sufficiently close. Numerical experiments, including the application to a neural network loss landscape and a Landau-de Gennes type model for nematic liquid crystal, demonstrate the practical applicability and the ability for escaping from "bad" areas of the algorithm.

math.NA↗

arXiv2025

Digital Low-Level RF system for the Linac Electronics Modernization Plan at LCLS

The LCLS began operations in 2009, utilizing SLAC's normal-conducting (NC) LINAC, which features control equipment dating back to the 1960s and 1980s. The Linac Electronics Modernization Plan (LEMP) aims to replace the legacy control equipment with a system based on the open-source Marble carrier board and Zest+ digitizer board, both of which are used in the LCLS-II HE LLRF system. Adaptation of the LLRF system developed for the continuous-wave (CW) superconducting RF (SRF) LCLS-II to the short-RF pulse NC LCLS includes leveraging the knowledge and experience gained from recent LLRF projects at SLAC and efficiently reusing the core functionality of the hardware and code base developed for previous projects, in collaboration with LBNL, FNAL and JLAB. A prototype has been deployed and tested at station 26-3, demonstrating RF generation/control, interlocks, triggers, and waveform capture. Here, we describe the hardware, firmware and software infrastructure, highlight key features, and present initial test results.

physics.acc-ph↗

arXiv2025

On parameterized nonlocal-fractional transmission problems and associated function spaces

In this paper, we consider a family of seamlessly coupled nonlocal models associated with transmission conditions across an interface. The models are derived from the variation of a parameterized family of energies consisting of a fractional type Dirichlet energy on one subdomain and a nonlocal Dirichlet energy involving a finite range of interactions on another subdomain. We present the rigorous mathematical formulation and its well-posedness. We also investigate the behavior of the model in various limiting regimes.

math.AP↗

arXiv2025

A discontinuous Galerkin method for one-dimensional nonlocal wave problems

This paper presents a fully discrete numerical scheme for one-dimensional nonlocal wave equations and provides a rigorous theoretical analysis. To facilitate the spatial discretization, we introduce an auxiliary variable analogous to the gradient field in local discontinuous Galerkin (DG) methods for classical partial differential equations (PDEs) and reformulate the equation into a system of equations. The proposed scheme then uses a DG method for spatial discretization and the Crank-Nicolson method for time integration. We prove optimal L2 error convergence for both the solution and the auxiliary variable under a special class of radial kernels at the semi-discrete level. In addition, for general kernels, we demonstrate the asymptotic compatibility of the scheme, ensuring that it recovers the classical DG approximation of the local wave equation in the zero-horizon limit. Furthermore, we prove that the fully discrete scheme preserves the energy of the nonlocal wave equation. A series of numerical experiments are presented to validate the theoretical findings.

math.NA↗

arXiv2025

Nonlinear Optimal Recovery in Hilbert Spaces

This paper investigates solution strategies for nonlinear problems in Hilbert spaces, such as nonlinear partial differential equations (PDEs) in Sobolev spaces, when only finite measurements are available. We formulate this as a nonlinear optimal recovery problem, establishing its well-posedness and proving its convergence to the true solution as the number of measurements increases. However, the resulting formulation might not have a finite-dimensional solution in general. We thus present a sufficient condition for the finite dimensionality of the solution, applicable to problems with well-defined point evaluation measurements. To address the broader setting, we introduce a relaxed nonlinear optimal recovery and provide a detailed convergence analysis. An illustrative example is given to demonstrate that our formulations and theoretical findings offer a comprehensive framework for solving nonlinear problems in infinite-dimensional spaces with limited data.

math.NA↗

arXiv2025

Beyond separability: convergence rate of vanishing viscosity approximations to mean field games via FBSDE stability

This paper studies the vanishing viscosity approximation to mean field games (MFGs) in $\mathbb{R}^d$ with a nonlocal and possibly non-separable Hamiltonian. We prove that the value function converges at a rate of $\mathcal{O}(\beta)$, where $\beta^2$ is the diffusivity constant, which matches the classical convergence rate of vanishing viscosity for Hamilton-Jacobi (HJ) equations. The same rate is also obtained for the approximation of the distribution of players as well as for the gradient of the value function. The proof is a combination of probabilistic and analytical arguments by first analyzing the forward-backward stochastic differential equation associated with the MFG, and then applying a general stability result for HJ equations. Applications of our result to $N$-player games, mean field control, and policy iteration for solving MFGs are also presented.

math.OC↗