arXiv subjects

Tao Cui

Publications and source records attributed to Tao Cui.

At least 19 recordsLinked to original sources

arXiv2026

Toward Certified Functional Safety for Industrial Humanoid Robots: The Fail-Passive Gap and a Feasibility Study

Industrial humanoid robots are constrained less by locomotion or manipulation capability than by the immaturity of functional safety certification for legged platforms. The root difficulty is that the safe state of a legged robot is an actively-controlled state, which violates the fail-passive assumption underlying ISO~13849-1 / EN~60204-1: removing power from a walking biped causes an uncontrolled fall, so classical de-energization is itself a hazard. We term this the fail-passive gap and use a certified external safety chain (light curtain, emergency stop, fail-safe input, fail-safe PLC, and wireless PROFIsafe) as an instrument to locate it precisely: because the external chain is closed and quantifiable with established methods (PFHD, DC, CCF, PL/SILCL), the residual uncertifiable element is pinpointed to the robot-side reaction chain. Using a Siemens fail-safe S7-1500 emergency-stop reference, we show its certifiable Reaction subsystem is contactor-based power removal (Stop Category~0)---exactly the element a balancing humanoid cannot have. We deliberately do not claim end-to-end certified PL~e / SIL~3. We validate the approach on a Unitree G1 EDU pick-and-place cell in a 3m x 1.5m semi-enclosed workspace, and contribute a humanoid-specific analysis of the active safe state (fall-as-hazard, single-support stop bounds, balancing-policy residual risk, ISO~13855 separation) and a provenance-labeled timing budget. Hosting an industrial software-defined automation (SDA) controller on the robot, co-located with the balancing policy, moves robot-side PROFINET/PROFIsafe reception onto a standardized IEC~61131-3 interface; because the G1's onboard compute is not safety-rated hardware, this endpoint is not a certified safety runtime, which reinforces rather than resolves the fail-passive gap and localizes it to the SDA-to-balancing-policy interface.

cs.RO↗

arXiv2026

A Symmetry Method for Key Vanishing Lemmas and Optimal $2$-Jet Thresholds for Hyperbolicity

This manuscript reports on an ongoing project. The finite full-column-rank computations underlying the Key Vanishing Lemmas isolated below are currently undergoing exact computer-assisted verification. Conditional on successful completion of that verification, the arguments presented here would establish the two positivity endpoints of Demailly's invariant two-jet Riemann--Roch calculation: every very general surface in $\mathbb{P}^3$ of degree $15$ would be Kobayashi hyperbolic, and the complement of every general smooth plane curve of degree $11$ would be Kobayashi hyperbolic. At the logarithmic endpoint the same conditional argument would also give a Second Main Theorem with coefficient $1422$; the preceding work treated all degrees $d\geqslant12$. The argument separates an infinite geometric range from a finite algebraic obstruction.An $\mathcal{O}(3)$ slanted-vector-field package combines a quadratic acceleration with a classical matrix lift. Their incompatible actions on the invariant fibre ring, together with the common-twist, prime-ideal, and relative-family interfaces, exclude the dependence alternative for every weight $m\geqslant3$. This improves the differentiation range from $t\geqslant8$ to $t\geqslant4$ and leaves, beyond the twist-one ranges, only five compact and thirteen logarithmic systems. The residual systems are reduced by symmetry. A two-term Fermat perturbation carries an involution, so a hypothetical negatively twisted two-jet differential has an invariant or anti-invariant component. Imposing this eigencondition before elimination adds exact linear constraints without adding unknowns. The required full-column-rank statements are isolated in the Key Vanishing Lemmas as finite computational targets. This paper records their finite reduction and proof-to-certificate interface. Their exact computer-assisted verification is in progress.

math.AG↗

arXiv2026

Learning Safe-Stoppability Monitors for Humanoid Robots

Emergency stop (E-stop) mechanisms are the de facto standard for robot safety. However, for humanoid robots, abruptly cutting power can itself cause catastrophic failures; instead, an emergency stop must execute a predefined fallback controller that preserves balance and drives the robot toward a minimum-risk condition. This raises a critical question: from which states can a humanoid robot safely execute such a stop? In this work, we formalize emergency stopping for humanoids as a policy-dependent safe-stoppability problem and use data-driven approaches to characterize the safe-stoppable envelope. We introduce PRISM (Proactive Refinement of Importance-sampled Stoppability Monitor), a simulation-driven framework that learns a neural predictor for state-level stoppability. PRISM iteratively refines the decision boundary using importance sampling, enabling targeted exploration of rare but safety-critical states. This targeted exploration significantly improves data efficiency while reducing false-safe predictions under a fixed simulation budget. We further demonstrate sim-to-real transfer by deploying the pretrained monitor on a real humanoid platform. Results show that modeling safety as policy-dependent stoppability enables proactive safety monitoring and supports scalable certification of fail-safe behaviors for humanoid robots.

cs.RO↗

arXiv2025

Exploration of Approaches for Robustness and Safety in a Low Code Open Environment for Factory Automation

This report is a compilation of technical knowledge and concepts that were produced by the authors and additional contributors in the context of the collaboration projects "Abstraction Requirements for Language of Choice in Industrial Automation" (FY21-22) and "Approaches for Robust and Safe Low-Code" (FY23-24) from Siemens Technology and the University of California, Berkeley. The primary objective of these projects was to assess Siemens Open Industrial Edge (OIE) engineering capabilities by defining a concept that ensures the satisfaction of coordination and safety requirements when using disparate OIE modules. The objective was to use the Lingua Franca (LF) coordination language to demonstrate how to address challenges in: 1. engineering modular, distributed, and flexible automation solutions that ensure, by design, robust and safe operation1; 2. the use of IEC 61499, the event driven execution model for specifying the execution order of OIE modules (defined as function blocks); 3. support large-scale distributed OIE automation solutions, and eventually 4. define optimal solutions with synchronization and time-optimal mechanisms.

cs.SE↗

arXiv2024

On the Combination of AI and Wireless Technologies: 3GPP Standardization Progress

Combing Artificial Intelligence (AI) and wireless communication technologies has become one of the major technologies trends towards 2030. This includes using AI to improve the efficiency of the wireless transmission and supporting AI deployment with wireless networks. In this article, the latest progress of the Third Generation Partnership Project (3GPP) standards development is introduced. Concentrating on AI model distributed transfer and AI for Beam Management (BM) with wireless network, we introduce the latest studies and explain how the existing standards should be modified to incorporate the results from academia.

cs.NI↗

arXiv2023

Finite element error estimates for the nonlinear Schr\"{o}dinger-Poisson model

In this paper, we study a priori error estimates for the finite element approximation of the nonlinear Schr\"{o}dinger-Poisson model. The electron density is defined by an infinite series over all eigenvalues of the Hamiltonian operator. To establish the error estimate, we present a unified theory of error estimates for a class of nonlinear problems. The theory is based on three conditions: 1) the original problem has a solution $u$ which is the fixed point of a compact operator $\Ca$, 2) $\Ca$ is Fr\'{e}chet-differentiable at $u$ and $\Ci-\Ca'[u]$ has a bounded inverse in a neighborhood of $u$, and 3) there exists an operator $\Ca_h$ which converges to $\Ca$ in the neighborhood of $u$. The theory states that $\Ca_h$ has a fixed point $u_h$ which solves the approximate problem. It also gives the error estimate between $u$ and $u_h$, without assumptions on the well-posedness of the approximate problem. We apply the unified theory to the finite element approximation of the Schr\"{o}dinger-Poisson model and obtain optimal error estimate between the numerical solution and the exact solution. Numerical experiments are presented to verify the convergence rates of numerical solutions.

math.NA↗

arXiv2023

Federated Learning over a Wireless Network: Distributed User Selection through Random Access

User selection has become crucial for decreasing the communication costs of federated learning (FL) over wireless networks. However, centralized user selection causes additional system complexity. This study proposes a network intrinsic approach of distributed user selection that leverages the radio resource competition mechanism in random access. Taking the carrier sensing multiple access (CSMA) mechanism as an example of random access, we manipulate the contention window (CW) size to prioritize certain users for obtaining radio resources in each round of training. Training data bias is used as a target scenario for FL with user selection. Prioritization is based on the distance between the newly trained local model and the global model of the previous round. To avoid excessive contribution by certain users, a counting mechanism is used to ensure fairness. Simulations with various datasets demonstrate that this method can rapidly achieve convergence similar to that of the centralized user selection approach.

cs.LG↗

arXiv2020

A Neural Network with Plane Wave Activation for Helmholtz Equation

This paper proposes a plane wave activation based neural network (PWNN) for solving Helmholtz equation, the basic partial differential equation to represent wave propagation, e.g. acoustic wave, electromagnetic wave, and seismic wave. Unlike using traditional activation based neural network (TANN) or $sin$ activation based neural network (SIREN) for solving general partial differential equations, we instead introduce a complex activation function $e^{\mathbf{i}{x}}$, the plane wave which is the basic component of the solution of Helmholtz equation. By a simple derivation, we further find that PWNN is actually a generalization of the plane wave partition of unity method (PWPUM) by additionally imposing a learned basis with both amplitude and direction to better characterize the potential solution. We firstly investigate our performance on a problem with the solution is an integral of the plane waves with all known directions. The experiments demonstrate that: PWNN works much better than TANN and SIREN on varying architectures or the number of training samples, that means the plane wave activation indeed helps to enhance the representation ability of neural network toward the solution of Helmholtz equation; PWNN has competitive performance than PWPUM, e.g. the same convergence order but less relative error. Furthermore, we focus a more practical problem, the solution of which only integrate the plane waves with some unknown directions. We find that PWNN works much better than PWPUM at this case. Unlike using the plane wave basis with fixed directions in PWPUM, PWNN can learn a group of optimized plane wave basis which can better predict the unknown directions of the solution. The proposed approach may provide some new insights in the aspect of applying deep learning in Helmholtz equation.

math.NA↗

arXiv2020

Restrained Generative Adversarial Network against Overfitting in Numeric Data Augmentation

In recent studies, Generative Adversarial Network (GAN) is one of the popular schemes to augment the image dataset. However, in our study we find the generator G in the GAN fails to generate numerical data in lower-dimensional spaces, and we address overfitting in the generation. By analyzing the Directed Graphical Model (DGM), we propose a theoretical restraint, independence on the loss function, to suppress the overfitting. Practically, as the Statically Restrained GAN (SRGAN) and Dynamically Restrained GAN (DRGAN), two frameworks are proposed to employ the theoretical restraint to the network structure. In the static structure, we predefined a pair of particular network topologies of G and D as the restraint, and quantify such restraint by the interpretable metric Similarity of the Restraint (SR). While for DRGAN we design an adjustable dropout module for the restraint function. In the widely carried out 20 group experiments, on four public numerical class imbalance datasets and five classifiers, the static and dynamic methods together produce the best augmentation results of 19 from 20; and both two methods simultaneously generate 14 of 20 groups of the top-2 best, proving the effectiveness and feasibility of the theoretical restraints.

cs.LG↗

arXiv2019

Study of Constrained Network Structures for WGANs on Numeric Data Generation

Some recent studies have suggested using GANs for numeric data generation such as to generate data for completing the imbalanced numeric data. Considering the significant difference between the dimensions of the numeric data and images, as well as the strong correlations between features of numeric data, the conventional GANs normally face an overfitting problem, consequently leads to an ill-conditioning problem in generating numeric and structured data. This paper studies the constrained network structures between generator G and discriminator D in WGAN, designs several structures including isomorphic, mirror and self-symmetric structures. We evaluates the performances of the constrained WGANs in data augmentations, taking the non-constrained GANs and WGANs as the baselines. Experiments prove the constrained structures have been improved in 17/20 groups of experiments. In twenty experiments on four UCI Machine Learning Repository datasets, Australian Credit Approval data, German Credit data, Pima Indians Diabetes data and SPECT heart data facing five conventional classifiers. Especially, Isomorphic WGAN is the best in 15/20 experiments. Finally, we theoretically proves that the effectiveness of constrained structures by the directed graphic model (DGM) analysis.

cs.LG↗

arXiv2018

Numerical Simulations of Polymer Flooding Process in Porous Media on Distributed-memory Parallel Computers

Polymer flooding is a mature enhanced oil recovery technique that has been successfully applied in many field projects. By injecting polymer into a reservoir, the viscosity of water is increased, and the efficiency of water flooding is improved. As a result, more oil can be recovered. This paper presents numerical simulations of a polymer flooding process using parallel computers, where the numerical modeling of polymer retention, inaccessible pore volumes, a permeability reduction and polymer absorption are considered. Darcy's law is employed to model the behavoir of a fluid in porous media, and the upstream finite difference (volume) method is applied to discretize the mass conservation equations. Numerical methods, including discretization schemes, linear solver methods, nonlinearization methods and parallel techniques are introduced. Numerical experiments show that, on one hand, computed results match those from the commercial simulator, Schlumberger-Eclipse, which is widely applied by the petroleum industry, and, on the other hand, our simulator has excellent scalability, which is demonstrated by field applications with up to 27 million grid blocks using up to 2048 CPU cores.

cs.CE↗

arXiv2018

Numerical Simulation of Two-phase Flow in Natural Fractured Reservoirs Using Dual Porosity Method on Parallel Computers

The two-phase oil-water flow in natural fractured reservoirs and its numerical methods are introduced in this paper, where the fracture is modeled by the dual porosity method. Efficient numerical method, including the finite difference method, CPR-FPF preconditioners for linear systems and effective decoupling method, are presented. Parallel computing techniques employed in simulation are also presented. Using those numerical methods and parallel techniques, a parallel reservoir simulator is developed, which is capable of simulating large-scale reservoir models. The numerical results show that our simulator is accurate and scalable compared to the commercial software, and the numerical methods are also effective.

cs.CE↗

arXiv2018

GPU Accelerated Finite Element Assembly with Runtime Compilation

In recent years, high performance scientific computing on graphics processing units (GPUs) have gained widespread acceptance. These devices are designed to offer massively parallel threads for running code with general purpose. There are many researches focus on finite element method with GPUs. However, most of the works are specific to certain problems and applications. Some works propose methods for finite element assembly that is general for a wide range of finite element models. But the development of finite element code is dependent on the hardware architectures. It is usually complicated and error prone using the libraries provided by the hardware vendors. In this paper, we present architecture and implementation of finite element assembly for partial differential equations (PDEs) based on symbolic computation and runtime compilation technique on GPU. User friendly programming interface with symbolic computation is provided. At the same time, high computational efficiency is achieved by using runtime compilation technique. As far as we know, it is the first work using this technique to accelerate finite element assembly for solving PDEs. Experiments show that a one to two orders of speedup is achieved for the problems studied in the paper.

cs.MS↗

arXiv2017

An hp-adaptive strategy for elliptic problems

In this paper a new hp-adaptive strategy for elliptic problems based on refinement history is proposed, which chooses h-, p- or hp-refinement on individual elements according to a posteriori error estimate, as well as smoothness estimate of the solution obtained by comparing the actual and expected error reduction rate. Numerical experiments show that exponential convergence can be achieved with this strategy.

math.NA↗

arXiv2017

Dynamic load balancing for large-scale adaptive finite element computation

For the parallel computation of partial differential equations, one key is the grid partitioning. It requires that each process owns the same amount of computations, and also, the partitioning quality should be proper to reduce the communications among processes. When calculating the partial differential equations using adaptive finite element methods, the grid and the basis functions adjust in each iteration, which introduce load balancing issues. The grid should be redistributed dynamically. This paper studies dynamic load balancing algorithms and the implementation on the adaptive finite element platform PHG. The numerical experiments show that algorithms studied in this paper have good partitioning quality, and they are efficient.

cs.DC↗

arXiv2016

Encoding and Decoding Algorithms for Arbitrary Dimensional Hilbert Order

Hilbert order is widely applied in many areas. However, most of the algorithms are confined to low dimensional cases. In this paper, algorithms for encoding and decoding arbitrary dimensional Hilbert order are presented. Eight algorithms are proposed. Four algorithms are based on arithmetic operations and the other four algorithms are based on bit operations. For the algorithms complexities, four of them are linear and the other four are constant for given inputs. In the end of the paper, algorithms for two dimensional Hilbert order are presented to demonstrate the usage of the algorithms introduced.

cs.SC↗

arXiv2013

An Error-Resilient Redundant Subspace Correction Method

As we stride toward the exascale era, due to increasing complexity of supercomputers, hard and soft errors are causing more and more problems in high-performance scientific and engineering computation. In order to improve reliability (increase the mean time to failure) of computing systems, a lot of efforts have been devoted to developing techniques to forecast, prevent, and recover from errors at different levels, including architecture, application, and algorithm. In this paper, we focus on algorithmic error resilient iterative linear solvers and introduce a redundant subspace correction method. Using a general framework of redundant subspace corrections, we construct iterative methods, which have the following properties: (1) Maintain convergence when error occurs assuming it is detectable; (2) Introduce low computational overhead when no error occurs; (3) Require only small amount of local (point-to-point) communication compared to traditional methods and maintain good load balance; (4) Improve the mean time to failure. With the proposed method, we can improve reliability of many scientific and engineering applications. Preliminary numerical experiments demonstrate the efficiency and effectiveness of the new subspace correction method.

math.NA↗

arXiv2012

An Information-Theoretic Approach to PMU Placement in Electric Power Systems

This paper presents an information-theoretic approach to address the phasor measurement unit (PMU) placement problem in electric power systems. Different from the conventional 'topological observability' based approaches, this paper advocates a much more refined, information-theoretic criterion, namely the mutual information (MI) between the PMU measurements and the power system states. The proposed MI criterion can not only include the full system observability as a special case, but also can rigorously model the remaining uncertainties in the power system states with PMU measurements, so as to generate highly informative PMU configurations. Further, the MI criterion can facilitate robust PMU placement by explicitly modeling probabilistic PMU outages. We propose a greedy PMU placement algorithm, and show that it achieves an approximation ratio of (1-1/e) for any PMU placement budget. We further show that the performance is the best that one can achieve in practice, in the sense that it is NP-hard to achieve any approximation ratio beyond (1-1/e). Such performance guarantee makes the greedy algorithm very attractive in the practical scenario of multi-stage installations for utilities with limited budgets. Finally, simulation results demonstrate near-optimal performance of the proposed PMU placement algorithm.

math.OC↗