Numerical simulation is important in real-world engineering systems, such as solid mechanics and aero-dynamics. Hierarchical GNNs can learn engineering simulation with low simulation time and acceptable accuracy, but fail to represent complex interactions in simulation systems. In this paper, we propose a novel multilevel Transformer on learnable clusters, namely SimFormer. The key novelty of SimFormer is to interweave the learning of a learnable soft-cluster assignment algorithm and the inter-cluster/cluster-to-node attention. In form of a closed-loop, SimFormer learns the soft cluster assignment possibility by the feedback signals provided by the attention, and the attention can leverage the learnable clusters to better represent long-range interactions. In this way, the learnable clusters can adaptively match actual simulation results, and the multilevel attention modules can also effectively represent node embeddings. Experiments on four datasets demonstrate the superiority of SimFormer over seven baseline approaches. For example, on the real dataset, ours outperforms the recent work Eagle by 17.36% lower RMSE and 27.03% smaller FLOPs. The code and datasets are available at: https://github.com/pro-orp/SimFormer.

This paper studies the distributed optimization problem of high-order multi-agent systems with unknown nonlinear terms and input saturation. Unlike existing results, nonlinear functions in the considered system are not required to satisfy the Lipschitz linear growth condition. Moreover, a more general convexity condition is provided for certain local functions, relaxing the traditional strong convexity condition. In addition, the contradiction issue between input saturation and the requirement of a large initial input in existing fixed-time control schemes is handled by constructing an appropriate auxiliary system. In the paper, to begin with, the original optimization problem is transformed into an unconstrained optimization one by constructing a quadratic penalty function. Furthermore, by resorting to fuzzy logic systems with adaptive technique, nonlinear functions in systems are dealt with. And, by the back-stepping method, a distributed fixed-time optimization control strategy based on a penalty function is developed. The proposed controllers can ensure the achievement of the output consensus and the expected optimization objective within a fixed time. Finally, stability analysis and simulation examples are provided to illustrate the effectiveness of the proposed control scheme.

The Surface Water and Ocean Topography (SWOT) mission offers significant potential in mapping sea surface height (SSH) for detecting mesoscale and submesoscale ocean signals. However, possible spurious signals caused by long-wavelength error (LWE) during SSH mapping pose a challenge in realizing the potential. We improved the widely used optimal interpolation method, to reduce the spurious mesoscale signal for SWOT. Since LWE remains in the SWOT SSH observations after cross-track calibration, the spatial differenced SSH observations instead of SSH observations were used as input for the mapping. The method was assessed using the Observing System Simulation Experiment (OSSE) and SWOT level 3 ocean products. The results show that LWE mainly has an effect on the mesoscale signal with wavelengths longer than 100 km, and the improved method can reduce spurious signals significantly compared to the standard optimal interpolation method. In addition, compared to the empirical optimal interpolation method commonly used in LWE reduction, the improved method has a comparable performance and no longer requires prior variance of LWE. For the uncorrected SWOT level 3 ocean products, the decimeter-level LWE can be reduced by the improved method and the mesoscale signal covered by it is successfully reconstructed. For the cross-track calibrated SWOT level 3 ocean products, residual centimeter-level LWE can also be reduced, and the SNR of mesoscale signals is improved by 62% for wavelengths longer than 100 km.

This article studies theH∞control problem for switched systems with dynamic event-triggering and quantization schemes subject to denial-of-service (DoS) attacks. First, the resilient event-triggering and quantization schemes against DoS are developed, allowing the triggering parameter and quantization density to be dynamically adjusted. Subsequently, we introduce a time-dependent piecewise Lyapunov function that remains nonincreasing at discontinuity points. This function, along with an auxiliary functional, is dedicated to establishing criteria for the stability withL2gain property of switched systems, under which the frequency of DoS attacks no longer directly impacts the exponential stability decay rate. In contrast to the general min-switching rule, the min-derivative switching strategy in this article is formulated based on the derivative of Lyapunov function and serves to make the time-dependent Lyapunov function decrease. Moreover, the switching law ensures that switches occur only at discrete sampling instants, thereby avoiding Zeno behavior. Finally, two simulation examples are provided to illustrate the feasibility and superiority of our approaches.

Using Graph Neural Networks (GNNs) to simulate complex physical systems is currently a popular field. Finite Element Analysis (FEA) is a numerical analysis solution in physical simulation and involves dividing a physical structure into finite elements. A mesh-based graph network is formed by interconnecting the nodes of the finite elements. Mesh-based simulations are central to the modeling of physical systems, and GNNs are used to overcome the high cost of the simulation. However, most existing GNNs-based methods lack the ability to generalize when small changes in structure occur. The cantilever beam, which is a fundamental component of many physical structures, is a classic study case for FEA stress analysis. In this paper, we propose a Mesh-based Graph Transfer Learning (MGTL) method for beams, in which the knowledge learned on a mesh-based graph network of one beam structure via contrastive learning, and then is transferred to another. Furthermore, an augmentation approach is proposed for the mesh-based graph in contrastive learning. Our experiments demonstrate the effectiveness of transfer learning in the MGTL method, as well as its generalization ability across different mesh sizes and structure types.

Complex physical system simulation is important in many real world applications. We study the general simulation scenario to generate the response result when a physical object is applied by external factors. Traditional solvers on Partial Differential Equations (PDEs) suffer from significantly high computational cost. Many recent learning-based approaches focus on multivariate time series alike simulation prediction problem and do not work for our case. In this paper, we propose a novel two-level graph neural networks (GNNs) to learn the simulation result of a physical object applied by external factors. The key is a two-level graph structure where one fine mesh graph is mapped to multiple coarse one. Our preliminary evaluation on both synthetic and real datasets demonstrates that our work outperforms three state-of-the-arts by much lower errors.

OBJECTIVES: The impacts of missing data in comparative effectiveness research (CER) using electronic health records (EHRs) may vary depending on the type and pattern of missing data. In this study, we aimed to quantify these impacts and compare the performance of different imputation methods. MATERIALS AND METHODS: We conducted an empirical (simulation) study to quantify the bias and power loss in estimating treatment effects in CER using EHR data. We considered various missing scenarios and used the propensity scores to control for confounding. We compared the performance of the multiple imputation and spline smoothing methods to handle missing data. RESULTS: When missing data depended on the stochastic progression of disease and medical practice patterns, the spline smoothing method produced results that were close to those obtained when there were no missing data. Compared to multiple imputation, the spline smoothing generally performed similarly or better, with smaller estimation bias and less power loss. The multiple imputation can still reduce study bias and power loss in some restrictive scenarios, eg, when missing data did not depend on the stochastic process of disease progression. DISCUSSION AND CONCLUSION: Missing data in EHRs could lead to biased estimates of treatment effects and false negative findings in CER even after missing data were imputed. It is important to leverage the temporal information of disease trajectory to impute missing values when using EHRs as a data resource for CER and to consider the missing rate and the effect size when choosing an imputation method.

This paper studies stability for a class of switched descriptor systems with state bumpless transfer performance and input bumpless transfer performance. Since the state jump is inevitable for switched descriptor systems when a switching occurs, to restrain the amplitude of the state jump induced by switchings, for the first time, the state bumpless transfer performance of switched descriptor systems is defined. Moreover, when switching occurs, to avoid the abrupt and large control input signals change damaging the system, we are the first to introduce the input bumpless transfer control scheme for switched descriptor systems. Furthermore, by using multiple Lyapunov functions, a sufficient condition is put forward to make sure the state bumpless transfer performance, input bumpless transfer performance and asymptotical stability for the closed-loop systems. Meanwhile, the switching rule and the state feedback controller are co-designed. In the end, a multiple inputs numerical example and an application on the DC motor model are used to exhibit the merit and validity of the presented control scheme.