Graph neural networks, recently introduced into the field of fluid flow surrogate modeling, have been successfully applied to model the temporal evolution of various fluid flow systems. Existing applications, however, are mostly restricted to cases where the domain is time-invariant. The present work extends the application of graph neural network-based modeling to fluid flow around structures rotating with respect to a certain axis. Specifically, we propose to apply a graph neural network-based surrogate modeling for fluid flow with the mesh corotating with the structure. Unlike conventional data-driven approaches that rely on structured Cartesian meshes, our framework operates on unstructured co-rotating meshes, enforcing rotation equivariance of the learned model by leveraging co-rotating polar (2D) and cylindrical (3D) coordinate systems. To model the pressure for systems without Dirichlet pressure boundaries, we propose a novel local directed pressure difference formulation that is invariant to the reference pressure point and value. For flow systems with large mesh sizes, we introduce a scheme to train the network in single or distributed graphics processing units by accumulating the backpropagated gradients from partitions of the mesh. The effectiveness of our proposed framework is examined on two test cases: (i) fluid flow in a 2D rotating mixer, and (ii) the flow past a 3D rotating cube. Our results show that the model achieves stable and accurate rollouts for over 2000 time steps in periodic regimes while capturing accurate short-term dynamics in chaotic flow regimes. In addition, the drag and lift force predictions closely match the CFD calculations, highlighting the potential of the framework for modeling both periodic and chaotic fluid flow around rotating structures.

Fast convolution algorithms, including Winograd and FFT, can efficiently accelerate convolution operations in deep models. However, these algorithms depend on high-precision arithmetic to maintain inference accuracy, which conflicts with the model quantization. To resolve this conflict and further improve the efficiency of quantized convolution, we proposes SFC, a new algebra transform for fast convolution by extending the Discrete Fourier Transform (DFT) with symbolic computing, in which only additions are required to perform the transformation at specific transform points, avoiding the calculation of irrational number and reducing the requirement for precision. Additionally, we enhance convolution efficiency by introducing correction terms to convert invalid circular convolution outputs of the Fourier method into effective ones. The numerical error analysis is presented for the first time in this type of work and proves that our algorithms can provide a 3.68x multiplication reduction for 3x3 convolution, while the Winograd algorithm only achieves a 2.25x reduction with similarly low numerical errors. Experiments carried out on benchmarks and FPGA show that our new algorithms can further improve the computation efficiency of quantized models while maintaining accuracy, surpassing both the quantization-alone method and existing works on fast convolution quantization.

Graph Neural Networks (GNNs) have excelled in learning from graph-structured data, especially in understanding the relationships within a single graph, i.e., intra-graph relationships. Despite their successes, GNNs are limited by neglecting the context of relationships across graphs, i.e., inter-graph relationships. Recognizing the potential to extend this capability, we introduce Relating-Up, a plug-and-play module that enhances GNNs by exploiting inter-graph relationships. This module incorporates a relation-aware encoder and a feedback training strategy. The former enables GNNs to capture relationships across graphs, enriching relation-aware graph representation through collective context. The latter utilizes a feedback loop mechanism for the recursively refinement of these representations, leveraging insights from refining inter-graph dynamics to conduct feedback loop. The synergy between these two innovations results in a robust and versatile module. Relating-Up enhances the expressiveness of GNNs, enabling them to encapsulate a wider spectrum of graph relationships with greater precision. Our evaluations across 16 benchmark datasets demonstrate that integrating Relating-Up into GNN architectures substantially improves performance, positioning Relating-Up as a formidable choice for a broad spectrum of graph representation learning tasks.

We present a new framework to address the non-convex robust hypothesis testing problem, wherein the goal is to seek the optimal detector that minimizes the maximum of worst-case type-I and type-II risk functions. The distributional uncertainty sets are constructed to center around the empirical distribution derived from samples based on Sinkhorn discrepancy. Given that the objective involves non-convex, non-smooth probabilistic functions that are often intractable to optimize, existing methods resort to approximations rather than exact solutions. To tackle the challenge, we introduce an exact mixed-integer exponential conic reformulation of the problem, which can be solved into a global optimum with a moderate amount of input data. Subsequently, we propose a convex approximation, demonstrating its superiority over current state-of-the-art methodologies in literature. Furthermore, we establish connections between robust hypothesis testing and regularized formulations of non-robust risk functions, offering insightful interpretations. Our numerical study highlights the satisfactory testing performance and computational efficiency of the proposed framework.

Machine learning (ML) models can underperform on certain population groups due to choices made during model development and bias inherent in the data. We categorize sources of discrimination in the ML pipeline into two classes: aleatoric discrimination, which is inherent in the data distribution, and epistemic discrimination, which is due to decisions made during model development. We quantify aleatoric discrimination by determining the performance limits of a model under fairness constraints, assuming perfect knowledge of the data distribution. We demonstrate how to characterize aleatoric discrimination by applying Blackwell's results on comparing statistical experiments. We then quantify epistemic discrimination as the gap between a model's accuracy when fairness constraints are applied and the limit posed by aleatoric discrimination. We apply this approach to benchmark existing fairness interventions and investigate fairness risks in data with missing values. Our results indicate that state-of-the-art fairness interventions are effective at removing epistemic discrimination on standard (overused) tabular datasets. However, when data has missing values, there is still significant room for improvement in handling aleatoric discrimination.

We present a rotation equivariant, quasi-monolithic graph neural network framework for the reduced-order modeling of fluid-structure interaction systems. With the aid of an arbitrary Lagrangian-Eulerian formulation, the system states are evolved temporally with two sub-networks. The movement of the mesh is reduced to the evolution of several coefficients via complex-valued proper orthogonal decomposition, and the prediction of these coefficients over time is handled by a single multi-layer perceptron. A finite element-inspired hypergraph neural network is employed to predict the evolution of the fluid state based on the state of the whole system. The structural state is implicitly modeled by the movement of the mesh on the solid-fluid interface; hence it makes the proposed framework quasi-monolithic. The effectiveness of the proposed framework is assessed on two prototypical fluid-structure systems, namely the flow around an elastically-mounted cylinder, and the flow around a hyperelastic plate attached to a fixed cylinder. The proposed framework tracks the interface description and provides stable and accurate system state predictions during roll-out for at least 2000 time steps, and even demonstrates some capability in self-correcting erroneous predictions. The proposed framework also enables direct calculation of the lift and drag forces using the predicted fluid and mesh states, in contrast to existing convolution-based architectures. The proposed reduced-order model via graph neural network has implications for the development of physics-based digital twins concerning moving boundaries and fluid-structure interactions.

Since analytical solutions are usually not available, numerical solutions on discretized space and time domains are considered for predictive modeling. Leveraging state-of-the-art computational fluid dynamics (CFD) approaches based on finite volume [3] or finite element [4, 5] methods, one could obtain high-fidelity solutions that can be suitable for downstream design optimization and control purposes. However, the cost of performing such simulations is significant, and becomes prohibitively high for complex problems arising from real-world applications. This limitation of traditional CFD approaches has inspired the development of data-driven projectionbased reduced-order modeling techniques. Such models are usually used in an offline-online manner. In the offline stage, an approximation of the governing flow dynamics in a low-order linear subspace is constructed based on available fluid flow data collected. This approximation reduces the complexity of the problem in the online stage, making it possible to acquire fast, accurate predictions. Popular methods in this category include proper orthogonal decomposition (POD) [6, 7], dynamic mode decomposition (DMD) [8], along with many variants (e.g., [9, 10, 11]). However, these methods encounter difficulty when applied to scenarios with high Reynolds numbers and convection-dominated problems, whereas one needs a significantly large number of linear subspaces to achieve a satisfactory approximation.

The major challenges of collision avoidance for robot navigation in crowded scenes lie in accurate environment modeling, fast perceptions, and trustworthy motion planning policies. This paper presents a novel adaptive environment model based collision avoidance reinforcement learning (i.e., AEMCARL) framework for an unmanned robot to achieve collision-free motions in challenging navigation scenarios. The novelty of this work is threefold: (1) developing a hierarchical network of gated-recurrent-unit (GRU) for environment modeling; (2) developing an adaptive perception mechanism with an attention module; (3) developing an adaptive reward function for the reinforcement learning (RL) framework to jointly train the environment model, perception function and motion planning policy. The proposed method is tested with the Gym-Gazebo simulator and a group of robots (Husky and Turtlebot) under various crowded scenes. Both simulation and experimental results have demonstrated the superior performance of the proposed method over baseline methods.

Decision-making problems under uncertainty have broad applications in operations research, machine learning, engineering, and economics. When the data involves uncertainty due to measurement error, insufficient sample size, contamination, and anomalies, or model misspecification, distributionally robust optimization (DRO) is a promising approach to data-driven optimization, by seeking a minimax robust optimal decision that minimizes the expected loss under the most adverse distribution within a given set of relevant distributions, called ambiguity set. It provides a principled framework to produce a solution with more promising out-of-sample performance than the traditional sample average approximation (SAA) method for stochastic programming [86]. We refer to [81] for a recent survey on DRO. At the core of DRO is the choice of the ambiguity set. Ideally, a good ambiguity set should take account of the properties of practical applications while maintaining the computational tractability of resulted DRO formulation; and it should be rich enough to contain all distributions relevant to the decision-making but, at the same time, should not include unnecessary distributions that lead to overly conservative decisions. Various DRO formulations have been proposed in the literature. Among them, the ambiguity set based on Wasserstein distance has recently received much attention [104, 67, 17, 46]. The Wasserstein distance incorporates the geometry of sample space, and thereby is suitable for comparing distributions with non-overlapping supports and hedging against data perturbations [46].

This paper is concerned with regularized extensions of hierarchical non-stationary temporal Gaussian processes (NSGPs) in which the parameters (e.g., length-scale) are modeled as GPs. In particular, we consider two commonly used NSGP constructions which are based on explicitly constructed non-stationary covariance functions and stochastic differential equations, respectively. We extend these NSGPs by including $L^1$-regularization on the processes in order to induce sparseness. To solve the resulting regularized NSGP (R-NSGP) regression problem we develop a method based on the alternating direction method of multipliers (ADMM) and we also analyze its convergence properties theoretically. We also evaluate the performance of the proposed methods in simulated and real-world datasets.