Nanophotonic structures have versatile applications including solar cells, anti-reflective coatings, electromagnetic interference shielding, optical filters, and light emitting diodes. To design and understand these nanophotonic structures, electrodynamic simulations are essential. These simulations enable us to model electromagnetic fields over time and calculate optical properties. In this work, we introduce frameworks and benchmarks to evaluate nanophotonic structures in the context of parametric structure design problems. The benchmarks are instrumental in assessing the performance of optimization algorithms and identifying an optimal structure based on target optical properties. Moreover, we explore the impact of varying grid sizes in electrodynamic simulations, shedding light on how evaluation fidelity can be strategically leveraged in enhancing structure designs.

Employing Stochastic Nonlinear Model Predictive Control (SNMPC) for real-time applications is challenging due to the complex task of propagating uncertainties through nonlinear systems. This difficulty becomes more pronounced in high-dimensional systems with extended prediction horizons, such as autonomous vehicles. To enhance closed-loop performance in and feasibility in SNMPCs, we introduce the concept of the Uncertainty Propagation Horizon (UPH). The UPH limits the time for uncertainty propagation through system dynamics, preventing trajectory divergence, optimizing feedback loop advantages, and reducing computational overhead. Our SNMPC approach utilizes Polynomial Chaos Expansion (PCE) to propagate uncertainties and incorporates nonlinear hard constraints on state expectations and nonlinear probabilistic constraints. We transform the probabilistic constraints into deterministic constraints by estimating the nonlinear constraints' expectation and variance. We then showcase our algorithm's effectiveness in real-time control of a high-dimensional, highly nonlinear system-the trajectory following of an autonomous passenger vehicle, modeled with a dynamic nonlinear single-track model. Experimental results demonstrate our approach's robust capability to follow an optimal racetrack trajectory at speeds of up to 37.5m/s while dealing with state estimation disturbances, achieving a minimum solving frequency of 97Hz. Additionally, our experiments illustrate that limiting the UPH renders previously infeasible SNMPC problems feasible, even when incorrect uncertainty assumptions or strong disturbances are present.

Several recent works have studied the societal effects of AI; these include issues such as fairness, robustness, and safety. In many of these objectives, a learner seeks to minimize its worst-case loss over a set of predefined distributions (known as uncertainty sets), with usual examples being perturbed versions of the empirical distribution. In other words, aforementioned problems can be written as min-max problems over these uncertainty sets. In this work, we provide a general framework for studying these problems, which we refer to as Responsible AI (RAI) games. We provide two classes of algorithms for solving these games: (a) game-play based algorithms, and (b) greedy stagewise estimation algorithms. The former class is motivated by online learning and game theory, whereas the latter class is motivated by the classical statistical literature on boosting, and regression. We empirically demonstrate the applicability and competitive performance of our techniques for solving several RAI problems, particularly around subpopulation shift.

The rapidly advancing fields of statistical modeling and machine learning have significantly enhanced data-driven design and optimization. This paper focuses on leveraging these design algorithms to optimize a medical walker, an integral part of gait rehabilitation and physiological therapy of the lower extremities. To achieve the desirable qualities of a walker, we train a predictive machine-learning model to identify trade-offs between performance objectives, thus enabling the use of efficient optimization algorithms. To do this, we use an Automated Machine Learning model utilizing a stacked-ensemble approach shown to outperform traditional ML models. However, training a predictive model requires vast amounts of data for accuracy. Due to limited publicly available walker designs, this paper presents a dataset of more than 5,000 parametric walker designs with performance values to assess mass, structural integrity, and stability. These performance values include displacement vectors for the given load case, stress coefficients, mass, and other physical properties. We also introduce a novel method of systematically calculating the stability index of a walker. We use MultiObjective Counterfactuals for Design (MCD), a novel genetic-based optimization algorithm, to explore the diverse 16-dimensional design space and search for high-performing designs based on numerous objectives. This paper presents potential walker designs that demonstrate up to a 30% mass reduction while increasing structural stability and integrity. This work takes a step toward the improved development of assistive mobility devices.

We study the generalized Procrustes analysis (GPA), as a minimal formulation to the simultaneous localization and mapping (SLAM) problem. We propose KernelGPA, a novel global registration technique to solve SLAM in the deformable environment. We propose the concept of deformable transformation which encodes the entangled pose and deformation. We define deformable transformations using a kernel method, and show that both the deformable transformations and the environment map can be solved globally in closed-form, up to global scale ambiguities. We solve the scale ambiguities by an optimization formulation that maximizes rigidity. We demonstrate KernelGPA using the Gaussian kernel, and validate the superiority of KernelGPA with various datasets. Code and data are available at \url{https://bitbucket.org/FangBai/deformableprocrustes}.

This work presents a graph neural network (GNN) framework for solving the maximum independent set (MIS) problem, inspired by dynamic programming (DP). Specifically, given a graph, we propose a DP-like recursive algorithm based on GNNs that firstly constructs two smaller sub-graphs, predicts the one with the larger MIS, and then uses it in the next recursive call. To train our algorithm, we require annotated comparisons of different graphs concerning their MIS size. Annotating the comparisons with the output of our algorithm leads to a self-training process that results in more accurate self-annotation of the comparisons and vice versa. We provide numerical evidence showing the superiority of our method vs prior methods in multiple synthetic and real-world datasets.

We study the problem of generating arbitrarily large environments to improve the throughput of multi-robot systems. Prior work proposes Quality Diversity (QD) algorithms as an effective method for optimizing the environments of automated warehouses. However, these approaches optimize only relatively small environments, falling short when it comes to replicating real-world warehouse sizes. The challenge arises from the exponential increase in the search space as the environment size increases. Additionally, the previous methods have only been tested with up to 350 robots in simulations, while practical warehouses could host thousands of robots. In this paper, instead of optimizing environments, we propose to optimize Neural Cellular Automata (NCA) environment generators via QD algorithms. We train a collection of NCA generators with QD algorithms in small environments and then generate arbitrarily large environments from the generators at test time. We show that NCA environment generators maintain consistent, regularized patterns regardless of environment size, significantly enhancing the scalability of multi-robot systems in two different domains with up to 2,350 robots. Additionally, we demonstrate that our method scales a single-agent reinforcement learning policy to arbitrarily large environments with similar patterns.

Distributed Artificial Intelligence (AI) model training over mobile edge networks encounters significant challenges due to the data and resource heterogeneity of edge devices. The former hampers the convergence rate of the global model, while the latter diminishes the devices' resource utilization efficiency. In this paper, we propose a generative AI-empowered federated learning to address these challenges by leveraging the idea of FIlling the MIssing (FIMI) portion of local data. Specifically, FIMI can be considered as a resource-aware data augmentation method that effectively mitigates the data heterogeneity while ensuring efficient FL training. We first quantify the relationship between the training data amount and the learning performance. We then study the FIMI optimization problem with the objective of minimizing the device-side overall energy consumption subject to required learning performance constraints. The decomposition-based analysis and the cross-entropy searching method are leveraged to derive the solution, where each device is assigned suitable AI-synthesized data and resource utilization policy. Experiment results demonstrate that FIMI can save up to 50% of the device-side energy to achieve the target global test accuracy in comparison with the existing methods. Meanwhile, FIMI can significantly enhance the converged global accuracy under the non-independently-and-identically distribution (non-IID) data.

The cutting plane method is a key technique for successful branch-and-cut and branch-price-and-cut algorithms that find the exact optimal solutions for various vehicle routing problems (VRPs). Among various cuts, the rounded capacity inequalities (RCIs) are the most fundamental. To generate RCIs, we need to solve the separation problem, whose exact solution takes a long time to obtain; therefore, heuristic methods are widely used. We design a learning-based separation heuristic algorithm with graph coarsening that learns the solutions of the exact separation problem with a graph neural network (GNN), which is trained with small instances of 50 to 100 customers. We embed our separation algorithm within the cutting plane method to find a lower bound for the capacitated VRP (CVRP) with up to 1,000 customers. We compare the performance of our approach with CVRPSEP, a popular separation software package for various cuts used in solving VRPs. Our computational results show that our approach finds better lower bounds than CVRPSEP for large-scale problems with 400 or more customers, while CVRPSEP shows strong competency for problems with less than 400 customers.

We consider a non-convex constrained optimization problem, where the objective function is weakly convex and the constraint function is either convex or weakly convex. To solve this problem, we consider the classical switching subgradient method, which is an intuitive and easily implementable first-order method whose oracle complexity was only known for convex problems. This paper provides the first analysis on the oracle complexity of the switching subgradient method for finding a nearly stationary point of non-convex problems. Our results are derived separately for convex and weakly convex constraints. Compared to existing approaches, especially the double-loop methods, the switching gradient method can be applied to non-smooth problems and achieves the same complexity using only a single loop, which saves the effort on tuning the number of inner iterations.