Ensuring high accuracy and efficiency of predictive models is paramount in the aerospace industry, particularly in the context of multidisciplinary design and optimization processes. These processes often require numerous evaluations of complex objective functions, which can be computationally expensive and time-consuming. To build efficient and accurate predictive models, we propose a new approach that leverages Bayesian Optimization (BO) to optimize the hyper-parameters of a lightweight and accurate Neural Network (NN) for aerodynamic performance prediction. To clearly describe the interplay between design variables, hierarchical and categorical kernels are used in the BO formulation. We demonstrate the efficiency of our approach through two comprehensive case studies, where the optimized NN significantly outperforms baseline models and other publicly available NNs in terms of accuracy and parameter efficiency. For the drag coefficient prediction task, the Mean Absolute Percentage Error (MAPE) of our optimized model drops from 0.1433\% to 0.0163\%, which is nearly an order of magnitude improvement over the baseline model. Additionally, our model achieves a MAPE of 0.82\% on a benchmark aircraft self-noise prediction problem, significantly outperforming existing models (where their MAPE values are around 2 to 3\%) while requiring less computational resources. The results highlight the potential of our framework to enhance the scalability and performance of NNs in large-scale MDO problems, offering a promising solution for the aerospace industry.

In 6G wireless networks, Artificial Intelligence (AI)-driven applications demand the adoption of Federated Learning (FL) to enable efficient and privacy-preserving model training across distributed devices. Over-The-Air Federated Learning (OTA-FL) exploits the superposition property of multiple access channels, allowing edge users in 6G networks to efficiently share spectral resources and perform low-latency global model aggregation. However, these advantages come with challenges, as traditional OTA-FL techniques suffer due to the joint effects of Additive White Gaussian Noise (AWGN) at the server, fading, and both data and system heterogeneity at the participating edge devices. In this work, we propose the novel Noise Resilient Over-the-Air Federated Learning (NoROTA-FL) framework to jointly tackle these challenges in federated wireless networks. In NoROTA-FL, the local optimization problems find controlled inexact solutions, which manifests as an additional proximal constraint at the clients. This approach provides robustness against straggler-induced partial work, heterogeneity, noise, and fading. From a theoretical perspective, we leverage the zeroth- and first-order inexactness and establish convergence guarantees for non-convex optimization problems in the presence of heterogeneous data and varying system capabilities. Experimentally, we validate NoROTA-FL on real-world datasets, including FEMNIST, CIFAR10, and CIFAR100, demonstrating its robustness in noisy and heterogeneous environments. Compared to state-of-the-art baselines such as COTAF and FedProx, NoROTA-FL achieves significantly more stable convergence and higher accuracy, particularly in the presence of stragglers.

Various parallelism, such as data, tensor, and pipeline parallelism, along with memory optimizations like activation checkpointing, redundancy elimination, and offloading, have been proposed to accelerate distributed training for Large Language Models. To find the best combination of these techniques, automatic distributed training systems are proposed. However, existing systems only tune a subset of optimizations, due to the lack of overlap awareness, inability to navigate the vast search space, and ignoring the inter-microbatch imbalance, leading to sub-optimal performance. To address these shortcomings, we propose Mist, a memory, overlap, and imbalance-aware automatic distributed training system that comprehensively co-optimizes all memory footprint reduction techniques alongside parallelism. Mist is based on three key ideas: (1) fine-grained overlap-centric scheduling, orchestrating optimizations in an overlapped manner, (2) symbolic-based performance analysis that predicts runtime and memory usage using symbolic expressions for fast tuning, and (3) imbalance-aware hierarchical tuning, decoupling the process into an inter-stage imbalance and overlap aware Mixed Integer Linear Programming problem and an intra-stage Dual-Objective Constrained Optimization problem, and connecting them through Pareto frontier sampling. Our evaluation results show that Mist achieves an average of 1.28$\times$ (up to 1.73$\times$) and 1.27$\times$ (up to 2.04$\times$) speedup compared to state-of-the-art manual system Megatron-LM and state-of-the-art automatic system Aceso, respectively.

Multivariate cortico-muscular analysis has recently emerged as a promising approach for evaluating the corticospinal neural pathway. However, current multivariate approaches encounter challenges such as high dimensionality and limited sample sizes, thus restricting their further applications. In this paper, we propose a structured and sparse partial least squares coherence algorithm (ssPLSC) to extract shared latent space representations related to cortico-muscular interactions. Our approach leverages an embedded optimization framework by integrating a partial least squares (PLS)-based objective function, a sparsity constraint and a connectivity-based structured constraint, addressing the generalizability, interpretability and spatial structure. To solve the optimization problem, we develop an efficient alternating iterative algorithm within a unified framework and prove its convergence experimentally. Extensive experimental results from one synthetic and several real-world datasets have demonstrated that ssPLSC can achieve competitive or better performance over some representative multivariate cortico-muscular fusion methods, particularly in scenarios characterized by limited sample sizes and high noise levels. This study provides a novel multivariate fusion method for cortico-muscular analysis, offering a transformative tool for the evaluation of corticospinal pathway integrity in neurological disorders.

Conformal prediction provides a principled framework for constructing predictive sets with finite-sample validity. While much of the focus has been on univariate response variables, existing multivariate methods either impose rigid geometric assumptions or rely on flexible but computationally expensive approaches that do not explicitly optimize prediction set volume. We propose an optimization-driven framework based on a novel loss function that directly learns minimum-volume covering sets while ensuring valid coverage. This formulation naturally induces a new nonconformity score for conformal prediction, which adapts to the residual distribution and covariates. Our approach optimizes over prediction sets defined by arbitrary norm balls, including single and multi-norm formulations. Additionally, by jointly optimizing both the predictive model and predictive uncertainty, we obtain prediction sets that are tight, informative, and computationally efficient, as demonstrated in our experiments on real-world datasets.

--Mining process optimization, particularly truck dispatch scheduling, is a critical factor in enhancing the efficiency of open-pit mining operations. However, the dynamic and stochastic nature of mining environments--characterized by uncertainties such as equipment failures, truck maintenance, and variable haul cycle times--poses significant challenges for traditional optimization methods. While Reinforcement Learning (RL) has demonstrated promise in adaptive decision-making for mining logistics, its practical deployment requires rigorous evaluation in realistic and customizable simulation environments. T o address this challenge, we introduce Mining-Gym, a configurable, open-source benchmarking environment designed for training, testing, and comparing RL algorithms in mining process optimization. Built on Discrete Event Simulation (DES) and seamlessly integrated with the OpenAI Gym interface, Mining-Gym offers a structured testbed that enables the direct application of advanced RL algorithms from Stable Baselines. The framework models key mining-specific uncertainties, such as equipment failures, queue congestion, and stochasticity of mining processes, ensuring a realistic and adaptive learning environment. Additionally, a graphic user interface (GUI) for easy parameter selection for mine-site configuration, comprehensive data logging system, a built-in KPI dashboard and real-time representative visualization of mine-site enables in-depth performance analysis, facilitating standardized, reproducible evaluation across multiple RL strategies and baseline heuristics. INING process optimization aims to enhance efficiency and productivity by improving resource allocation, equipment scheduling, and material handling. However, these operations are highly complex, influenced by dynamic factors such as equipment failures, fluctuating ore quality, and unpredictable environmental conditions. Traditional optimization methods, such as linear programming and heuristics, struggle to adapt in real time, leading to inefficiencies and increased costs.

Recovering the underlying Directed Acyclic Graph (DAG) structures from observational data presents a formidable challenge, partly due to the combinatorial nature of the DAG-constrained optimization problem. Recently, researchers have identified gradient vanishing as one of the primary obstacles in differentiable DAG learning and have proposed several DAG constraints to mitigate this issue. By developing the necessary theory to establish a connection between analytic functions and DAG constraints, we demonstrate that analytic functions from the set $\{f(x) = c_0 + \sum_{i=1}^{\infty}c_ix^i | \forall i > 0, c_i > 0; r = \lim_{i\rightarrow \infty}c_{i}/c_{i+1} > 0\}$ can be employed to formulate effective DAG constraints. Furthermore, we establish that this set of functions is closed under several functional operators, including differentiation, summation, and multiplication. Consequently, these operators can be leveraged to create novel DAG constraints based on existing ones. Using these properties, we design a series of DAG constraints and develop an efficient algorithm to evaluate them. Experiments in various settings demonstrate that our DAG constraints outperform previous state-of-the-art comparators. Our implementation is available at https://github.com/zzhang1987/AnalyticDAGLearning.

Classically, to solve differential equation problems, it is necessary to specify sufficient initial and/or boundary conditions so as to allow the existence of a unique solution. Well-posedness of differential equation problems thus involves studying the existence and uniqueness of solutions, and their dependence to such pre-specified conditions. However, in part due to mathematical necessity, these conditions are usually specified "to arbitrary precision" only on (appropriate portions of) the boundary of the space-time domain. This does not mirror how data acquisition is performed in realistic situations, where one may observe entire "patches" of solution data at arbitrary space-time locations; alternatively one might have access to more than one solutions stemming from the same differential operator. In our short work, we demonstrate how standard tools from machine and manifold learning can be used to infer, in a data driven manner, certain well-posedness features of differential equation problems, for initial/boundary condition combinations under which rigorous existence/uniqueness theorems are not known. Our study naturally combines a data assimilation perspective with an operator-learning one.

The problem of finding the sparsest solution to a linear underdetermined system of equations, as it often appears in data analysis, optimal control and system identification problems, is considered. This non-convex problem is commonly solved by convexification via $\ell_1$-norm minimization, also known as basis pursuit. In this work, a class of structured matrices, representing the system of equations, is introduced for which the basis pursuit approach tractably fails to recover the sparsest solution. In particular, we are able to identify matrix columns that correspond to unrecoverable non-zero entries of the sparsest solution, as well as to conclude the uniqueness of the sparsest solution in polynomial time. These deterministic guarantees contrast popular probabilistic ones, and as such, provide valuable insights into the a priori design of sparse optimization problems. As our matrix structure appears naturally in optimal control problems, we exemplify our findings by showing that it is possible to verify a priori that basis pursuit may fail in finding fuel optimal regulators for a class of discrete-time linear time-invariant systems.

Saddle point optimization is a critical problem employed in numerous real-world applications, including portfolio optimization, generative adversarial networks, and robotics. It has been extensively studied in cases where the objective function is known and differentiable. Existing work in black-box settings with unknown objectives that can only be sampled either assumes convexity-concavity in the objective to simplify the problem or operates with noisy gradient estimators. In contrast, we introduce a framework inspired by Bayesian optimization which utilizes Gaussian processes to model the unknown (potentially nonconvex-nonconcave) objective and requires only zeroth-order samples. Our approach frames the saddle point optimization problem as a two-level process which can flexibly integrate existing and novel approaches to this problem. The upper level of our framework produces a model of the objective function by sampling in promising locations, and the lower level of our framework uses the existing model to frame and solve a general-sum game to identify locations to sample. This lower level procedure can be designed in complementary ways, and we demonstrate the flexibility of our approach by introducing variants which appropriately trade off between factors like runtime, the cost of function evaluations, and the number of available initial samples. We experimentally demonstrate these algorithms on synthetic and realistic datasets in black-box nonconvex-nonconcave settings, showcasing their ability to efficiently locate local saddle points in these contexts.