A Momentum-Based Variance-Reduced Algorithm for Federated Multiobjective Optimization

Federated learning has traditionally been formulated as a single-objective optimization problem, primarily focused on maximizing model utility. In real-world applications, however, machine learning models often need to optimize multiple and potentially conflicting objectives simultaneously. This motivates federated multiobjective optimization (FMOO), which provides a natural framework for jointly handling multiple task-specific objectives in federated learning. In this paper, we propose a momentum-based variance-reduced algorithm for federated multiobjective optimization. The method incorporates a momentum-driven gradient estimator into the local updates to reduce the variance of stochastic updates, leading to an improved convergence rate. We establish theoretical guarantees showing that the expected Pareto stationarity measure of a randomly selected output iterate decays at a rate of $\mathcal{O}(T^{-2/3})$, improving upon the $\mathcal{O}(T^{-1/2})$ rates established for existing methods such as FSMGDA and FedCMOO. Numerical experiments on federated multiobjective optimization benchmarks demonstrate the effectiveness and competitive performance of the proposed algorithm.

Surrogate Assisted Pedestrian Protection Design via a Foundation Model Orchestrated Workflow

AI-driven engineering workflows face particular challenges in crash safety design: unlike aerodynamics, crash events involve highly nonlinear contact dynamics, material nonlinearity, and discrete state transitions that are difficult to capture with data-driven surrogate models. To the best of our knowledge, we present the first foundation model--orchestrated workflow for crash safety design that enables surrogate-assisted exploration for pedestrian protection, reducing evaluation time from hours per CAE simulation to seconds. The workflow integrates four components: (1) a surrogate trained on CAE crash simulations to predict pedestrian leg injury metrics from design parameters, achieving an average $R^2=0.87$ and providing distribution-free conformal prediction intervals; (2) multiobjective evolutionary search (NSGA-II) to discover diverse feasible parameter sets under user-specified constraints; (3) a morphing-based geometry generator that maps parameters to topology-preserving 3D shapes; and (4) a natural-language interface in which an LLM orchestrates the workflow and a vision--language model supports semantic comparison of generated designs. In an automotive front-bumper case study, the workflow produces 35 distinct safety-compliant alternatives from a single exploration, a process that would require weeks with conventional CAE iteration. These results suggest that foundation models can serve as integration layers between ML surrogates and physics-based simulation, helping bring AI capabilities to safety-critical engineering domains.