Is Flow Matching Just Trajectory Replay for Sequential Data?

Flow matching (FM) is increasingly used for time-series generation, but it is not well understood whether it learns a general dynamical structure or simply performs an effective "trajectory replay". We study this question by deriving the velocity field targeted by the empirical FM objective on sequential data, in the limit of perfect function approximation. For the Gaussian conditional paths commonly used in practice, we show that the implied sampler is an ODE whose dynamics constitutes a nonparametric, memory-augmented continuous-time dynamical system. The optimal field admits a closed-form expression as a similarity-weighted mixture of instantaneous velocities induced by past transitions, making the dataset dependence explicit and interpretable. This perspective positions neural FM models trained by stochastic optimization as parametric surrogates of an ideal nonparametric solution. Using the structure of the optimal field, we study sampling and approximation schemes that improve the efficiency and numerical robustness of ODE-based generation. On nonlinear dynamical system benchmarks, the resulting closed-form sampler yields strong probabilistic forecasts directly from historical transitions, without training.

UAV-Supported Maritime Search System: Experience from Valun Bay Field Trials

This paper presents the integration of flow field reconstruction, dynamic probabilistic modeling, search control, and machine vision detection in a system for autonomous maritime search operations. Field experiments conducted in Valun Bay (Cres Island, Croatia) involved real-time drifter data acquisition, surrogate flow model fitting based on computational fluid dynamics and numerical optimization, advanced multi-UAV search control and vision sensing, as well as deep learning-based object detection. The results demonstrate that a tightly coupled approach enables reliable detection of floating targets under realistic uncertainties and complex environmental conditions, providing concrete insights for future autonomous maritime search and rescue applications.

A Methodology for Effective Surrogate Learning in Complex Optimization

Solving complex problems requires continuous effort in developing theory and practice to cope with larger, more difficult scenarios. Working with surrogates is normal for creating a proxy that realistically models the problem into the computer. Thus, the question of how to best define and characterize such a surrogate model is of the utmost importance. In this paper, we introduce the PTME methodology to study deep learning surrogates by analyzing their Precision, Time, Memory, and Energy consumption. We argue that only a combination of numerical and physical performance can lead to a surrogate that is both a trusted scientific substitute for the real problem and an efficient experimental artifact for scalable studies. Here, we propose different surrogates for a real problem in optimally organizing the network of traffic lights in European cities and perform a PTME study on the surrogates' sampling methods, dataset sizes, and resource consumption. We further use the built surrogates in new optimization metaheuristics for decision-making in real cities. We offer better techniques and conclude that the PTME methodology can be used as a guideline for other applications and solvers.

Distribution-Free Robust Functional Predict-Then-Optimize

The solution of PDEs in decision-making tasks is increasingly being undertaken with the help of neural operator surrogate models due to the need for repeated evaluation. Such methods, while significantly more computationally favorable compared to their numerical counterparts, fail to provide any calibrated notions of uncertainty in their predictions. Current methods approach this deficiency typically with ensembling or Bayesian posterior estimation. However, these approaches either require distributional assumptions that fail to hold in practice or lack practical scalability, limiting their applications in practice. We, therefore, propose a novel application of conformal prediction to produce distribution-free uncertainty quantification over the function spaces mapped by neural operators. We then demonstrate how such prediction regions enable a formal regret characterization if leveraged in downstream robust decision-making tasks. We further demonstrate how such posited robust decision-making tasks can be efficiently solved using an infinite-dimensional generalization of Danskin's Theorem and calculus of variations and empirically demonstrate the superior performance of our proposed method over more restrictive modeling paradigms, such as Gaussian Processes, across several engineering tasks.

Green Optimization: Energy-aware Design of Metaheuristics by Using Machine Learning Surrogates to Cope with Real Problems

Addressing real-world optimization challenges requires not only advanced metaheuristics but also continuous refinement of their internal mechanisms. This paper explores the integration of machine learning in the form of neural surrogate models into metaheuristics through a recent lens: energy consumption. While surrogates are widely used to reduce the computational cost of expensive objective functions, their combined impact on energy efficiency, algorithmic performance, and solution accuracy remains largely unquantified. We provide a critical investigation into this intersection, aiming to advance the design of energy-aware, surrogate-assisted search algorithms. Our experiments reveal substantial benefits: employing a state-of-the-art pre-trained surrogate can reduce energy consumption by up to 98\%, execution time by approximately 98%, and memory usage by around 99\%. Moreover, increasing the training dataset size further enhances these gains by lowering the per-use computational cost, while static pre-training versus continuous (iterative) retraining have relatively different advantages depending on whether we aim at time/energy or accuracy and general cost across problems, respectively. Surrogates also have a negative impact on costs and accuracy at times, and then they cannot be blindly adopted. These findings support a more holistic approach to surrogate-assisted optimization, integrating energy with time and predictive accuracy into performance assessments.

Optimizing Chlorination in Water Distribution Systems via Surrogate-assisted Neuroevolution

Ensuring the microbiological safety of large, heterogeneous water distribution systems (WDS) typically requires managing appropriate levels of disinfectant residuals including chlorine. WDS include complex fluid interactions that are nonlinear and noisy, making such maintenance a challenging problem for traditional control algorithms. This paper proposes an evolutionary framework to this problem based on neuroevolution, multi-objective optimization, and surrogate modeling. Neural networks were evolved with NEAT to inject chlorine at strategic locations in the distribution network at select times. NSGA-II was employed to optimize four objectives: minimizing the total amount of chlorine injected, keeping chlorine concentrations homogeneous across the network, ensuring that maximum concentrations did not exceed safe bounds, and distributing the injections regularly over time. Each network was evaluated against a surrogate model, i.e. a neural network trained to emulate EPANET, an industry-level hydraulic WDS simulator that is accurate but infeasible in terms of computational cost to support machine learning. The evolved controllers produced a diverse range of Pareto-optimal policies that could be implemented in practice, outperforming standard reinforcement learning methods such as PPO. The results thus suggest a pathway toward improving urban water systems, and highlight the potential of using evolution with surrogate modeling to optimize complex real-world systems.

Adaptive Acquisition Selection for Bayesian Optimization with Large Language Models

Bayesian Optimization critically depends on the choice of acquisition function, but no single strategy is universally optimal; the best choice is non-stationary and problem-dependent. Existing adaptive portfolio methods often base their decisions on past function values while ignoring richer information like remaining budget or surrogate model characteristics. To address this, we introduce LMABO, a novel framework that casts a pre-trained Large Language Model (LLM) as a zero-shot, online strategist for the BO process. At each iteration, LMABO uses a structured state representation to prompt the LLM to select the most suitable acquisition function from a diverse portfolio. In an evaluation across 50 benchmark problems, LMABO demonstrates a significant performance improvement over strong static, adaptive portfolio, and other LLM-based baselines. We show that the LLM's behavior is a comprehensive strategy that adapts to real-time progress, proving its advantage stems from its ability to process and synthesize the complete optimization state into an effective, adaptive policy.

Nonparametric Bayesian Optimization for General Rewards

This work focuses on Bayesian optimization (BO) under reward model uncertainty. We propose the first BO algorithm that achieves no-regret guarantee in a general reward setting, requiring only Lipschitz continuity of the objective function and accommodating a broad class of measurement noise. The core of our approach is a novel surrogate model, termed as infinite Gaussian process ($\infty$-GP). It is a Bayesian nonparametric model that places a prior on the space of reward distributions, enabling it to represent a substantially broader class of reward models than classical Gaussian process (GP). The $\infty$-GP is used in combination with Thompson Sampling (TS) to enable effective exploration and exploitation. Correspondingly, we develop a new TS regret analysis framework for general rewards, which relates the regret to the total variation distance between the surrogate model and the true reward distribution. Furthermore, with a truncated Gibbs sampling procedure, our method is computationally scalable, incurring minimal additional memory and computational complexities compared to classical GP. Empirical results demonstrate state-of-the-art performance, particularly in settings with non-stationary, heavy-tailed, or other ill-conditioned rewards.

Revisiting Robustness for LLM Safety Alignment via Selective Geometry Control

Safety alignment of large language models remains brittle under domain shift and noisy preference supervision. Most existing robust alignment methods focus on uncertainty in alignment data, while overlooking optimization-induced fragility in preference-based objectives. In this work, we revisit robustness for LLM safety alignment from an optimization geometry perspective, and argue that robustness failures cannot be addressed by data-centric methods alone. We propose ShaPO, a geometry-aware preference optimization framework that enforces worst-case alignment objectives via selective geometry control over alignment-critical parameter subspace. By avoiding uniform geometry constraints, ShaPO mitigates the over-regularization that can harm robustness under distribution shift. We instantiate ShaPO at two levels: token-level ShaPO stabilizes likelihood-based surrogate optimization, while reward-level ShaPO enforces reward-consistent optimization under noisy supervision. Across diverse safety benchmarks and noisy preference settings, ShaPO consistently improves safety robustness over popular preference optimization methods. Moreover, ShaPO composes cleanly with data-robust objectives, yielding additional gains and empirically supporting the proposed optimization-geometry perspective.

Fine-Grained Model Merging via Modular Expert Recombination

Model merging constructs versatile models by integrating task-specific models without requiring labeled data or expensive joint retraining. Although recent methods improve adaptability to heterogeneous tasks by generating customized merged models for each instance, they face two critical limitations. First, the instance-specific merged models lack reusability, restricting the exploitation of high-quality merging configurations and efficient batch inference. Second, these methods treat each task-specific model as a monolithic whole, overlooking the diverse mergeability of homologous components such as attention and multilayer perceptron layers, and the differing merging sensitivities across components. To address these limitations, we propose MERGE (\underline{M}odular \underline{E}xpert \underline{R}ecombination for fine-\underline{G}rained m\underline{E}rging), a method that enables component-wise model merging and input-aware, on-demand module recombination at inference. MERGE formulates component-wise merging as a bi-objective optimization problem that balances cross-task performance and storage efficiency, and develops a surrogate-assisted evolutionary algorithm to efficiently identify Pareto-optimal merging configurations. These high-quality configurations underpin a reusable modular expert library, from which a lightweight routing network dynamically activates and recombines modular experts to assemble input-specific models and enable efficient inference under storage constraints. Extensive experiments across various model scales, task types, and fine-tuning strategies demonstrate that MERGE consistently outperforms strong baselines and generalizes effectively.