This acquisition function generalizes and parallelizes previously proposed knowledge-gradient methods for single-IS Bayesian optimization [7, 8, 28, 26, 37] to MISO. We prove that this algorithm provides an asymptotically near-optimal solution.

Computational models provide crucial insights into complex biological processes such as cancer evolution, but their mechanistic nature often makes them nonlinear and parameter-rich, complicating calibration. We systematically evaluate parameter probability distributions in cell migration models using Bayesian calibration across four complementary strategies: parametric and surrogate models, each with and without explicit model discrepancy. This approach enables joint analysis of parameter uncertainty, predictive performance, and interpretability. Applied to a real data experiment of glioblastoma progression in microfluidic devices, surrogate models achieve higher computational efficiency and predictive accuracy, whereas parametric models yield more reliable parameter estimates due to their mechanistic grounding. Incorporating model discrepancy exposes structural limitations, clarifying where model refinement is necessary. Together, these comparisons offer practical guidance for calibrating and improving computational models of complex biological systems.

--Federated Learning (FL) enables edge devices to collaboratively learn a global model, but it may not perform well when clients have high data heterogeneity. In this paper, we propose a dynamic clustering algorithm for personalized federated learning system ( DC-PFL) to address the problem of data heterogeneity. DC-PFL starts with all clients training a global model and gradually groups the clients into smaller clusters for model personalization based on their data similarities. T o address the challenge of estimating data heterogeneity without exposing raw data, we introduce a discrepancy metric called model discrepancy, which approximates data heterogeneity solely based on the model weights received by the server . We demonstrate that model discrepancy is strongly and positively correlated with data heterogeneity and can serve as a reliable indicator of data heterogeneity. T o determine when and how to change grouping structures, we propose an algorithm based on the rapid decrease period of the training loss curve. Moreover, we propose a layer-wise aggregation mechanism that aggregates the low-discrepancy layers at a lower frequency to reduce the amount of transmitted data and communication costs. We conduct extensive experiments on various datasets to evaluate our proposed algorithm, and our results show that DC-PFL significantly reduces total training time and improves model accuracy compared to baselines. In recent years, there has been significant growth in intelligent applications based on deep neural networks, driven by the availability of large amounts of data collected from the Internet. However, the increasing concern about privacy and trust risks associated with this kind of data collection cannot be ignored [1].

The transfer-based black-box adversarial attack setting poses the challenge of crafting an adversarial example (AE) on known surrogate models that remain effective against unseen target models. Due to the practical importance of this task, numerous methods have been proposed to address this challenge. However, most previous methods are heuristically designed and intuitively justified, lacking a theoretical foundation. To bridge this gap, we derive a novel transferability bound that offers provable guarantees for adversarial transferability. Our theoretical analysis has the advantages of \textit{(i)} deepening our understanding of previous methods by building a general attack framework and \textit{(ii)} providing guidance for designing an effective attack algorithm. Our theoretical results demonstrate that optimizing AEs toward flat minima over the surrogate model set, while controlling the surrogate-target model shift measured by the adversarial model discrepancy, yields a comprehensive guarantee for AE transferability. The results further lead to a general transfer-based attack framework, within which we observe that previous methods consider only partial factors contributing to the transferability. Algorithmically, inspired by our theoretical results, we first elaborately construct the surrogate model set in which models exhibit diverse adversarial vulnerabilities with respect to AEs to narrow an instantiated adversarial model discrepancy. Then, a \textit{model-Diversity-compatible Reverse Adversarial Perturbation} (DRAP) is generated to effectively promote the flatness of AEs over diverse surrogate models to improve transferability. Extensive experiments on NIPS2017 and CIFAR-10 datasets against various target models demonstrate the effectiveness of our proposed attack.

Digital twins have been actively explored in many engineering applications, such as manufacturing and autonomous systems. However, model discrepancy is ubiquitous in most digital twin models and has significant impacts on the performance of using those models. In recent years, data-driven modeling techniques have been demonstrated promising in characterizing the model discrepancy in existing models, while the training data for the learning of model discrepancy is often obtained in an empirical way and an active approach of gathering informative data can potentially benefit the learning of model discrepancy. On the other hand, Bayesian experimental design (BED) provides a systematic approach to gathering the most informative data, but its performance is often negatively impacted by the model discrepancy. In this work, we build on sequential BED and propose an efficient approach to iteratively learn the model discrepancy based on the data from the BED. The performance of the proposed method is validated by a classical numerical example governed by a convection-diffusion equation, for which full BED is still feasible. The proposed method is then further studied in the same numerical example with a high-dimensional model discrepancy, which serves as a demonstration for the scenarios where full BED is not practical anymore. An ensemble-based approximation of information gain is further utilized to assess the data informativeness and to enhance learning model discrepancy. The results show that the proposed method is efficient and robust to the active learning of high-dimensional model discrepancy, using data suggested by the sequential BED. We also demonstrate that the proposed method is compatible with both classical numerical solvers and modern auto-differentiable solvers.

We consider Bayesian methods for multi-information source optimization (MISO), in which we seek to optimize an expensive-to-evaluate black-box objective function while also accessing cheaper but biased and noisy approximations ("information sources"). We present a novel algorithm that outperforms the state of the art for this problem by using a Gaussian process covariance kernel better suited to MISO than those used by previous approaches, and an acquisition function based on a one-step optimality analysis supported by efficient parallelization. We also provide a novel technique to guarantee the asymptotic quality of the solution provided by this algorithm. Experimental evaluations demonstrate that this algorithm consistently finds designs of higher value at less cost than previous approaches.

Active learning (AL) has achieved great success by selecting the most valuable examples from unlabeled data. However, they usually deteriorate in real scenarios where open-set noise gets involved, which is studied as open-set annotation (OSA). In this paper, we owe the deterioration to the unreliable predictions arising from softmax-based translation invariance and propose a Dirichlet-based Coarse-to-Fine Example Selection (DCFS) strategy accordingly. Our method introduces simplex-based evidential deep learning (EDL) to break translation invariance and distinguish known and unknown classes by considering evidence-based data and distribution uncertainty simultaneously. Furthermore, hard known-class examples are identified by model discrepancy generated from two classifier heads, where we amplify and alleviate the model discrepancy respectively for unknown and known classes. Finally, we combine the discrepancy with uncertainties to form a two-stage strategy, selecting the most informative examples from known classes. Extensive experiments on various openness ratio datasets demonstrate that DCFS achieves state-of-art performance.

This work presents a novel data-driven multi-layered planning and control framework for the safe navigation of a class of unmanned ground vehicles (UGVs) in the presence of unknown stationary obstacles and additive modeling uncertainties. The foundation of this framework is a novel robust model predictive planner, designed to generate optimal collision-free trajectories given an occupancy grid map, and a paired ancillary controller, augmented to provide robustness against model uncertainties extracted from learning data. To tackle modeling discrepancies, we identify both matched (input discrepancies) and unmatched model residuals between the true and the nominal reduced-order models using closed-loop tracking errors as training data. Utilizing conformal prediction, we extract probabilistic upper bounds for the unknown model residuals, which serve to construct a robustifying ancillary controller. Further, we also determine maximum tracking discrepancies, also known as the robust control invariance tube, under the augmented policy, formulating them as collision buffers. Employing a LiDAR-based occupancy map to characterize the environment, we construct a discrepancy-aware cost map that incorporates these collision buffers. This map is then integrated into a sampling-based model predictive path planner that generates optimal and safe trajectories that can be robustly tracked by the augmented ancillary controller in the presence of model mismatches. The effectiveness of the framework is experimentally validated for autonomous high-speed trajectory tracking in a cluttered environment with four different vehicle-terrain configurations. We also showcase the framework's versatility by reformulating it as a driver-assist program, providing collision avoidance corrections based on user joystick commands.

A digital twin is a computer model that represents an individual, for example, a component, a patient or a process. In many situations, we want to gain knowledge about an individual from its data while incorporating imperfect physical knowledge and also learn from data from other individuals. In this paper, we introduce a fully Bayesian methodology for learning between digital twins in a setting where the physical parameters of each individual are of interest. A model discrepancy term is incorporated in the model formulation of each personalized model to account for the missing physics of the low-fidelity model. To allow sharing of information between individuals, we introduce a Bayesian Hierarchical modelling framework where the individual models are connected through a new level in the hierarchy. Our methodology is demonstrated in two case studies, a toy example previously used in the literature extended to more individuals and a cardiovascular model relevant for the treatment of Hypertension. The case studies show that 1) models not accounting for imperfect physical models are biased and over-confident, 2) the models accounting for imperfect physical models are more uncertain but cover the truth, 3) the models learning between digital twins have less uncertainty than the corresponding independent individual models, but are not over-confident.

The conventional approach to Bayesian decision-theoretic experiment design involves searching over possible experiments to select a design that maximizes the expected value of a specified utility function. The expectation is over the joint distribution of all unknown variables implied by the statistical model that will be used to analyze the collected data. The utility function defines the objective of the experiment where a common utility function is the information gain. This article introduces an expanded framework for this process, where we go beyond the traditional Expected Information Gain criteria and introduce the Expected General Information Gain which measures robustness to the model discrepancy and Expected Discriminatory Information as a criterion to quantify how well an experiment can detect model discrepancy. The functionality of the framework is showcased through its application to a scenario involving a linearized spring mass damper system and an F-16 model where the model discrepancy is taken into account while doing Bayesian optimal experiment design.