measure model fidelity

Multi-fidelity modeling faces the core challenge of scarce and expensive high-fidelity (HF) data versus abundant yet biased low-fidelity (LF) data. This paper proposes a generic three-stage framework: (1) using a deterministic LF model as the foundation, (2) enabling cross-fidelity knowledge transfer via transfer learning, and (3) quantifying residual uncertainty through Bayesian residual modeling. It is the first to reveal the complementary expressive power between transfer learning and Bayesian modeling, unifying treatment of both noisy and noise-free multi-fidelity settings while substantially simplifying existing approaches. Technically, it supports flexible combinations—e.g., kernel ridge regression or deep neural networks for LF modeling, and Gaussian processes or Bayesian neural networks for HF modeling—under a staged training strategy. Extensive benchmark experiments demonstrate significant improvements over state-of-the-art methods in prediction accuracy, uncertainty calibration, and computational efficiency, achieving both theoretical rigor and engineering practicality.

This paper addresses Gaussian process regression modeling with non-nested, noisy multi-fidelity data. We propose an efficient, scalable multi-fidelity surrogate model that abandons the conventional recursive autoregressive assumption and instead introduces parameterized linear predictors, for which we derive closed-form update rules and integrate an expectation-maximization (EM) algorithm to estimate high-fidelity hyperparameters. A decoupled optimization strategy is further designed to substantially reduce computational complexity. Our key contributions are threefold: (i) the first method supporting simultaneous non-nested data structures and observation noise in multi-source fusion; (ii) a theoretically grounded analytical framework for learning closed-form solutions; and (iii) consistent superiority over state-of-the-art approaches in both prediction accuracy and training efficiency across multiple benchmarks and real-world tasks, with systematic experiments confirming strong generalizability and scalability.

Model fidelity—the degree of correspondence between simulation and reality—lacks a formal, axiomatic foundation in digital engineering, resulting in ambiguous evaluation criteria and poor cross-domain comparability. Method: This paper introduces the first rigorous, verifiable theoretical framework for fidelity assessment, grounded in seven foundational axioms encompassing consistency, measurability, scale invariance, and other essential properties; the framework enables formal verification and comparative analysis of fidelity metrics. Empirical validation is conducted via integration into ground-vehicle modeling, demonstrating feasibility and practical guidance within existing evaluation paradigms. Contribution/Results: The work fills a critical theoretical gap in fidelity science and establishes a universal, standards-ready paradigm for fidelity assessment—directly advancing digital twin development, simulation verification and validation (V&V), and model-based systems engineering. It further provides a clear, principled roadmap for future methodological evolution and standardization.

In multi-fidelity Gaussian process Bayesian optimization, fidelity selection is complex, high-fidelity evaluations are prohibitively expensive, and existing strategies lack consistency. To address these challenges, this paper proposes a unified multi-fidelity acquisition framework grounded in proximity. Its core contributions are: (1) a tunable multi-fidelity upper confidence bound (MF-UCB) strategy that explicitly controls the frequency of high-fidelity evaluations; and (2) a weighted proximity-based acquisition function that jointly optimizes fidelity selection and candidate point selection by integrating information from all fidelity-level surrogate models. Evaluated on chemical kinetics optimization tasks—including homogeneous and heterogeneous catalysis—the method achieves significantly faster convergence while reducing high-fidelity evaluations by 30–50%, striking a superior trade-off between exploration efficiency and evaluation cost.

This work addresses the challenge that high-fidelity data are scarce and costly, while abundant low-fidelity data lack sufficient accuracy, thereby limiting surrogate model performance. To overcome this, the authors propose a probabilistic multi-fidelity surrogate framework that integrates transfer learning with generative modeling. Built upon a normalizing flow architecture incorporating surjective layers, the model is first pre-trained on extensive low-fidelity data and then fine-tuned with only a small amount of high-fidelity data, enabling efficient knowledge transfer and uncertainty quantification. This approach transcends the dimensional constraints of conventional bijective flows by supporting learnable dimensionality reduction while preserving exact likelihood-based training, marking the first deep integration of generative AI into multi-fidelity modeling. Validated on ballasted railway sleeper and reinforced concrete slab systems, the method achieves highly accurate probabilistic predictions using minimal high-fidelity simulations, significantly outperforming low-fidelity-only baselines.

This study addresses the challenges of high data requirements and ineffective fusion of multi-source, heterogeneous (multi-fidelity) data in agent-based modeling for manufacturing systems. The authors propose a hierarchical multi-task, multi-fidelity Gaussian process framework that decomposes each task’s response into a shared global trend and task-specific local residuals. By jointly modeling inter-task similarities and fidelity-level relationships, the approach enables efficient data fusion and rigorous uncertainty quantification. Notably, this work presents the first unified integration of multi-task learning and multi-fidelity modeling, accommodating an arbitrary number of tasks, design points, and fidelity levels. In both synthetic benchmarks and a real-world engine surface topography prediction case, the method achieves up to 19% and 23% higher prediction accuracy, respectively, compared to state-of-the-art multi-task models and independent stochastic kriging approaches.

This work addresses the challenge of high computational cost associated with high-fidelity simulations, which hinders extensive evaluation. To overcome this limitation, the authors propose a multi-fidelity surrogate modeling framework that integrates data of varying fidelity levels. The approach employs an ensemble of hierarchical Kriging models as base learners, whose predictions are combined via Bayesian model averaging. Crucially, the method introduces an innovative uncertainty quantification mechanism based on inter-model variance, which informs an adaptive sampling strategy to optimize the selection of training samples. Evaluated on multiple benchmark problems, the proposed framework consistently outperforms single-model approaches, achieving superior prediction accuracy, enhanced robustness, and improved data efficiency under constrained computational budgets.

This work addresses the challenge of constructing high-accuracy surrogate models in scenarios where high-fidelity data are scarce. We propose a novel multi-fidelity Gaussian process regression method that innovatively embeds low-fidelity data as augmented features into an expanded input space, thereby synergistically combining the strengths of co-kriging and autoregressive modeling. The approach achieves a balanced trade-off between modeling accuracy and computational efficiency within a unified framework, effectively leveraging heterogeneous multi-source data without requiring additional assumptions. Experimental results across multiple benchmark problems demonstrate that the proposed method significantly outperforms existing techniques, delivering higher predictive accuracy at lower computational cost.

This study addresses the challenge of evaluating whether open-source language models can effectively serve as proxies to interpret the behavior of closed-source large language models when internal access is unavailable. Employing API-compatible methods—including log-odds probing, leave-one-out attribution, attention analysis, and input ablation—the authors conduct cross-model comparisons across 11 models spanning four major families: Llama, Qwen, GPT, and Gemini. Their findings reveal that predictive consistency substantially exceeds attribution consistency across model pairs. While white-box signals exhibit stability, they often fail to accurately reflect underlying causal mechanisms; in contrast, black-box input ablation more reliably captures the attribution behavior of closed-source models. These results uncover an “access-effectiveness inversion,” demonstrating that alignment in predictions alone is insufficient to support the transferability of mechanistic interpretations.

This study addresses the high computational cost of high-fidelity modeling in composite materials, which arises from their multiscale nature, anisotropy, and coupling with manufacturing history, thereby hindering efficient design space exploration. To overcome this challenge, the work proposes a unified multifidelity surrogate modeling paradigm that systematically integrates co-kriging, autoregressive Gaussian processes, multifidelity deep Gaussian processes, and multifidelity neural networks. A general analytical framework is developed to model cross-fidelity correlations, characterize approximation errors, and quantify uncertainties. By effectively fusing abundant low-fidelity data with scarce high-fidelity observations, the proposed approach significantly enhances both predictive accuracy and computational efficiency. The methodology has been successfully demonstrated in forward design, inverse parameter identification, and heterogeneous data-driven engineering optimization workflows for composite materials.