Multi-Fidelity

Many LLM inference problems, including model routing, prefix-cache management, prompt trimming, and test-time search, can be viewed as optimization over a tree. This structure arises naturally from autoregressive generation: every prefix defines a node, and its continuations form a subtree below it. Internal nodes of the tree provide cheap but biased estimates of a region's value, while leaf evaluations are expensive but accurate. Hierarchical bandit methods can exploit this structure, but typically require a specific smoothness schedule to be specified in advance, even though real objectives are often only piecewise smooth and their optima may lie near sharp boundaries. We introduce CANOPY, a multi-fidelity tree bandit that learns where the smoothness prior is valid rather than assuming it globally. CANOPY uses cheap random-path probes to construct an online certificate of local aggregation bias, then directs expensive leaf evaluations toward cells where the certificate detects a smoothness violation. We prove fixed-budget and regret guarantees whose additional cost is additive in the number of discontinuities, recovering the smooth-tree rate when no violations are present and approaching structure-blind search as violations become dense. Across routing, top-$k$ identification, test-time search, caching, and prompt trimming, CANOPY consistently improves matched-budget performance, including $2.9\times$ higher top-10 recall on a 1000-model pool, $1.6\times$ more SWE-bench Verified issues resolved than best-of-$N$, and $3.6\times$ lower median time-to-first-token with prefix caching.

Many real-world optimization problems rely on expensive simulations or experiments, making the efficient use of available data essential. Multi-fidelity optimization of high-dimensional black-box functions subject to black-box constraints is increasingly relevant as the cost of objective evaluations continues to rise in applications such as machine learning, engineering, and control. To our knowledge, no existing method simultaneously addresses high-dimensionality, black-box constraints, an arbitrary number of fidelity levels, and non-nested sampling. In this work, we extend the Scalable Constrained Bayesian Optimization method to the multi-fidelity setting, resulting in the MF-SCBO method. The proposed approach is evaluated on standard benchmark functions as well as challenging problems. The experimental results demonstrate that MF-SCBO generally achieves better convergence than both the single-fidelity SCBO and the other multi-fidelity method considered in this high-dimensional and constrained settings.

Human feedback can vary in cost and informativeness. Strong feedback can reveal severe errors but is costly, so cheaper quality ratings can help decide which items to annotate. We propose MICRO (Multi-Fidelity Impact Clustered Rollout), an active search framework that allocates a shared budget to these feedback types to maximise confirmed severe error discoveries. MICRO jointly models ratings and annotation losses conditional on item features to steer acquisition. It clusters acquisitions by their predicted impact on severity probabilities to select diverse candidates, then uses rollout to estimate their discovery value. Experiments on WMT20 English-German show that ratings improve both loss reconstruction and severity prediction. MICRO achieves the highest mean discovery count across four budget and rating cost settings, with similar performance to adapted MF-ENS in one and significant gains over all six comparison policies, including two rollout controls, in the other three $(p<.001)$.

Optimizing industrial process flowsheets is often computationally prohibitive due to the high cost of rigorous simulations and the curse of dimensionality inherent in complex design spaces. To address these challenges, we present a reduced-space multi-fidelity Bayesian optimization (RS-MFBO) framework designed for high-dimensional, expensive black-box functions. The approach integrates Global Sensitivity Analysis (GSA) for dimensionality reduction with a fidelity-augmented Gaussian process that captures correlations between low-cost approximations and expensive high-fidelity evaluations. A cost-aware acquisition strategy, augmented with cooldown and promotion mechanisms, adaptively guides the allocation of samples across fidelities. The framework is validated on two distinct industrial process simulators: a plasmid DNA bioprocess in SuperPro Designer and a green fuel synthesis plant in Aspen HYSYS. Results across diverse economic and physical objectives demonstrate that the proposed method substantially reduces the number of high-fidelity simulator evaluations while maintaining competitive optimization performance compared to single-fidelity baselines. These results highlight RS-MFBO as a scalable, simulator-agnostic approach for cost-constrained black-box optimization.

Multi-object tracking (MOT) is dominated by the tracking-by-detection paradigm, whose methods typically rely on a small set of hyperparameters that are conventionally chosen by hand. Tuning them requires repeated expert-guided experimentation, while the procedures used to select reported values are often not systematically evaluated or fully documented. Hyperparameter optimization (HPO) automates this process, yet it remains rarely used in MOT, and existing studies applying HPO to MOT predate modern deep-detector-based trackers and HOTA evaluation. We systematically apply HPO across two datasets and four tracking-by-detection methods. We also propose Multi-Fidelity Greedy Coordinate Search (MFGCS), which optimizes one hyperparameter at a time by first evaluating candidate values on a small subset of scenes and re-evaluating only promising candidates on the full dataset. Across all eight tracker-dataset combinations, the Tree-structured Parzen Estimator (TPE) and MFGCS outperform both our hand-tuned configurations and the corresponding published results, with improvements of up to 4.38 and 16.05 HOTA points, respectively. MFGCS also reaches a predefined HOTA target faster than TPE in seven of the eight combinations. Within each tracker-dataset pair, all optimizers share the same search space and evaluation pipeline, isolating the effect of the search strategy. We release the code and tuned configurations to enable future work to compare against systematically optimized rather than default or manually tuned baselines.

Black-box optimization is a ubiquitous problem in science and engineering, often dealing with expensive objective functions with cheaper lower-fidelity proxies available. Multi-fidelity Bayesian optimization (MF-BO) is a principled approach to this problem, leveraging correlations across different fidelities when querying the objective. However, for many important MF-BO tasks, the true highest-fidelity function is prohibitively expensive to be part of the optimization loop. Nevertheless, practitioners often have gold standard data (observations of the highest-fidelity function) obtained from previous experiments that might provide information for the current task. For instance, in molecular optimization, chemists often pick the top-$k$ candidate molecules using various computer simulations, and later reveal their true objective function values. In this work, we demonstrate the suboptimality of standard MF-BO algorithms in the real-world scenarios above, even under ideal assumptions. Next, we mitigate this problem by incorporating historical high-fidelity data accompanied by task descriptors---which can be explicitly given or extracted from unstructured metadata. We demonstrate the effectiveness of our methods on synthetic functions, as well as real-world problems in chemistry and hyperparameter optimization.

This study presents a multi-fidelity framework for the systematic optimization of genetic algorithm (GA) hyperparameters. The framework integrates three fidelity levels: high-fidelity Fast Fourier Transform (FFT) homogenization for validation, a medium-fidelity 3D convolutional neural network surrogate for rapid property evaluation, and a low-fidelity Gaussian process (GP) surrogate within a Bayesian optimization (BO) framework to guide the hyperparameter search. Various acquisition functions are evaluated, with logNEI achieving the best performance by effectively accounting for the noise inherent in GA evaluations. The proposed framework identifies hyperparameter configurations that enable a 25-generation GA run to achieve elastic modulus values comparable to those obtained in a full 75-generation optimization. Furthermore, introducing a penalized BO objective significantly reduces the number of required lattices with only minor decreases in absolute achieved elastic modulus, revealing a practical trade-off between performance and the number of structures that must be evaluated. High-fidelity FFT validation verifies the effectiveness of the surrogate-driven optimization strategy. The optimized hyperparameters allow for rapid convergence, eliminate the need for lattice mutation, and reduce the overall computational cost by 24% (from 225 to 171 hours) while preserving mechanical performance. These results demonstrate the potential of multi-fidelity optimization as an efficient and practical approach for GA hyperparameter tuning and future experimental lattice design studies.

Background. The widespread deployment of ambient digital scribes is driving large-scale capture of clinician-patient dialogues. Human coding of clinical communication data remains costly, inconsistent, and difficult to scale, motivating AI-driven communication coding systems. However, evaluating these systems requires real-world dialogues and human-coded labels, both hard to obtain at scale. Methods. We developed SIMAX (Scalable and Interpretable Framework for Multi-Fidelity and Annotated Clinician-Patient Dialogue Simulation), a framework for generating controlled clinical dialogue data with reference behavioral annotations. SIMAX generates clinician-patient dialogues from predefined clinical scenarios, personas and voice conditions, and target communication behaviors. Behaviors are controlled using two codebooks: the Global Codebook for overall communication quality and the WISER Codebook for specific countable behaviors. We evaluated SIMAX using automated and human quality assessments and an example communication coding system. Results. SIMAX generated 3,388 simulated dialogues across three specialties, multiple visit stages, persona characteristics, and accent conditions. Automated assessment showed mean UTMOS and WV-MOS scores of 3.03 and 2.61, WER and CER of 0.07 and 0.05, and CLAP cosine similarity of 0.41, suggesting reasonable speech naturalness, high transcription fidelity, and positive text-audio correspondence. Human evaluation showed a median MOS of 4.67 and a median clinical realism score of 3.00. Downstream evaluation suggests that SIMAX can assess how a communication coding system responds to behavioral targets and reveal insufficient sensitivity in some dimensions. Conclusions. SIMAX generates controlled and reproducible simulated clinician-patient dialogues, providing a data foundation for developing, validating, and refining communication coding systems.

Guided wave-based structural health monitoring (GWSHM) with onboard transducers offers significant potential for the early diagnosis of damage in engineering structures. However, the practical deployment of deep learning models is often hindered by the limited availability of labelled experimental data and the high computational cost of generating large-scale high-fidelity simulation datasets. This study presents a multifidelity transfer learning framework that integrates lightweight physics-based simulations, convolutional autoencoder (CAE)-based deep feature learning, a feed-forward neural network, and limited experimental measurements for accurate damage localisation and sizing in plate-like structures instrumented with piezoelectric transducers. A computationally efficient one-dimensional time-domain spectral element model is employed to generate a large synthetic dataset for pretraining, while transfer learning adapts the model to experimental domains using only a small amount of labelled data. The CAE-based transfer learning framework significantly outperforms its CNN-based counterpart in damage localisation accuracy. The model achieves excellent predictive performance with $R^2$ scores exceeding 0.93 for damage localisation and 0.99 for damage sizing. Its generalisation capability is demonstrated on previously unseen data, showing high prediction accuracy for damage scenarios not represented during pretraining or fine-tuning. The results establish the proposed framework as an accurate, computationally efficient, and practically viable solution for real-world GWSHM applications.

How fast could a deep-learning model run on target hardware, and how far is today's implementation from that limit? These questions are central to software, hardware, and algorithm optimizations. Speed-of-Light (SOL) analysis answers them by computing a workload's theoretical minimum execution time on a given architecture. Yet deriving SOL bounds remains manual, error-prone, and disconnected from rapid model development. To close this gap, we introduce SOLAR, a framework that automatically derives validated SOL bounds from PyTorch and JAX source code. SOLAR leverages both generative and deterministic components in its flow: an LLM frontend translates any source programs into an executable Affine Loop IR, validated by output comparison; a deterministic flow lifts the IR into an einsum graph; and an analytical backend computes unfused, fused, and cache-aware SOL bounds. SOLAR provides comprehensive operator and language coverage, produces validated bounds with zero observed SOL violations, and offers multi-fidelity analysis that tightens bounds and surfaces optimization insights. We evaluate SOLAR across KernelBench, JAX/Flax models, and robotics workloads. These experiments demonstrate four use cases: headroom analysis at multiple fidelity levels, identifying optimization opportunities, cross-platform exploration, and inverse-roofline hardware provisioning.

This paper presents a scalable framework for multi-robot task allocation in complex environments where estimating task execution costs is computationally expensive. While combinatorial auction-based approaches offer reliable solutions, the exponential complexity of bundle generation typically renders them intractable for real-time reactive applications, particularly when accurate path planning is required for cost validation. We address this through a distributed, two-stage multi-fidelity bundle generation approach. Agents utilize a local search tree guided by a low-fidelity heuristic (such as euclidean distance) to rapidly explore the bundle space, applying high-fidelity path planning only to the most promising candidates in a best-first manner. These refined bids are then submitted to a central coordinator that solves a set packing problem to ensure global feasibility and maximize the overall utility. Simulation results in multiple environments demonstrate that the framework is able to improve the performance of reactive auction-based task allocation. Overall, the presented framework is shown to enable reactive task allocation with dynamic bundle sizes in multiple settings without exposing the agents' state and internal cost estimation models.

We perform a realistic KiDS-Legacy mock analysis with field-level neural compression and simulation-based inference using just 60 $N$-body simulations. The weak lensing shear field encodes substantially more cosmological information than standard two-point summary statistics such as the power spectrum. Field-level inference can fully exploit this information, but physical realism at the field-level requires very high-fidelity simulations. This poses a major challenge for simulation-based inference (SBI): accurate empirical density modelling and deep-learning-based neural compression require tens of thousands of training samples, but achieving physical realism at the field level makes each simulation extremely costly. We demonstrate that multifidelity SBI can alleviate this tension by substantially reducing the number of high-fidelity simulations needed for accurate cosmological inference. We pre-train neural inference models on realistic KiDS-Legacy-like shear mocks using fast log-normal \texttt{GLASS} simulations and fine-tune them on a small set of high-fidelity $N$-body simulations. We show that $60$ high-fidelity simulations are sufficient to obtain informative and well-calibrated cosmological posteriors, enabling at least an order-of-magnitude reduction in simulation cost for accurate field-level inference in a realistic setting.

Woody breast (WB) is a myopathy in modern broiler chickens that causes the breast muscle to become unusually stiff and fibrous, leading to decreased meat quality and significant economic losses. State-of-the-art automated WB detection relies on a side-view imaging system to analyze the bending behavior of a single fillet as it falls off a conveyor belt. While highly accurate, this approach is constrained by its single-fillet field of view, creating throughput bottlenecks on commercial processing lines. In this paper, we address this limitation via a novel multi-fillet detection architecture utilizing a top-down camera configuration. To validate our approach, we first develop a high-fidelity digital twin of an industrial conveyor system. Next, we synthesize a diverse dataset of 3D fillet meshes and model their viscoelastic bending dynamics using a physics-based simulation engine. Lastly, a continuous 2D shape deformation score is extracted from the top-down perspective as the simulated fillets traverse the roller precipice. Experimental results demonstrate that the top-down shape score effectively captures the contour changes of the fillets as it bends, providing a robust and scalable alternative to a side-view imaging system for simultaneous multi-fillet WB evaluation.

Machine learning has accelerated quantum chemistry but is hindered by the prohibitive cost of generating high fidelity training data. Multifidelity machine learning (MFML) mitigates this overhead by systematically combining abundant low fidelity data with sparse high fidelity data. In spite of its success, standard MFML schemes rely on pre-defined scaling factors to determine sparse data ratio across fidelities, often generating redundant multifidelity data resulting in a loss of efficiency. Here, we introduce an adaptive on-the-fly multifidelity framework for machine learning that autonomously determines training dataset composition. By dynamically querying training samples at each fidelity, the algorithm saturates model accuracy at lower fidelities before moving up to more expensive reference calculations. We benchmark the novel adaptive-MFML across diverse chemical properties including the computational chemistry gold standard coupled cluster energies, and the more chemically challenging excitation energies. In our numerical experiments we show that our adaptive algorithm reduces data generation costs by up to a factor of 30 compared to single fidelity methods and improves upon standard MFML by up to a factor of 5. The mitigation of data redundancy establishes a high-accuracy low-cost pathway for sustainable cost-aware machine learning in quantum chemistry.

Reduced-order models (ROMs) provide an efficient surrogate for complex multiscale systems, but their predictive accuracy is often compromised by truncation errors and the inadequate representation of interactions between resolved and unresolved scales. The missing effect of truncated (unresolved) scales on ROM (resolved) scales is often denoted as the closure problem. In this work, we formulate ROM closure modeling as a multi-fidelity (MF) learning problem and propose an uncertainty-aware MF framework based on conditional normalizing flow to enhance ROM predictive accuracy. The proposed approach learns a probabilistic mapping from low-fidelity (LF) ROM coefficients to high-fidelity (HF) coefficients, thereby improving predictive fidelity while quantifying the uncertainty associated with the learned closure. Two correction strategies are investigated: direct learning, in which HF coefficients are predicted directly from LF inputs, and residual learning, which learns the discrepancy between LF and HF coefficients and uses it to recover the corrected HF solution. The framework is demonstrated on a vortex merging problem governed by the two-dimensional Navier Stokes equations. Results show that both correction strategies improve ROM accuracy over uncorrected ROM, with residual learning achieving consistently better performance than direct learning. Moreover, the two proposed deep generative model-based strategies provide uncertainty quantification for the corrected ROM coefficients, which is critical for assessing prediction confidence and supporting the reliable use of ROMs in practical applications.

In reactor physics, neutronics can be treated with different fidelity levels, according to the needs of the user. On one hand, the precise modeling of neutrons' behaviour in reactor physics is often expensive and time-consuming due to the high computational costs to numerically solve the Boltzmann transport equation. Conversely, by adopting suitable assumptions, such as the SP$_N$, diffusion theory, and point kinetics, it is possible to generate efficiently low-fidelity data. From the perspective of surrogate models, this computational limitation translates into a scarcity of high-fidelity data and a significant amount of low-fidelity data. Given this difference in fidelity levels, it would be interesting to develop a suitable procedure to map low-fidelity models towards higher fidelity models; for instance, one could obtain the solution to a multi-group diffusion equation starting from time-series data obtained from a point kinetics model. Indeed, this work investigates this possibility by leveraging multi-fidelity information with Shallow Recurrent Decoders, a novel machine learning architecture able to map time-series observations to the full state of the reactor. This technique has been designed to use local or global measurements as input and map their temporal trajectories to the high-dimensional state; by the same logic, in principle, this architecture can also be used when the input is formed by the solution of a lumped model. This work applies this idea to a benchmark reactor geometry, mapping the point kinetics model to the diffusion solution under various input conditions, with much less computational costs.

Solving nonlinear partial differential equations (PDEs) using kernel methods offers a compelling alternative to traditional numerical solvers. However, the performance of these methods strongly depends on the choice of kernel. In this work, as the available information is inherently multifidelity, we propose a kernel learning approach based on cokriging, leveraging empirical information from multifidelity simulations. In the first step, we fit a differentiable non-stationary kernel to an empirical kernel obtained from low-fidelity simulations. In the second step, we derive a high-fidelity kernel with estimated hyperparameters, and construct a corresponding high-fidelity mean using the multifidelity framework. These components can then be used within a Gaussian process framework for solving PDEs. Finally, we demonstrate the performance of the proposed physics-informed method on the Burgers' equation.

High-fidelity experimental characterization of turbulent premixed flames remains limited by the cost and complexity of advanced diagnostics, particularly under elevated pressures and intense turbulence where measurements of coupled flame morphology and burning dynamics are sparse. Here, we develop a hierarchical multi-fidelity neural network framework (MuFiNNs) to address this challenge by integrating sparse high-fidelity experimental data with structured low-fidelity representations encoding dominant physical trends. The framework combines hierarchical low-fidelity construction with nonlinear multi-fidelity correction to learn coupled geometric and reactive flame behavior while recovering discrepancies that simplified models alone cannot capture. The methodology is applied to expanding turbulent premixed flames to predict three-dimensional flame wrinkling dynamics and turbulent mass burning velocity across varying fuels, pressures, and turbulence intensities. Using experimentally informed low-fidelity trend models with sparse high-fidelity measurements, MuFiNNs accurately reconstruct observed flame behavior, enable interpolation across unseen operating conditions, and demonstrate robust extrapolation beyond the training domain. Importantly, the framework remains effective in noisy, weakly structured, or experimentally inaccessible regimes where conventional data-driven approaches often fail. These results show that hierarchical multi-fidelity learning provides a scalable and physically grounded strategy for predictive combustion modeling in data-limited regimes. More broadly, this work establishes multi-fidelity scientific machine learning as a practical framework for extracting physically meaningful predictive models from sparse experiments, particularly for instability-dominated and turbulence-sensitive reactive flows where high-fidelity data acquisition is demanding.

Atmospheric correction is a critical preprocessing step in optical remote sensing, but repeated high-fidelity radiative transfer simulations remain computationally expensive for dense look-up-table generation, sensitivity analysis, retrieval support, and operational preprocessing. This study presents a physics-aware multi-fidelity surrogate framework for emulating atmospheric correction coefficients using paired 6S and libRadtran simulations. Atmospheric and geometric states are sampled using Latin Hypercube Sampling, and both radiative transfer models are evaluated under matched conditions for Sentinel-2 bands using spectral-response-function-aware coefficient generation. The high-fidelity targets are path reflectance, total transmittance, and spherical albedo. A physics-guided Kolmogorov-Arnold Network, termed pKANrtm, receives the atmospheric state and low-fidelity 6S coefficients, predicts the residual relative to libRadtran, and reconstructs the high-fidelity coefficients. The pKANrtm model uses an Efficient-KAN architecture and is trained with a physics-consistency penalty applied in the original coefficient space. The proposed model is evaluated against state-of-the-art regression-based RTM surrogates. Across both standard and out-of-distribution evaluation settings, pKANrtm achieves the strongest overall predictive performance among the compared models. Runtime benchmarking demonstrates substantial acceleration relative to libRadtran, with GPU inference providing approximately four orders of magnitude single-sample speedup and batched inference reaching tens of thousands of samples per second. These results indicate that physics-aware multi-fidelity pKANrtm emulation provides an accurate, physically structured, and computationally efficient strategy for atmospheric correction coefficient generation.

Composite materials exhibit strongly hierarchical and anisotropic properties governed by coupled mechanisms spanning constituents, plies, laminates, structures, and manufacturing history. This intrinsic complexity makes predictive modeling of composites expensive, because repeated experiments and high-fidelity simulations are needed to cover large design spaces of material, structure, and manufacturing. Multi-fidelity surrogate modeling addresses this challenge by combining abundant, less expensive data with limited high-accuracy data to recover reliable high-fidelity predictions. This review presents a structured overview of multi-fidelity modeling for composite mechanics, covering Gaussian-process or Kriging-based methods, including co-Kriging, coregionalization models, autoregressive formulations, nonlinear autoregressive Gaussian processes, multi-fidelity deep Gaussian processes, and multi-fidelity neural networks. Their distinctions are examined in terms of cross-fidelity correlation, discrepancy representation, uncertainty quantification, and scalability. Selected examples of their applications to composites are introduced according to the roles that multi-fidelity surrogates play in engineering problems, including forward prediction for rapid exploration of material design spaces, inverse optimization for composite parameter identification and design search under limited high-fidelity access, and workflow integration, where heterogeneous data sources, constraints, and validation requirements determine model utility. Open question discussions highlight recurring challenges specific to composites, such as regime-dependent fidelity gaps associated with nonlinear damage and manufacturing history, mismatches between simulations and experiments, and uncertainty propagation across multi-fidelity models.

Modern container ships face higher wind loads due to increased windage areas, making accurate predictions of wind loads essential for mooring design. Existing empirical models, largely developed for container ships with smaller windage areas and simpler geometrical configurations than those of modern large-scale vessels, often lack accuracy and do not account for the influence of nearby structures. This study proposes a multi-fidelity surrogate modelling framework for the prediction of wind-load coefficients, combining empirical correlations with simplified and detailed CFD models for ships in open-sea and harbor environments. The approach relies on recursive co-kriging to consistently fuse information across fidelity levels, enabling accurate predictions at a reduced computational cost. A sensitivity analysis is used to identify the most influential geometric parameters, and the resulting reduced parameter space is explored through sequential sampling to efficiently construct the training database. The surrogate models are validated over a wide range of loading configurations and for two distinct harbor environments. The results demonstrate that the multi-fidelity approach significantly improves prediction accuracy compared to single-fidelity models, while substantially reducing the reliance on high-fidelity simulations. In particular, the proposed framework captures the dependence of wind loads on key geometric parameters and consistently outperforms traditional empirical correlations, providing a robust and efficient tool for engineering applications.

In multi-fidelity optimization, biased approximations of varying costs of the target function are available. This paper studies the problem of optimizing a locally smooth function with a limited budget, where the learner has to make a tradeoff between the cost and the bias of these approximations. We first prove lower bounds for the simple regret under different assumptions on the fidelities, based on a cost-to-bias function. We then present the Kometo algorithm which achieves, with additional logarithmic factors, the same rates without any knowledge of the function smoothness and fidelity assumptions, and improves previously proven guarantees. We finally empirically show that our algorithm outperforms previous multi-fidelity optimization methods without the knowledge of problem-dependent parameters.

Supervised machine learning describes the practice of fitting a parameterized model to labeled input-output data. Supervised machine learning methods have demonstrated promise in learning efficient surrogate models that can (partially) replace expensive high-fidelity models, making many-query analyses, such as optimization, uncertainty quantification, and inference, tractable. However, when training data must be obtained through the evaluation of an expensive model or experiment, the amount of training data that can be obtained is often limited, which can make learned surrogate models unreliable. In many engineering and scientific settings, cheaper low-fidelity models may be available, for example arising from simplified physics modeling or coarse grids. These models may be used to generate additional low-fidelity training data. The goal of multifidelity machine learning is to use both high- and low-fidelity training data to learn a surrogate model which is cheaper to evaluate than the high-fidelity model, but more accurate than any available low-fidelity model. This work proposes a new multifidelity training approach for Gaussian process regression which uses low-fidelity data to define additional features that augment the input space of the learned model. Similarly to cokriging estimators, the proposed approach conditions the high-fidelity surrogate model on the predictions of all available low-fidelity surrogate models, while benefiting from the computational efficiency of autoregressive estimators. Numerical experiments on several test problems demonstrate both increased predictive accuracy and reduced computational cost relative to the state of the art.

Active multi-fidelity surrogate modeling is developed for multi-condition airfoil shape optimization to reduce high-fidelity CFD cost while retaining RANS-consistent aerodynamic metrics. The framework couples a low-fidelity-informed Gaussian process regression transfer model with uncertainty-triggered sampling and a synchronized elitism rule embedded in a hybrid genetic algorithm. Low-fidelity XFOIL evaluations provide inexpensive features, while sparse RANS simulations are adaptively allocated when predictive uncertainty exceeds a threshold; elite candidates are mandatorily validated at high fidelity, and the population is re-evaluated to prevent evolutionary selection based on outdated fitness values produced by earlier surrogate states. The method is demonstrated for a two-point problem at $Re=6\times10^6$ with cruise at $α=2^\circ$ (maximize $E=L/D$) and take-off at $α=10^\circ$ (maximize $C_L$) using a 12-parameter CST representation. Independent multi-fidelity surrogates per flight condition enable decoupled refinement. The optimized design improves cruise efficiency by 41.05% and take-off lift by 20.75% relative to the best first-generation individual. Over the full campaign, RANS evaluations were required for only 14.78% and 9.5% of the condition-specific candidate evaluations at cruise and take-off, respectively. These percentages quantify the reduction in high-fidelity usage relative to the fixed automated RANS workflow adopted as the high-fidelity reference in this study.

We present a bifidelity method for uncertainty quantification of parameter estimates in complex systems, leveraging generative models trained to sample the target conditional distribution. In the Bayesian inference setting, traditional parameter estimation methods rely on repeated simulations of potentially expensive forward models to determine the posterior distribution of the parameter values, which may result in computationally intractable workflows. Furthermore, methods such as Markov Chain Monte Carlo (MCMC) necessitate rerunning the entire algorithm for each new data observation, further increasing the computational burden. Hence, we propose a novel method for efficiently obtaining posterior distributions of parameter estimates for high-fidelity models given data observations of interest. The method first constructs a low-fidelity, conditional generative model capable of amortized Bayesian inference and hence rapid posterior density approximation over a wide-range of data observations. When higher accuracy is needed for a specific data observation, the method employs adaptive refinement of the density approximation. It uses outputs from the low-fidelity generative model to refine the parameter sampling space, ensuring efficient use of the computationally expensive high-fidelity solver. Subsequently, a high-fidelity, unconditional generative model is trained to achieve greater accuracy in the target posterior distribution. Both low- and high- fidelity generative models enable efficient sampling from the target posterior and do not require repeated simulation of the high-fidelity forward model. We demonstrate the effectiveness of the proposed method on several numerical examples, including cases with multi-modal densities, as well as an application in plasma physics for a runaway electron simulation model.