Surrogate Modeling

High-fidelity simulations and complex inverse problems, such as detector modeling and unfolding, are computationally intensive bottlenecks across subatomic physics, yet essential for accurate physical interpretation. While Conditional Flow Matching (CFM) offers a robust acceleration approach, we demonstrate its standard training loss is fundamentally misleading. Specifically, utilizing a Jefferson Lab Nuclear Physics (NP) kinematic dataset ($γp \to ρ^0 p \to π^+π^- p$), we expose that CFM loss plateaus prematurely, obscuring ongoing physical refinement. To verify this disconnect is a dataset-agnostic pathology, we introduce ScatterPrism, an efficient generative surrogate evaluated against both the NP data and synthetic stress tests modeling challenging 1D distribution topologies. Coupling these benchmarks, we establish that physics-informed metrics continue improving long after standard loss converges. Consequently, we propose a multi-metric diagnostic protocol to ensure true kinematic fidelity without data memorization. Driven by NP challenges relevant to the forthcoming Electron-Ion Collider (EIC), this unified machinery has strong potential to extend to High-Energy Physics (HEP) applications, such as jet modeling. Furthermore, the framework holds promise for broader domains requiring rigorous generative reliability, including medical imaging, astrophysics, and quantitative finance.

We consider the problem of constructing surrogate operators for parameter-to-solution maps arising from parametric partial differential equations, where repeated forward model evaluations are computationally expensive. We present a systematic empirical comparison of neural operator surrogates, including a reduced-basis neural operator trained with $L^2_μ$ and $H^1_μ$ objectives and the Fourier neural operator, against polynomial surrogate methods, specifically a reduced-basis sparse-grid surrogate and a reduced-basis tensor-train surrogate. All methods are evaluated on a linear parametric diffusion problem and a nonlinear parametric hyperelasticity problem, using input fields with algebraically decaying spectral coefficients at varying rates of decay $s$. To enable fair comparisons, we analyze ensembles of surrogate models generated by varying hyperparameters and compare the resulting Pareto frontiers of cost versus approximation accuracy, decomposing cost into contributions from data generation, setup, and evaluation. Our results show that no single method is universally superior. Polynomial surrogates achieve substantially better data efficiency for smooth input fields ($s \geq 2$), with convergence rates for the sparse-grid surrogate in agreement with theoretical predictions. For rough inputs ($s \leq 1$), the Fourier neural operator displays the fastest convergence rates. Derivative-informed training consistently improves data efficiency over standard $L^2_μ$ training, providing a competitive alternative for rough inputs in the low-data regime when Jacobian information is available at reasonable cost. These findings highlight the importance of matching the surrogate methodology to the regularity of the problem as well as accuracy demands and computational constraints of the application.

We develop a machine learning (ML) surrogate model to approximate solutions to Maxwell's equations in one dimension, focusing on scenarios involving a material interface that reflects and transmits electro-magnetic waves. Derived from high-fidelity Finite Volume (FV) simulations, our training data includes variations of the initial conditions, as well as variations in one material's speed of light, allowing for the model to learn a range of wave-material interaction behaviors. The ML model autoregressively learns both the physical and frequency embeddings in a vision transformer-based framework. By incorporating Fourier transforms in the latent space, the wave number spectra of the solutions aligns closely with the simulation data. Prediction errors exhibit an approximately linear growth over time with a sharp increase at the material interface. Test results show that the ML solution has adequate relative errors below $10\%$ in over $75$ time step rollouts, despite the presence of the discontinuity and unknown material properties.

The Linear Parameter-Varying (LPV) framework enables the construction of surrogate models of complex nonlinear and high-dimensional systems, facilitating efficient stability and performance analysis together with controller design. Despite significant advances in data-driven LPV modelling, existing approaches do not quantify the uncertainty of the obtained LPV models. Consequently, assessing model reliability for analysis and control or detecting operation outside the training regime requires extensive validation and user expertise. This paper proposes a Bayesian approach for the joint estimation of LPV state-space models, including their scheduling map, together with characterization of the model uncertainty and confidence bounds on the predicted model response directly from input-output data. Both aleatoric uncertainty due to measurement noise and epistemic uncertainty arising from limited training data and structural bias are considered. The resulting model preserves the LPV structure required for controller synthesis while enabling computationally efficient simulation and uncertainty propagation. The approach is demonstrated on the surrogate modelling of a two-dimensional nonlinear interconnection of mass-spring-damper systems.

High-density through-substrate vias (TSVs) enable 2.5D/3D heterogeneous integration but introduce significant signal-integrity and thermal-reliability challenges due to electrical coupling, insertion loss, and self-heating. Conventional full-wave finite-element method (FEM) simulations provide high accuracy but become computationally prohibitive for large design-space exploration. This work presents a scalable electro--thermal modeling and optimization framework that combines physics-informed analytical modeling, graph neural network (GNN) surrogates, and full-wave sign-off validation. A multi-conductor analytical model computes broadband S-parameters and effective anisotropic thermal conductivities of TSV arrays, achieving $5\%$--$10\%$ relative Frobenius error (RFE) across array sizes up to $15\times15$. A physics-informed GNN surrogate (TSV-PhGNN), trained on analytical data and fine-tuned with HFSS simulations, generalizes to larger arrays with mean RFE below $5\%$ in-distribution. The surrogate is integrated into a multi-objective Pareto optimization framework targeting reflection coefficient, insertion loss, worst-case crosstalk (NEXT/FEXT), and effective thermal conductivity. Millions of TSV configurations can be explored within minutes, enabling exhaustive layout and geometric optimization that would be infeasible using FEM alone. Final designs are validated with Ansys HFSS and Mechanical, showing strong agreement. The proposed framework enables rapid electro--thermal co-design of TSV arrays while reducing per-design evaluation time by more than six orders of magnitude.

We study training-free flow matching between two Gaussian mixture models (GMMs) using explicit velocity fields that transport one mixture into the other over time. Our baseline approach constructs component-wise Gaussian paths with affine velocity fields satisfying the continuity equation, which yields to a closed-form surrogate for the pairwise kinetic transport cost. In contrast to the exact Gaussian Wasserstein cost, which relies on matrix square-root computations, the surrogate admits a simple analytic expression derived from the kinetic energy of the induced flow. We then analyze how closely this surrogate approximates the exact cost. We prove second-order agreement in a local commuting regime and derive an explicit cubic error bound in the local commuting regime. To handle nonlocal regimes, we introduce a path-splitting strategy that localizes the covariance evolution and enables piecewise application of the bound. We finally compare the surrogate with an exact construction based on the Gaussian Wasserstein geodesic and summarize the results in a practical regime map showing when the surrogate is accurate and the exact method is preferable.

This study presents a probabilistic surrogate model for localized wildfire spread based on a conditional flow matching algorithm. The approach models fire progression as a stochastic process by learning the conditional distribution of fire arrival times given the current fire state along with environmental and atmospheric inputs. Model inputs include current burned area, near-surface wind components, temperature, relative humidity, terrain height, and fuel category information, all defined on a high-resolution spatial grid. The outputs are samples of arrival time within a three-hour time window, conditioned on the input variables. Training data are generated from coupled atmosphere-wildfire spread simulations using WRF-SFIRE, paired with weather fields from the North American Mesoscale model. The proposed framework enables efficient generation of ensembles of arrival times and explicitly represents uncertainty arising from incomplete knowledge of the fire-atmosphere system and unresolved variables. The model supports localized prediction over subdomains, reducing computational cost relative to physics-based simulators while retaining sensitivity to key drivers of fire spread. Model performance is evaluated against WRF-SFIRE simulations for both single-step (3-hour) and recursive multi-step (24-hour) forecasts. Results demonstrate that the method captures variability in fire evolution and produces accurate ensemble predictions. The framework provides a scalable approach for probabilistic wildfire forecasting and offers a pathway for integrating machine learning models with operational fire prediction systems and data assimilation.

We develop a tensor-network surrogate for option pricing, targeting large-scale portfolio revaluation problems arising in market risk management (e.g., VaR and Expected Shortfall computations). The method involves representing high-dimensional price surfaces in tensor-train (TT) form using TT-cross approximation, constructing the surrogate directly from black-box price evaluations without materializing the full training tensor. For inference, we use a Laplacian kernel and derive TT representations of the kernel matrix and its closed-form inverse in the noise-free setting, enabling TT-based Gaussian process regression without dense matrix factorization or iterative linear solves. We found that hyperparameter optimization consistently favors a large kernel length-scale and show that in this regime the GPR predictor reduces to multilinear interpolation for off-grid inputs; we also derive a low-rank TT representation for this limit. We evaluate the approach on five-asset basket options over an eight dimensional parameter space (asset spot levels, strike, interest rate, and time to maturity). For European geometric basket puts, the tensor surrogate achieves lower test error at shorter training times than standard GPR by scaling to substantially larger effective training sets. For American arithmetic basket puts trained on LSMC data, the surrogate exhibits more favorable scaling with training-set size while providing millisecond-level evaluation per query, with overall runtime dominated by data generation.

Tuning control policies manually to meet high-level objectives is often time-consuming. Bayesian optimization provides a data-efficient framework for automating this process using numerical evaluations of an objective function. However, many systems, particularly those involving humans, require optimization based on subjective criteria. Preferential Bayesian optimization addresses this by learning from pairwise comparisons instead of quantitative measurements, but relying solely on preference data can be inefficient. We propose a multi-fidelity, multi-modal Bayesian optimization framework that integrates low-fidelity numerical data with high-fidelity human preferences. Our approach employs Gaussian process surrogate models with both hierarchical, autoregressive and non-hierarchical, coregionalization-based structures, enabling efficient learning from mixed-modality data. We illustrate the framework by tuning an autonomous vehicle's trajectory planner, showing that combining numerical and preference data significantly reduces the need for experiments involving the human decision maker while effectively adapting driving style to individual preferences.

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.

Accurate power flow analysis is critical for modern distribution systems, yet classical solvers face scalability issues, and current machine learning models often struggle with generalization. We introduce BOOST-RPF, a novel method that reformulates voltage prediction from a global graph regression task into a sequential path-based learning problem. By decomposing radial networks into root-to-leaf paths, we leverage gradient-boosted decision trees (XGBoost) to model local voltage-drop regularities. We evaluate three architectural variants: Absolute Voltage, Parent Residual, and Physics-Informed Residual. This approach aligns the model architecture with the recursive physics of power flow, ensuring size-agnostic application and superior out-of-distribution robustness. Benchmarked against the Kerber Dorfnetz grid and the ENGAGE suite, BOOST-RPF achieves state-of-the-art results with its Parent Residual variant which consistently outperforms both analytical and neural baselines in standard accuracy and generalization tasks. While global Multi-Layer Perceptrons (MLPs) and Graph Neural Networks (GNNs) often suffer from performance degradation under topological shifts, BOOST-RPF maintains high precision across unseen feeders. Furthermore, the framework displays linear $O(N)$ computational scaling and significantly increased sample efficiency through per-edge supervision, offering a scalable and generalizable alternative for real-time distribution system operator (DSO) applications.

High-fidelity vehicle drag evaluation is constrained less by solver runtime than by workflow friction: geometry cleanup, meshing retries, queue contention, and reproducibility failures across teams. We present a contract-centric blueprint for self-evolving coding agents that discover executable surrogate pipelines for predicting drag coefficient $C_d$ under industrial constraints. The method formulates surrogate discovery as constrained optimization over programs, not static model instances, and combines Famou-Agent-style evaluator feedback with population-based island evolution, structured mutations (data, model, loss, and split policies), and multi-objective selection balancing ranking quality, stability, and cost. A hard evaluation contract enforces leakage prevention, deterministic replay, multi-seed robustness, and resource budgets before any candidate is admitted. Across eight anonymized evolutionary operators, the best system reaches a Combined Score of 0.9335 with sign-accuracy 0.9180, while trajectory and ablation analyses show that adaptive sampling and island migration are primary drivers of convergence quality. The deployment model is explicitly ``screen-and-escalate'': surrogates provide high-throughput ranking for design exploration, but low-confidence or out-of-distribution cases are automatically escalated to high-fidelity CFD. The resulting contribution is an auditable, reusable workflow for accelerating aerodynamic design iteration while preserving decision-grade reliability, governance traceability, and safety boundaries.

Interpreting complex machine learning models is a critical challenge, especially for tabular data where model transparency is paramount. Local Interpretable Model-Agnostic Explanations (LIME) has been a very popular framework for interpretable machine learning, also inspiring many extensions. While traditional surrogate models used in LIME variants (e.g. linear regression and decision trees) offer a degree of stability, they can struggle to faithfully capture the complex non-linear decision boundaries that are inherent in many sophisticated black-box models. This work contributes toward bridging the gap between high predictive performance and interpretable decision-making. Specifically, we propose the NDT-LIME variant that integrates Neural Decision Trees (NDTs) as surrogate models. By leveraging the structured, hierarchical nature of NDTs, our approach aims at providing more accurate and meaningful local explanations. We evaluate its effectiveness on several benchmark tabular datasets, showing consistent improvements in explanation fidelity over traditional LIME surrogates.

Stochastic differential equations (SDEs), which serve as the governing equations for dynamical systems in a broad range of applications, can become cost-prohibitive for numerical simulation at scales necessary for quantifying key properties. Surrogate models of the drift function of an SDE, learned from data of the high-fidelity system, are routinely used to increase the efficiency of simulation and prediction of properties. However, standard choices of loss function for learning the surrogate model fail to provide error guarantees in certain path-dependent observables, such as transition times. This paper introduces an error bound for path-space observables and employs it as a novel variational loss for the goal-oriented learning of the drift function of a SDE. We show the error bound holds for a broad class of observables, including mean first hitting times on unbounded time domains. We derive an analytical gradient of the goal-oriented loss by leveraging the formula for Fréchet derivatives of expected path functionals, which remains tractable for implementation in stochastic gradient descent schemes. We demonstrate that surrogate models of overdamped Langevin systems developed via goal-oriented learning achieve improved accuracy in predicting the statistics of a first hitting time observable and robustness to distributional shift in the data.

For decades, physics-based climate models have been used to provide insights for climate decision-making. Their application is, however, constrained by significant computational and technical demands. Machine learning (ML) emulators offer a way to reduce these high computational costs; yet, it remains challenging to use ML emulators effectively in climate research. In practice, climate scientists often bypass emulators altogether, and machine learning researchers frequently develop them as methodological showcases without proving their practical utility. The reasons are diverse, ranging from limited accessibility and a lack of specialized knowledge to broader concerns about the physical grounding of ML methods. Here, we discuss limitations and introduce a framework for guiding emulator development, considering both climate science and machine learning perspectives. We argue that designing easy-to-adopt emulators that address clearly defined tasks and demonstrate their reliability is essential. This offers a promising path towards making machine-learning approaches more relevant and usable for applied climate research.

Task-driven design of soft robots requires models that are physically accurate and computationally efficient, while remaining transferable across actuator designs and task scenarios. However, existing modeling approaches typically face a fundamental trade-off between physical fidelity and computational efficiency, which limits model reuse across design and task variations and constrains scalable task-driven optimization. This paper presents a unified reduced-order finite element method (FEM)-based surrogate modeling pipeline for generalized task-driven soft robot design. High-fidelity FEM simulations characterize actuator behavior at the modular level, from which compact surrogate joint models are constructed for evaluation within a pseudo-rigid body model (PRBM). A meta-model maps actuator design parameters to surrogate representations, enabling rapid instantiation across a parameterized actuator family. The resulting models are embedded into a PRBM-based simulation environment, supporting task-level simulation and optimization under realistic physical constraints. The proposed pipeline is validated through sim-to-real transfer across multiple actuator types, including bellow-type pneumatic actuators and a tendon-driven soft finger, as well as two task-driven design studies: soft gripper co-design via Reinforcement Learning (RL) and 3D actuator shape matching via evolutionary optimization. The results demonstrate high accuracy, efficiency, and reliable reuse, providing a scalable foundation for autonomous task-driven soft robot design.

Recursive partitioning methods provide computationally efficient surrogates for the Wasserstein distance, yet their statistical behavior and their resolution in the small-discrepancy regime remain insufficiently understood. We study Recursive Rank Matching (RRM) as a representative instance of this class under a population-anchored reference. In this setting, we establish consistency and an explicit convergence rate for the anchored empirical RRM under the quadratic cost. We then identify a dominant mismatch mechanism responsible for the loss of resolution in the small-discrepancy regime. Based on this analysis, we introduce Selective Recursive Rank Matching (SRRM), which suppresses the resulting dominant mismatches and yields a higher-fidelity practical surrogate for the Wasserstein distance at moderate additional computational cost.

Physics-informed machine learning surrogates are increasingly explored to accelerate dynamic simulation of generators, converters, and other power grid components. The key question, however, is not only whether a surrogate matches a stand-alone component model on average, but whether it remains accurate after insertion into a differential-algebraic simulator, where the surrogate outputs enter the algebraic equations coupling the component to the rest of the system. This paper formulates that in-simulator use as a verification and validation (V&V) problem. A finite-horizon bound is derived that links allowable component-output error to algebraic-coupling sensitivity, dynamic error amplification, and the simulation horizon. Two complementary settings are then studied: model-based verification against a reference component solver, and data-based validation through conformal calibration of the component-output variables exchanged with the simulator. The framework is general, but the case study focuses on physics-informed neural-network surrogates of second-, fourth-, and sixth-order synchronous-machine models. Results show that good stand-alone surrogate accuracy does not by itself guarantee accurate in-simulator behavior, that the largest discrepancies concentrate in stressed operating regions, and that small equation residuals do not necessarily imply small state-trajectory errors.

This paper presents a particle swarm optimization algorithm that leverages surrogate modeling to replace the conventional global best solution with the minimum of an n-dimensional quadratic form, providing a better-conditioned dynamic attractor for the swarm. This refined convergence target, informed by the local landscape, enhances global convergence behavior and increases robustness against premature convergence and noise, while incurring only minimal computational overhead. The surrogate-augmented approach is evaluated against the standard algorithm through a numerical study on a set of benchmark optimization functions that exhibit diverse landscapes. To ensure statistical significance, 400 independent runs are conducted for each function and algorithm, and the results are analyzed based on their statistical characteristics and corresponding distributions. The quadratic surrogate attractor consistently outperforms the conventional algorithm across all tested functions. The improvement is particularly pronounced for quasi-convex functions, where the surrogate model can exploit the underlying convex-like structure of the landscape.

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.

The dynamic multi-mode resource-constrained project scheduling problem (DMRCPSP) is of practical importance, as it requires making real-time decisions under changing project states and resource availability. Genetic Programming (GP) has been shown to effectively evolve heuristic rules for such decision-making tasks; however, the evolutionary process typically relies on a large number of simulation-based fitness evaluations, resulting in high computational cost. Surrogate models offer a promising solution to reduce evaluation cost, but their application to GP requires problem-specific phenotypic characterisation (PC) schemes of heuristic rules. There is currently a lack of suitable PC schemes for GP applied to DMRCPSP. This paper proposes a rank-based PC scheme derived from heuristic-driven ordering of eligible activity-mode pairs and activity groups in decision situations. The resulting PC vectors enable a surrogate model to estimate the fitness of unevaluated GP individuals. Based on this scheme, a surrogate-assisted GP algorithm is developed. Experimental results demonstrate that the proposed surrogate-assisted GP can identify high-quality heuristic rules consistently earlier than the state-of-the-art GP approach for DMRCPSP, while introducing only marginal computational overhead. Further analyses demonstrate that the surrogate model provides useful guidance for offspring selection, leading to improved evolutionary efficiency.

Model routing determines whether to use an accurate black-box model or a simpler surrogate that approximates it at lower cost or greater interpretability. In deployment settings, practitioners often wish to restrict surrogate use to inputs where its degradation relative to a reference model is controlled. We study proactive (input-based) routing, in which a lightweight gate selects the model before either runs, enabling distribution-free control of the fraction of routed inputs whose degradation exceeds a tolerance τ. The gate is trained to distinguish safe from unsafe inputs, and a routing threshold is chosen via Clopper-Pearson conformal calibration on a held-out set, guaranteeing that the routed-set violation rate is at most α with probability 1-δ. We derive a feasibility condition linking safe routing to the base safe rate π and risk budget α, along with sufficient AUC thresholds ensuring that feasible routing exists. Across 35 OpenML datasets and multiple black-box model families, gate-based conformal routing maintains controlled violation while achieving substantially higher coverage than regression conformal and naive baselines. We further show that probabilistic calibration primarily affects routing efficiency rather than distribution-free validity.

This study presents a geometric deep learning framework for predicting cold spray particle impact responses using finite element simulation data. A parametric dataset was generated through automated Abaqus simulations spanning a systematic range of particle velocity, particle temperature, and friction coefficient, yielding five output targets including maximum equivalent plastic strain, average contact plastic strain, maximum temperature, maximum von Mises stress, and deformation ratio. Four novel algorithms i.e. a GraphSAGE-style inductive graph neural network, a Chebyshev spectral graph convolution network, a topological data analysis augmented multilayer perceptron, and a geometric attention network were implemented and evaluated. Each input sample was treated as a node in a k-nearest-neighbour feature-space graph, enabling the models to exploit spatial similarity between process conditions during training. Three-dimensional feature space visualisations and two-dimensional contour projections confirmed the highly non-linear and velocity-dominated nature of the input-output relationships. Quantitative evaluation demonstrated that GraphSAGE and GAT consistently achieved R-square values exceeding 0.93 across most targets, with GAT attaining peak performance of R-square equal to 0.97 for maximum plastic strain. ChebSpectral and TDA-MLP performed considerably worse, yielding negative R-square values for several targets. These findings establish spatial graph-based neighbourhood aggregation as a robust and physically interpretable surrogate modelling strategy for cold spray process optimisation.

High-fidelity computational fluid dynamics (CFD) simulations are widely used to analyze nuclear reactor transients, but are computationally expensive when exploring large parameter spaces. Multifidelity surrogate models offer an approach to reduce cost by combining information from simulations of varying resolution. In this work, several multifidelity machine learning methods were evaluated for predicting the time to onset of natural circulation (ONC) and the temperature after ONC for a high-temperature gas reactor (HTGR) depressurized loss of forced cooling transient. A CFD model was developed in Ansys Fluent to generate 1000 simulation samples at each fidelity level, with low and medium-fidelity datasets produced by systematically coarsening the high-fidelity mesh. Multiple surrogate approaches were investigated, including multifidelity Gaussian processes and several neural network architectures, and validated on analytical benchmark functions before application to the ONC dataset. The results show that performance depends strongly on the informativeness of the input variables and the relationship between fidelity levels. Models trained using dominant inputs identified through prior sensitivity analysis consistently outperformed models trained on the full input set. The low- and high-fidelity pairing produced stronger performance than configurations involving medium-fidelity data, and two-fidelity configurations generally matched or exceeded three-fidelity counterparts at equivalent computational cost. Among the methods evaluated, multifidelity GP provided the most robust performance across input configurations, achieving excellent metrics for both time to ONC and temperature after ONC, while neural network approaches achieved comparable accuracy with substantially lower training times.

Yield Multi-Corner Analysis validates circuits across 25+ Process-Voltage-Temperature corners, resulting in a combinatorial simulation cost of $O(K \times N)$ where $K$ denotes corners and $N$ exceeds $10^4$ samples per corner. Existing methods face a fundamental trade-off: simple models achieve automation but fail on nonlinear circuits, while advanced AI models capture complex behaviors but require hours of hyperparameter tuning per design iteration, forming the Tuning Barrier. We break this barrier by replacing engineered priors (i.e., model specifications) with learned priors from a foundation model pre-trained on millions of regression tasks. This model performs in-context learning, instantly adapting to each circuit without tuning or retraining. Its attention mechanism automatically transfers knowledge across corners by identifying shared circuit physics between operating conditions. Combined with an automated feature selector (1152D to 48D), our method matches state-of-the-art accuracy (mean MREs as low as 0.11%) with zero tuning, reducing total validation cost by over $10\times$.

Surrogate models provide compact relations between user-defined input parameters and output quantities of interest, enabling the efficient evaluation of complex parametric systems in many-query settings. Such capabilities are essential in a wide range of applications, including optimisation, control, data assimilation, uncertainty quantification, and emerging digital twin technologies in various fields such as manufacturing, personalised healthcare, smart cities, and sustainability. This article reviews established methodologies for constructing surrogate models exploiting either knowledge of the governing laws and the dynamical structure of the system (physics-based) or experimental observations (data-driven), as well as hybrid approaches combining these two paradigms. By revisiting the design of a surrogate model as a functional approximation problem, existing methodologies are reviewed in terms of the choice of (i) a reduced basis and (ii) a suitable approximation criterion. The paper reviews methodologies pertaining to the field of Scientific Machine Learning, and it aims at synthesising established knowledge, recent advances, and new perspectives on: dimensionality reduction, physics-based, and data-driven surrogate modelling based on proper orthogonal decomposition, proper generalised decomposition, and artificial neural networks; multi-fidelity methods to exploit information from sources with different fidelities; adaptive sampling, enrichment, and data augmentation techniques to enhance the quality of surrogate models.

Active learning (AL) has emerged as a powerful paradigm for accelerating materials discovery by iteratively steering experiments toward promising candidates, reducing the number of costly synthesis-and-characterization cycles needed to identify optimal materials. However, current AL relies predominantly on Gaussian Process (GP) and Random Forest (RF) surrogates, which suffer from complementary limitations: GP underfits complex composition-property landscapes due to rigid kernel assumptions, while RF produces unreliable heuristic uncertainty estimates in small-data regimes. This small-data challenge is pervasive in materials science, making reliable surrogate modeling extremely difficult with models trained from scratch on each new dataset. Here we propose In-Context Active Learning (ICAL), which addresses this bottleneck by replacing conventional surrogates with TabPFN, a transformer-based foundation model (FM) pre-trained on millions of synthetic regression tasks to meta-learn a universal prior over tabular data, upon which TabPFN performs principled Bayesian inference in a single forward pass without dataset-specific retraining, delivering strong small-data regression performance and well-calibrated predictive uncertainty (required for effective AL). We benchmark ICAL against GP and RF across 10 materials datasets and TabPFN wins on 8 out of 10 datasets, achieving a mean saving of 52% in extra evaluations relative to GP and 29.77% relative to RF. Cross-validation analysis confirms that TabPFN's advantage stems from superior uncertainty calibration, achieving the lowest Negative Log-Likelihood and Area Under the Sparsification Error curve among all surrogates. These results demonstrate that pre-trained FMs can serve as effective surrogates for active learning, enabling data-efficient discovery across diverse materials systems and small-data experimental sciences.

Building design optimization often depends on physics-based simulation tools such as EnergyPlus, which, although accurate, are computationally expensive and slow. Surrogate models provide a faster alternative, yet most are location-specific, and even weather-informed variants require simulations from many sites to generalize to unseen locations. This limitation arises because existing methods do not fully exploit the short-term weather-driven energy patterns shared across regions, restricting their scalability and reusability. This study introduces a high-resolution (weekly) weather-informed surrogate modeling approach that enhances model reusability across locations. By capturing recurring short-term weather-energy demand patterns common to multiple regions, the proposed method produces a generalized surrogate that performs well beyond the training location. Unlike previous weather-informed approaches, it does not require extensive simulations from multiple sites to achieve strong generalization. Experimental results show that when trained on a single location, the model maintains high predictive accuracy for other sites within the same climate zone, with no noticeable performance loss, and exhibits only minimal degradation when applied across different climate zones. These findings demonstrate the potential of climate-informed generalization for developing scalable and reusable surrogate models, supporting more sustainable and optimized building design practices.

Surrogate modeling is an essential data-driven technique for quantifying relationships between input variables and system responses in manufacturing and engineering systems. Two major challenges limit its effectiveness: (1) large data requirements for learning complex nonlinear relationships, and (2) heterogeneous data collected from sources with varying fidelity levels. Multi-task learning (MTL) addresses the first challenge by enabling information sharing across related processes, while multi-fidelity modeling addresses the second by accounting for fidelity-dependent uncertainty. However, existing approaches typically address these challenges separately, and no unified framework simultaneously leverages inter-task similarity and fidelity-dependent data characteristics. This paper develops a novel hierarchical multi-task multi-fidelity (H-MT-MF) framework for Gaussian process-based surrogate modeling. The proposed framework decomposes each task's response into a task-specific global trend and a residual local variability component that is jointly learned across tasks using a hierarchical Bayesian formulation. The framework accommodates an arbitrary number of tasks, design points, and fidelity levels while providing predictive uncertainty quantification. We demonstrate the effectiveness of the proposed method using a 1D synthetic example and a real-world engine surface shape prediction case study. Compared to (1) a state-of-the-art MTL model that does not account for fidelity information and (2) a stochastic kriging model that learns tasks independently, the proposed approach improves prediction accuracy by up to 19% and 23%, respectively. The H-MT-MF framework provides a general and extensible solution for surrogate modeling in manufacturing systems characterized by heterogeneous data sources.

Offline model-based optimization (MBO) seeks to discover high-performing designs using only a fixed dataset of past evaluations. Most existing methods rely on learning a surrogate model via regression and implicitly assume that good predictive accuracy leads to good optimization performance. In this work, we challenge this assumption and study offline MBO from a learnability perspective. We argue that offline optimization is fundamentally a problem of ranking high-quality designs rather than accurate value prediction. Specifically, we introduce an optimization-oriented risk based on ranking between near-optimal and suboptimal designs, and develop a unified theoretical framework that connects surrogate learning to final optimization. We prove the theoretical advantages of ranking over regression, and identify distributional mismatch between the training data and near-optimal designs as the dominant error. Inspired by this, we design a distribution-aware ranking method to reduce this mismatch. Empirical results across various tasks show that our approach outperforms twenty existing methods, validating our theoretical findings. Additionally, both theoretical and empirical results reveal intrinsic limitations in offline MBO, showing a regime in which no offline method can avoid over-optimistic extrapolation.