Surrogate Modeling

Residential energy estimates are often needed before detailed envelope characteristics, equipment efficiencies, infiltration, sensor, or billing data are available. This study quantifies the trade-off between predictive accuracy and input accessibility using two nationally representative U.S. residential-energy datasets: the survey-based Residential Energy Consumption Survey (RECS) and the simulation-based ResStock dataset. Full-feature models were first used to establish dataset-specific performance benchmarks. For total-energy estimation, the models were subsequently restricted to ten low-burden variables obtainable from occupants, administrative records, or location-based weather data without an on-site energy audit. Among CatBoost, XGBoost, LightGBM, Random Forest, and Neural Networks, CatBoost consistently achieved the highest predictive performance for the full-feature analysis, reaching R2 = 0.90 for ResStock and R2 = 0.73 for RECS. When the feature set was restricted to ten homeowner-accessible inputs to simulate realistic deployment conditions, model performance converged to R2 = 0.61 for RECS and R2 = 0.62 for ResStock, showing that algorithmic complexity cannot fully compensate for missing physical and behavioral information. However, for a more homogeneous ResStock cohort consisting of single-family detached, natural-gas-heated homes in Climate Zone 6A constructed between 2000 and 2010, a reduced-input model improved accuracy to R2 = 0.85, demonstrating the value of targeted modeling for homogeneous populations. The results indicate that tree-based ensemble models can serve as high-fidelity emulators of national-scale residential energy datasets. However, careful consideration of feature availability, dataset origin (empirical vs. synthetic), and applicable use cases are also important.

Agent skills are increasingly used to equip large language model (LLM) agents with reusable procedural knowledge. Although recent work has substantially improved skill retrieval due to the increasing skill libraries, retrieving a plausible skill bundle does not guarantee that executing it is worthwhile. Since every skill-conditioned rollout is computationally expensive, deciding whether a retrieved bundle should be executed has become an increasingly important challenge. To this end, we introduce the Reward-Aware Dynamic Execution Gate (RADEG), a lightweight, retriever-agnostic decision layer between skill retrieval and agent execution. RADEG learns a low-cost surrogate model that predicts the execution utility of a query--bundle pair before the expensive rollout is launched. To obtain informative supervision while controlling for task difficulty, we locally perturb each retrieved bundle by deleting, adding, or replacing one skill, producing matched same-query rollouts that isolate the effect of bundle composition on verifier reward. During deployment, RADEG updates only a warm-started logistic head as new verifier feedback becomes available, enabling inexpensive adaptation of the execute/skip boundary without retraining either the retriever or the agent. Under a query-level held-out evaluation on 288 collected rollouts, RADEG substantially reduces unnecessary agent executions while preserving a large fraction of the downstream verifier reward. It consistently outperforms relevance-based and random gating across different execution budgets, demonstrating that execution-aware surrogate modeling provides a practical and cost-effective complement to skill retrieval.

Organic photovoltaic (OPV) materials are promising candidates for distributed solar energy in tropical regions, yet existing virtual screening tools report static power conversion efficiency (PCE) values at standard testing conditions (STC) that fail to capture the temperature-driven performance degradation experienced under real deployment conditions. Here we introduce a Climate-Native computational framework that forecasts the annual PCE profile of OPV donor molecules under geographically realistic operating conditions. The framework combines GFN2-xTB molecular dynamics with an equivariant graph neural network surrogate ($268$ Neyman-stratified CEP molecules; $120,600$ training geometries; $\sim 1050\times$ speedup over explicit quantum chemistry) and sequential deep learning models trained on annual time series anchored in NASA POWER climate data for Douala, Cameroon, and validated by zero-shot transfer to Yaoundé and Maroua. Applied to $\sim 30,000$ molecules from the Harvard Clean Energy Project (CEP) and validated against $350$ HOPV15 experimental device measurements, the framework demonstrates that sequential models trained on full molecular dynamics trajectories outperform time-averaged baselines ($35\%$-$48\%$ relative MAE improvement over static baselines), confirming that thermal conformational dynamics carry information beyond mean geometry. We further introduce a seasonal stability score that reranks OPV candidates by performance consistency under tropical conditions, identifying molecules whose deployment suitability differs substantially from their static PCE ranking.

Machine learning offers a promising avenue to accelerate physical simulations by replacing computationally expensive traditional Partial Differential Equation (PDE) solvers with fast, differentiable surrogate models. However, standard auto-regressive ML emulators often suffer from error accumulation over long horizons and struggle to capture the stochasticity of complex physical systems. In this paper, we propose Kastor, a comprehensive methodology to adapt a deterministic physics foundation model into a highly efficient and accurate generative surrogate. First, we introduce a two-stage inference scheme that combines a large-stride causal auto-regressive model with a non-causal temporal super-resolution network, significantly reducing error accumulation while minimizing computational cost. Second, we present Mean prediction regularization (MPR), a novel training objective that constrains the generative model to predict the deterministic distribution mean under null noise conditioning. This regularization dramatically improves the performance and stability of both Functional Generative Networks (FGN) and diffusion-based emulators. Finally, we demonstrate that incorporating spatial gradient matching improves the accuracy and physical fidelity of the simulations as measured by power spectrum density. Extensive evaluations on diverse simulation datasets of the benchmark The Well show that with these components, our model outperforms competing methods in forecasting accuracy, spectral consistency, and computational efficiency. Our model achieves a 42.9% average reduction in forecasting compared to our reference based on the Walrus finetuning methodology, and outperforms Walrus for 8 out of 10 datasets on variance-normalized RMSE (VRMSE).

The development of nanotherapeutics often involves extensive empirical optimization due to the sensitivity of nanoparticle properties, such as size and polydispersity index (PDI), to minor changes in process parameters. Factors like formulation concentration, flow rates, and mixing ratios can significantly influence clinical efficacy and therapeutic outcomes. The absence of predictive mathematical frameworks has made iterative experimental screening necessary, increasing both costs and development time. This study introduces and validates a predictive modeling approach based on shape constraints, aiming to enhance the estimation of nanoparticle characteristics across various process conditions. Using controlled microfluidic methods, liposomes and lipid nanoparticles were systematically prepared under varying lipid concentrations, flow rates, and aqueous-to-organic mixing ratios. The shape-constrained model, informed by both experimental data and expert knowledge, was subsequently validated for a pharmaceutical application using minimal empirical data. Results reveal that shape-constrained modeling facilitates accurate prediction of nanoparticle size and dispersity, reducing the need for extensive experimental workflows. This framework supports rational and efficient process development for manufacturing nanomedicine systems.

Supervised training of finite-element (FE) surrogate models requires reference solutions, and each reference solution is obtained by solving the system that the surrogate is intended to replace. The assembled discrete potential energy provides a training signal that requires no reference solution. This note records, with proofs, the identities that make this signal exact for linear elastostatics: the difference between the energy of a prediction and the energy of the reference solution equals one half of the squared stiffness-norm error, and the gradient of the energy equals the stiffness-weighted error. Label-free discrete-energy minimisation and supervised regression in the stiffness norm therefore have the same unique minimiser and identical gradients at every point. Around this central result, the note states a conditioning lemma that bounds the displacement error by the energy gap, a modewise contraction identity that explains why the Euclidean displacement error is an unsuitable primary metric, the Chebyshev bound that governs conjugate-gradient post-processing of surrogate predictions, and a conditional latent-separation proposition for joint-embedding predictive architecture (JEPA) pretraining on a shared stiffness operator, with an explicit numerical counterexample that delimits its scope. Every claim with numeric content is implemented as an executable falsification check; the checks were executed twice, on synthetic test problems and on a probe set of 16 instances from the validation split of a pre-registered experimental run, and every inequality holds, with the measured tightness reported. A closing section explains why the construction does not extend to elastodynamics through direct minimisation of the action functional, and which time-discrete formulation restores exactness.

Metamodels are instrumental in reducing the computational burden associated with nested reliability analyses and optimization loops in Performance-Based Risk Optimization (PBRO) of structures under stochastic loads. In this context, stochastic emulators are particularly useful because they approximate response distributions while accounting for the intrinsic stochasticity of the simulator. Among these methods, Stochastic Polynomial Chaos Expansion (SPCE) is especially attractive because it does not require replications of nonlinear analyses at fixed input conditions. However, SPCE may present limitations in accurately representing extreme responses in the tails of structural response distributions. To address this limitation, this study proposes a framework that combines Generalized Stratified Sampling (GSS) with SPCE. The GSS scheme partitions the input space into strata according to the intensity of the hazard, improving the representation of extreme responses, while independent SPCE emulators are trained within each stratum. The conditional exceedance probabilities estimated in each stratum are then recombined using the total probability theorem to evaluate the probabilistic constraints. The proposed GSS-SPCE framework is applied to the optimal design of buckling-restrained brace cross-sectional areas in a two-story steel building. The objective is to minimize the initial construction cost while satisfying prescribed probabilistic performance constraints. Results show that the proposed framework accurately estimates structural response distributions, including their tail regions, while substantially reducing the number of nonlinear model evaluations required for PBRO.

The widespread adoption of proprietary Large Language Models (LLMs) accessed strictly through closed APIs has created a critical challenge for responsible deployment: a fundamental lack of interpretability. To address this, we propose a model-agnostic, post-hoc attribution interpreter operating at the sentence level. Our approach trains an Energy-Based Model (EBM) as a surrogate to capture the LLM's internal conceptual consistency between prompts and responses. This energy landscape guides the training of a lightweight interpreter network. Uniquely, our interpreter operates as a standalone tool; once trained, it quantifies the influence of prompt sentences on a user-specified target output without requiring further API queries to the LLM. By globally training a local interpreter across diverse inputs, our framework captures broader generation patterns and mitigates instance-specific biases. Experiments demonstrate that our EBM accurately simulates the target LLM, allowing the interpreter to effectively identify the prompt sentences most influential in generating specific target outputs.

An ensemble of surrogate models helps improve the prediction quality and robustness of surrogate models, and in turn, the search performance of surrogate-assisted evolutionary algorithms (SAEAs). Although different degrees of smoothness of the approximated fitness landscapes need to be carefully designed for an effective ensemble, little attention has been paid to the explicit tuning of the degree of smoothness derived by surrogate models. This study proposes an adaptive ensemble SAEA, which automatically constructs plausible ensemble models by optimizing their parameter settings. Unlike existing adaptive/ensemble SAEAs, which consider prediction accuracy alone, the proposed algorithm optimizes the structure of radial basis function networks (RBFNs) by solving bi-objective minimization problems of approximation error and model complexity, resulting in robust ensemble models of accurate surrogate models with different degrees of smoothness of the approximated fitness landscapes. As a result, the over/under-fittings are reduced. Additionally, an infill criterion is designed so that surrogate models with different degrees of smoothness can contribute to the solution prescreening. The experimental results demonstrated the statistical superiority of our algorithm over state-of-the-art SAEAs on a single-objective benchmark and real-world problem sets under an expensive optimization scenario. The source code of the proposed algorithm is available at https://github.com/haranychan/EPOS

Design campaigns in chemistry, materials science, and machine learning share a bottleneck: determining how good a candidate truly is requires an expensive evaluation - an experiment, a first-principles simulation, or a full training run. Machine-learning surrogates that predict these outcomes are increasingly used not only to propose candidates but to grade them, and even to feed their own predictions back into the search as though they were measurements. Through mathematical analysis validated on three exhaustively ground-truthed design tasks, we establish when this practice is safe, what any certificate of safety must cost, and when the substitution provably pays. Predictive accuracy cannot anchor trust: near-perfect R^2 is compatible with worst-possible selections, and screening N candidates inflates the over-prediction at the selected candidate by a quantifiable "selection tax" with matching upper and lower bounds. Safety follows instead from an architectural rule - predictions may propose and train without restriction, but every certified conclusion must rest on true evaluations - which is sufficient with no assumptions on the surrogate, and necessary, since admitting predictions into certification with the standing of measurements opens a deterministic self-confirmation failure mode. We derive the minimal criterion under which a model may act as an oracle (rank preservation, not accuracy), show that trust must be purchased through selection-aware audits that are optimal in query complexity, and prove a dichotomy fixing when audited surrogates cut certified evaluation cost. Across 432 surrogate fits over six task-regime conditions, the audit statistic tracks deployed search performance at Spearman rank correlation 0.80-0.99, while the rank correlation of R^2 with deployed regret falls as low as 0.33; audited screening reduces certified oracle cost by a measured factor of 25.

A broad range of models face the mismatch where they are updated through trajectory losses but are evaluated by downstream task reward. Here, a trajectory is a training instance that induces a surrogate loss whose reduction might not track the model's decision utility update. Theoretically, we ask when one step of trajectory training reduces both population surrogate loss and decision risk, and how transfer accumulates along repeated updates. To formalize this, we first fix a checkpoint and a restricted update space, and define the reductions in population surrogate risk and decision risk induced by a trajectory as its learnability and decision utility, respectively. On this basis, our theory yields four main results. First, a one-step transfer bound separates their discrepancy into first-order gradient misalignment after nonnegative calibration and second-order curvature; and a pathwise extension accumulates the same terms over repeated updates. Second, when the accessible surrogate gradient is nonzero, universal first-order transfer over every accessible direction holds exactly when the accessible surrogate and decision gradients are positively collinear. Third, the calibration gap bounds the decision regret of learnability-based trajectory selection, while a candidate-difference refinement tightens this guarantee by retaining only directions that affect pairwise rankings. Finally, we establish an approximation--calibration trade-off across nested update spaces. Controlled gridworld and LLM post-training experiments yield results consistent with our predictions.

Understanding and controlling complex dynamical systems often requires executing thousands of numerical simulations across vast parametric landscapes, which is time-consuming. Machine learning surrogates significantly accelerate simulation by predicting state trajectories across different initializations and parameter values. However, surrogate models are specialized to one simulation model. Modifying the underlying differential equations - e.g., adding a physiological state or altering an epidemiological contact network - renders trained models obsolete and forces computationally expensive retraining from scratch. We introduce HyperODE, a surrogate capable of operating across an entire class of approximately mass-conserving compartmental models without retraining. By mapping the structure of ordinary differential equations (ODEs) into directed hypergraphs, HyperODE decouples the functional form of system interactions from the neural network architecture. HyperODE takes a compartmental model in the form of an ODE with an arbitrary parameter distribution defined through quantiles and transforms it into a hypergraph. It outputs the distribution of the trajectories for all the states in the original ODE in the form of quantiles. We then use this surrogate to build an encoder that takes a noisy trajectory and outputs a distribution over the parameters of the original ODE, thus calibrating the model in a single pass. On families and system sizes never seen in training, HyperODE produces calibrated quantile bands in a single forward pass, with weighted-interval score and coverage on par with specialized surrogates for each structure. For inverse inference, HyperODE produces calibration from noisy state trajectories in a few milliseconds with a single shared encoder, competitive with existing methods. HyperODE extends zero-shot to ODEs that break mass conservation and to external forcing.

Bayesian Optimization (BO) is widely adopted for data-efficient optimization in scientific and engineering applications, yet its computational cost is rarely evaluated alongside optimization performance. Here we present a systematic, compute-aware study of BO that evaluates surrogate models along two axes: optimization quality and computational frugality. Across eight benchmark functions and nine real-world datasets spanning materials science, mechanics, robotics, chemistry, and machine learning, we benchmark four surrogate models: Gaussian Processes, Random Forests, NGBoost, and Bayesian Adaptive Spline Surfaces. We show that Gaussian Process-based BO consistently incurs the highest time and memory overhead without delivering superior optimization or sample efficiency. In contrast, scalable alternatives achieve equal or better performance at a fraction of the computational cost. Motivated by these findings, we introduce a surrogate-recommendation framework that predicts the most suitable BO surrogate from inexpensive dataset characteristics. Together, these results establish FruBO as a reproducible, compute-aware baseline for Bayesian Optimization and provide practical guidance for surrogate selection under limited computational and experimental budgets.

Transcranial focused ultrasound (tFUS) is a non-invasive technique that delivers focused acoustic energy through the skull for neuromodulation and therapeutic applications. However, the heterogeneous structure of the skull induces complex, patient-specific phase and amplitude aberrations that distort the acoustic focus and deviate it from the intended target, compromising therapeutic efficacy and safety. Conventional time-reversal (TR) simulations can correct these aberrations but rely on computationally expensive full-wave solvers, making them impractical for real-time use and iterative treatment planning. We propose a few-shot deep surrogate framework that predicts per-element phase and amplitude corrections for a 96-element 3D phased-array transducer from patient CT images. A geometry-aware encoder extracts skull-path features shared across dedicated phase classification and amplitude regression branches, where phase periodicity is handled via circular expectation decoding. The framework is pretrained on diverse skull geometries and fine-tuned with only ten target points, enabling rapid adaptation to unseen patients without full patient-specific simulation. Evaluated via leave-one-out cross-validation across 12 skulls, it achieves a mean phase CMAE of 0.155 rad and amplitude rMAE of 9.089%, a focal centroid error of 0.467 mm, Dice score of 94.422%, and peak pressure ratio of 92.332%, with an approximately 2,535 times speedup over TR simulation. The code is available at https://github.com/Minju-Seol/fewshot-tfus-correction.

We present a novel approach to regression tasks using classification which is motivated by the mechanism used by fruitflies to sense their environment. Specifically, we formulate a general framework for learning nonlinear input-output relationships by replacing complex global surrogate models with a finite library of representative local patterns. Since scientific data often occupy limited and recurring regions of the input space, we generate predictions by measuring similarities between a query and stored patterns, then combining their associated responses through weighted reconstruction. We apply this approach to nonlinear dynamical systems, data-driven regression, and physics-informed learning using suitable embeddings and similarity measures. For dynamical systems, our offline-online workflow extracts patterns from data or governing equations during the offline phase, while online prediction requires only similarity evaluation and response aggregation. This structure helps us reduce computational and memory demands while providing explicit control over the trade-off among accuracy, storage, and inference cost.

Self-driving laboratories increasingly rely on multi-fidelity Bayesian optimization (MFBO) to balance cheap, approximate evaluations against scarce, expensive ones, with a predictive surrogate at its core. Gaussian processes (GPs) are the default choice, but they scale poorly as data accumulate and assume a smooth landscape that molecular and materials search spaces routinely violate. Transfer learning offers an alternative suited to this regime: it learns a representation from abundant cheap data and adapts it to sparse expensive data. Despite its use in property prediction, transfer learning has not been tested as the engine of a closed-loop optimization. Here we benchmark eleven transfer-learning surrogates against four GP methods under an identical selection rule, fidelity budget, and model size, across nine tasks spanning synthetic functions to real chemistry and materials problems. GPs win on smooth, low-dimensional functions but perform worst on molecular and materials problems, where transfer-learning surrogates reach substantially better solutions using far less computation. Because acquisition policy is held fixed across surrogates, this advantage is attributable to the surrogate itself. Uncertainty-driven exploration is not reliably beneficial, and calibration does not predict optimization performance, so greedy exploitation of the transfer-learned mean is the more robust default. Transfer learning is therefore the surrogate of choice for molecular and materials MFBO.

Gene regulatory network modeling often requires balancing predictive accuracy and mechanistic interpretability. In this work, we compare continuous surrogate models and a discrete mechanistic model on the same \textit{Arabidopsis thaliana} induced systemic resistance (ISR) dataset, using both the raw continuous gene-expression measurements and their sign-binarized representation. The study considers eight defense-related genes measured over nine time points and evaluates two continuous predictors, Random Forest (RF) regression and a Multi-Layer Perceptron (MLP), against a threshold Boolean network (TBN). The models are assessed using rolling-origin one-step prediction, recursive multi-step rollout, and interpretability analysis. RF achieved the best average one-step numerical performance in the continuous domain, with an MAE of 1.910 and an RMSE of 2.836, compared with 2.089 and 3.106 for the MLP. In the binary domain, the TBN obtained the best average one-step qualitative performance, with a binary accuracy of 0.550 and a Hamming distance of 3.600, compared with 0.500 and 4.000 for RF, and 0.495 and 4.040 for the MLP. In recursive rollout, the TBN exactly reproduced the observed binarized trajectory, while the MLP also showed near-perfect fidelity, with a trajectory binary accuracy of 0.986, and RF accumulated substantially larger deviation, with a trajectory binary accuracy of 0.708. These results highlight that local numerical accuracy and global qualitative dynamical fidelity are not necessarily aligned, and suggest that continuous surrogates and threshold Boolean networks should be viewed as complementary tools for modeling biological regulation.

Simulating societies of many large language model (LLM) agents is expensive, yet the questions asked of such simulations are usually macroscopic: phase behaviour, stylised facts, and scaling with the number of agents $N$, not the cognition of any single agent. We turn a statistical-physics observation into a method: replace each LLM agent by a low-parameter model fitted from a few hundred to a few thousand cheap queries, then run the society at any $N$ on a laptop. Whether this works is decided before the simulation runs, chiefly by what each agent perceives. We introduce an [interaction order x memory] taxonomy that maps perception and memory to an effective theory and a predicted $N$-trend of the surrogate error. We validate it on a faithful reimplementation of the LLM macroeconomy EconAgent and seven further named LLM simulations, with agent decisions cloned from genuine LLM elicitations (primarily DeepSeek) for a few dollars; the predicted error trends hold cell by cell, and the two refuted predictions, both on a strongly saturating response and traced to its curvature, are themselves matched quantitatively by the theory with no free parameters.

Security rating platforms summarize externally observable cyber exposure and are expected to help organizations prioritize remediation. A platform may want to tell an organization how a candidate remediation action would affect its score, but repeatedly exposing exact score responses can reveal information about the hidden scoring engine. We propose a surrogate based approach for remediation score impact prediction that is designed to respect this opacity constraint. The surrogate predicts scores from organization configurations while explicitly representing checkpoint (i.e., a security check) applicability and the observed checkpoint set. A main challenge is that such predictions are not uniformly reliable: they depend on the amount and structure of the observable checkpoint evidence available for a given configuration. To address this, the approach combines applicability-aware surrogate construction, sensitivity analysis under controlled checkpoint restriction, a reliability layer for identifying unstable predictions, and score-impact prediction for supported remediation actions. Explicit modeling of checkpoint applicability is central throughout: it improves score prediction and provides the feature basis used by the reliability layer to identify unstable cases. We evaluate the approach on a real-world dataset of 5,188 organization configurations from a commercial security rating platform. The results show that the applicability-aware surrogate improves score prediction over simpler feature representations. For remediation, the surrogate predicts the score impact of supported actions, while the reliability layer helps identify cases in which these predicted impacts should be interpreted cautiously.

Developing autonomous hydraulic excavators is constrained by limited access to physical machines and the high cost of real-world experimentation. This paper proposes a simulation-to-real framework for learning a system-level digital surrogate using Long Short-Term Memory (LSTM) networks. Instead of modeling internal dynamics, the excavator is treated as an input-output operator, and the surrogate is trained to reproduce its closed-loop behavior under identical control inputs. The approach is first validated in a MuJoCo simulation environment and then transferred to a real excavator. To address measurement inconsistencies in real-world data, a consistency-aware state estimation method based on adaptive Kalman filtering is introduced. Experimental results demonstrate that the learned surrogate achieves high fidelity in both angular velocity and long-horizon trajectory reproduction under closed-loop autoregressive evaluation. These results confirm that the proposed model can serve as a drop-in surrogate for both simulation and physical systems, enabling scalable and efficient development of excavation automation algorithms.

Emerging sustainable materials increasingly rely on engineered hierarchy and microstructure to achieve control of their properties and mechanical behavior. Optimizing these materials with controllable microstructures requires efficient multiscale simulations. Data-driven surrogate models for the microscale can accelerate multiscale simulations, but require large amounts of data even for a fixed microstructure. When a range of microstructures is considered, as is the case in multiscale optimization, even more data is needed to train a surrogate. To overcome this challenge, we condition a hybrid physics-data surrogate on microstructural variables using a hypernetwork. This approach enables accurate predictions of multiscale mechanical behavior for a mycelium-woodchip composite material, even when trained on small datasets. The conditioned surrogate makes multiscale simulations of functionally graded structures tractable, and we validate it against a full FE^2 simulation. We optimize a graded multiscale disk, and reduce the peak stress by 42% compared to one with a random microstructure. Then, we go one step further, conditioning the network directly on manufacturing variables that can have a complex influence on the microstructure. This is a practical route to engineer the microscale for desired macroscale behavior. This contribution highlights the benefits of microarchitectured structures and demonstrates how conditioned surrogate models enable their multiscale optimization, which will accelerate the development and design of future sustainable materials and structures.

Many nonlinear physical systems exhibit an initial transient phase in which perturbations grow before nonlinear interactions lead to a statistically steady state. While this saturated regime is of primary interest, direct numerical simulations must resolve the full transient dynamics before reaching it, incurring significant computational cost. In Computational Fluid Dynamics, reduced-order approaches such as Large Eddy Simulation mitigate computational cost by modeling small-scale dynamics, enabling tractable approximations of turbulent flows. In contrast, for systems such as gyrokinetics, comparably effective closures for the full dynamics are not generally available, and high-fidelity simulations remain necessary. Existing surrogate modeling approaches for these systems are autoregressive, hence they suffer from accumulating error. We instead propose to bypass explicit time evolution by directly modeling the distribution of saturated states under an ergodicity assumption, stating that ensemble averages over samples are equivalent to time averages of a single long simulation. We introduce GyroFlow, a latent generative model that directly estimates steady-state statistics of gyrokinetic turbulence in 5D phase space, without resolving the transient phase. GyroFlow generates saturated snapshots from noise, conditioned on dimensionless operating parameters and outperforms autoregressive, reduced-order, and other generative approaches, while providing substantial speedup. To evaluate generation quality we propose FGyD, a distributional metric computed in the latent space of a pretrained gyrokinetic model, and show that it correlates with downstream flux accuracy and solver convergence. Finally, GyroFlow can be used to warm-start the numerical code used to produce the data.

Machine-learned surrogates for the AC power flow (ACPF) problem amortize the cost of repeated solves on a fixed network, but lose one to two orders of magnitude of accuracy when a line outage changes the topology. This degradation is an operator shift. The altered admittance matrix changes the input-to-output map, so identical inputs yield a different output distribution. Existing methods correct this with target-topology data and per-topology gradient steps. We ask whether the correction can instead be made statistical and gradient-free. We propose In-Context Whitening (ICW), which trains an ACPF surrogate in an output space whitened by the base topology's first two moments, and adapts it to an unseen N-1 or N-2 topology by re-estimating that whitening from a few hundred solved cases on the new topology. This adaptation is gradient-free, weight-free, and architecture-agnostic. We prove that among affine whiteners the unique choice that preserves the coordinate-wise semantics of the physical output vector is ZCA whitening, so within efficient invertible corrections, two moments are sufficient. Across the IEEE 30-, 118-, and 300-bus systems under N-1 and N-2 contingencies, ICW reduces overall error by 6$\times$ to 28$\times$ over frozen surrogates (up to 54$\times$ per-quantity under N-2) and cuts worst-bus power-balance mismatch by up to 30$\times$, with consistent gains across three backbones. At deployment scale it matches or beats gradient-based adaptation in accuracy while adapting 21$\times$ to 34$\times$ faster, with a cost that parallelizes on commodity CPU cores rather than requiring one GPU per contingency.

Small-data inverse design is challenging in engineering informatics when observations are heterogeneous, mixed-type, and constrained by physical relations among design variables. This work proposes a topology-aware surrogate framework guided by an Incremental Transformer (INCRT) for physics-constrained inverse design, applied to geopolymer mixture design. The method integrates intrinsic-dimensionality analysis, mixed-variable design-space representation, tabular surrogate prediction, INCRT-based manifold rationalisation, and constrained inverse optimisation. Using a public benchmark of fly-ash and slag-based geopolymer concrete mixtures with compressive-strength and carbon-emission targets, the high-dimensional design space proves strongly redundant, organising around fewer effective mixture regimes. Compressive strength requires nonlinear tabular surrogates, while carbon emission is largely determined by composition and well recovered by regularised linear models. INCRT thus acts not as a replacement for tabular predictors but as a rationalisation layer providing prototype regimes and a manifold-support score for inverse design. Three strategies are compared: unconstrained surrogate optimisation, physics-constrained optimisation, and topology-aware physics-constrained optimisation. Unconstrained optimisation can match target strength but may yield physically invalid or off-manifold candidates; physics-only constraints do not always ensure data support. The topology-aware strategy yields candidates balancing target compliance, carbon reduction, physical admissibility, and proximity to the learned feasible manifold. The framework aims not to replace experimental validation but to support screening of credible candidate mixtures from small, mixed, physically constrained engineering datasets.

Long-horizon physics-based simulations of battery degradation provide mechanistic insight but remain computationally expensive, limiting their use for dense exploration of operating conditions over extended cycle life. Here, we propose a hybrid physics-probabilistic learning framework for surrogate modeling of lithium-ion battery degradation trajectories at unseen charging rates. Cycle-resolved degradation data generated with a DFN/P2D electrochemical model in PyBaMM are first transformed into capacity-aligned voltage and derivative features and encoded using a Variational Autoencoder (VAE). The resulting two-dimensional latent space organizes degradation trajectories according to both cycle progression and charging protocol. A sparse multitask Gaussian process (GP) is then trained in this latent space using cycle number and C-rate as input variables, providing continuous interpolation of latent degradation dynamics together with posterior uncertainty estimates. Under protocol-level holdout evaluation, the latent-space GP accurately recovers unseen C-rate trajectories and exhibits uncertainty behavior consistent with the support of the training data. When queried at unseen interior C-rates, the model generates latent trajectories that remain coherently positioned between neighboring simulated protocols. Decoding the GP-predicted latent states through the frozen VAE decoder yields smooth voltage-capacity evolution, while Monte Carlo propagation of the GP latent posterior through an auxiliary latent to State of Health (SOH) predictor provides uncertainty-aware SOH estimates. The proposed BattVAE-GP framework therefore offers a computationally efficient and uncertainty-aware surrogate for long-horizon degradation modeling, providing a structured basis for extending battery health prediction toward richer operating conditions and future simulation-experiment fusion.

Many real-world processes can be represented as compositions of functions along a directed acyclic graph (DAG). In causal modelling, these correspond to the underlying mechanisms; in engineering, to multiple fidelity levels; and in gene-regulatory networks, to transcription factors. These functions are partially observed across the DAG, with noisy and heterogeneously sampled measurements, posing significant challenges for reconstruction, uncertainty propagation, and inference. To tackle these challenges, we place priors over functions and naturally arrive at Deep Gaussian Processes over DAGs. We theoretically study their prior-collapse behaviour, and the effect of graph topology and intermediate observations on the preservation of information. We obtain almost-sure lower bounds on the asymptotic frequency of depths at which the distinction between inputs is preserved, identify broad kernel classes for which these hold, and prove an observation by \cite{dunlop2018} on the role of input connections. We offer a structured variational approximation that retains graph dependencies, preserves compositional uncertainty, and captures the explaining-away behaviour of colliders. Finally, we empirically validate our theoretical results and our methodology, and model a latent-collider DAG, a protein signalling network, and a multi-fidelity heavy-ion collision emulation task, attaining state-of-the-art performance while recovering low-fidelity contributions and yielding interpretability of the simulator hierarchy.

We present a physics-constrained machine learning framework for accelerating the direct numerical simulation (DNS) of turbulent reacting flows. The model replaces the direct evaluation of detailed chemical source terms with a surrogate that predicts reaction rates from a reduced thermochemical state. To improve physical consistency, the second law of thermodynamics is incorporated as a training constraint by enforcing non-negative entropy generation, which restricts the evolution of the thermochemical state to physically admissible directions and improves stability during time integration. The approach is demonstrated on DNS of a two-dimensional planar lean premixed methane-air flame interacting with a turbulent flow field. The model reproduces detailed-chemistry results with high fidelity while achieving more than an order-of-magnitude reduction in computational cost. Furthermore, a residual-based synthetic data augmentation strategy enables parametric exploration by constructing new training data from the original dataset, allowing accurate simulation at new inlet conditions without additional detailed-chemistry CFD runs. These results demonstrate that thermodynamically constrained machine learning can provide reliable and computationally efficient surrogates for detailed chemistry in high-fidelity combustion simulations.

Precise control and positioning of autonomous underwater vehicles (AUVs) is critical for sampling, maintenance, and survey applications. Reinforcement learning (RL) offers rapid controller development while handling a range of deployment parameters via domain randomization (DR). However, DR is limited by the underlying simulation's capacity to model real physics such as drag, which is a large contributor to sim-to-real gaps. Computational fluid dynamics (CFD) provides high-fidelity drag models but has significant computational cost. Thus, in this paper we train surrogate approximations of CFD data of a given vehicle, providing drag estimates 700,000x faster than solving for drag at each time step with CFD within the RL training pipeline. We deploy a Proximal Policy Optimization (PPO) policy zero-shot on a 6-DOF AUV in which policy training is performed on these surrogate drag models (SDMs), providing analysis on zero-shot transfer, reward shaping sensitivity, and physical parameter perturbations. On 15 identical segments in the ocean, we observe median gains of 19% in mean tracking error and 31% in control effort compared to the equivalent inertia box model. Our SDM based RL controller better predicts zero-shot transfer and reaches the most waypoints across all three reward shaping choices that we evaluate. Finally, we add 0.907 kg to the vehicle perturbing the mass, center-of-mass, and center-of-buoyancy. The policy reaches 100% of waypoints only when the SDM drag model is used; the policy fails to reach any of the 15 waypoints when the other drag models are used.

Cyber-physical power systems are vulnerable to cascading failures caused by tight interdependencies between power and communication infrastructures. Evaluating these failures over large N-k contingency sets with a high-fidelity simulator is computationally prohibitive for resilience planning. Using the previously published Modified Implicative Interdependency Model (MIIM) as the ground-truth cascade simulator, this paper develops a machine-learning surrogate that predicts contingency severity from leakage-free structural features and derives a component-criticality ranking for prioritized hardening analysis. On the IEEE 118-bus system, the Gradient Boosting surrogate achieves Spearman correlations of 0.849 for per-contingency severity prediction and 0.853 for per-component criticality ranking, while remaining stable across three independently sampled datasets. MIIM-derived component criticality itself reproduces only to a Spearman of approximately 0.85 under the present sampling pipeline, and the surrogate operates at this empirical ceiling to within sampling variation. Topological centrality measures on the full interdependent network provide meaningful baselines (Spearman 0.60-0.69), and feature ablation shows that the surrogate's advantage is driven primarily by inter-layer dependency information. These results support a two-stage workflow in which the surrogate rapidly ranks candidate components and MIIM is reserved for selective verification.

In physically dominated machining processes, experimental datasets are small, expensive, and material-specific; in this regime, data curation, evaluation design, and the form of physics integration can matter as much as the learning algorithm. Using an abrasive waterjet milling dataset ($n{=}155$, Inconel,718), we make three methodological contributions. First, we separate physics-based data \emph{cleaning} from statistical \emph{curation} and treat the latter as competing modelling hypotheses rather than silent preprocessing. Second, we find that model rankings from a 15-point hold-out set can be unstable: the single-split winner drops from rank1 to rank7 under 10-fold cross-validation, while Gaussian Process (GP) variants occupy the top ranks. Third, we study a spectrum of physics integration levels and find that residual learning on a compact physics baseline is competitive for GP, yielding lower variance and an interpretable decomposition, but degrades tree-based models. Bayesian hyper parameter tuning improves parameter-sensitive baselines such as gradient boosting and SVR, yet harms multi-stage hybrid pipelines at this sample size. GP uncertainty intervals are approximately calibrated ($86\%$ empirical coverage at nominal $90\%$). The resulting picture is methodological: for small, expensive process datasets, our results suggest that, in this setting, reliable model comparison benefits from explicit curation hypotheses, robust evaluation, and careful choices about how physics enters the model.