Why and When Neural Networks Improve Local Approximation in Optimization

Published experience with neural surrogates in derivative-free optimisation is contradictory: the same family of models that cuts the evaluation count of one solver leaves another unchanged, or makes it worse. We show that the contradiction dissolves once three factors are stated, and that these, rather than the fit accuracy a training curve reports, are what delimit when a learned local model pays. Role: a surrogate that proposes candidates the true objective must still approve helps, while one that replaces a gradient the solver depends on hurts. Radius: a model fitted to an optimisation path is reliable only inside a bounded neighbourhood, and its error neither vanishes as that neighbourhood shrinks nor survives its growth. Room: a surrogate can only accelerate progress the base method is still able to make. We formalise radius-aware local generalisation, relate it to the classical fully linear condition, and test each factor with the surrogate class, training pipeline and base method held fixed. Over 117 benchmark instances safeguarded assistance raises the instances solved to high accuracy from 67 to 84 while gradient replacement lowers them to 65; removing the gradient term from the training loss cuts surrogate acceptance from 0.703 to 0.148; and 1000 paired comparisons over ten noise levels show no noise threshold, only a base method that stops early. The same factors bound the gain: a model-based trust-region solver, which leaves little room, drops from 88 to 86 when the identical surrogate is attached, and released interpolation software stays ahead at 103, and on a Monte-Carlo inventory model repairing the acceptance interface is worth 10.40 cost units against 0.00 for the surrogate.

GeoQ: Geometry-Aware Conditional Quantile Error Estimation for Scientific Surrogate Models

Neural-network surrogate models are increasingly used to accelerate scientific simulations, but their deployment in extrapolative and autoregressive settings requires input-dependent estimates of prediction error. In this work, we introduce GeoQ (Geometry-Aware Conditional Quantile Error Estimation), a non-intrusive calibration framework for estimating surrogate error at individual query points. GeoQ represents the error at a query point as an anchor-averaged calibration error plus a learned nonnegative correction. This correction is modeled as an upper conditional quantile of the anchor-relative error increment, using geometry-based features that encode representation-space displacement and local support density. A cross-fitting procedure generates approximately out-of-sample calibration tuples, while a feature-space k-nearest-neighbor support score identifies regions \textcolor{black}{where the learned error model is supported by calibration data}. We evaluate GeoQ on scalar regression, chaotic dynamics, medium-range weather forecasting, and Richtmyer-Meshkov instability prediction. The results demonstrate that geometry-aware conditional quantile modeling provides a practical and non-intrusive approach for validity-aware error estimation in scientific surrogate models.

Tools to Explain Neural Networks for Power System Dynamics

This paper presents, for the first time in power systems literature to our knowledge, analytical tools to explain the training performance of machine learning surrogate models for power system dynamics. Power system simulations are increasingly challenged by stiff and multi-timescale dynamics arising from converter-interfaced resources and fast control loops. Machine learning surrogates emerge as promising tools to handle this complexity and accelerate dynamic simulations. However, their performance remains difficult to interpret, which limits their adoption. Building on the small-signal eigenvalue analysis in power systems, this paper uses the Neural Tangent Kernel (NTK) method. NTK delivers a modal interpretation of the learning performance, identifying error modes that decay rapidly versus others that converge slowly. This connection explains how physical stiffness and timescale separation in power system dynamic models appear as optimization stiffness during Neural Network (NN) training. Based on this analysis, we develop adaptive loss-weighting strategies to improve and explain why structure-aware neural architectures, such as ActNet, perform better than vanilla NNs. We assess the proposed approach on physics-informed machine learning surrogate models of \acp{SM} and power electronic converters. The methods introduced in this paper can deliver the necessary analytical tools to interpret and improve the performance of machine learning surrogates, paving the way for the systematic, physics-aware design of NN architectures and training strategies. By moving beyond trial-and-error development, these tools reveal training dynamics and failure modes, support more reliable design decisions, and strengthen confidence in machine-learning surrogates for engineering applications.

ArchEGraph: A Large-Scale Graph Dataset for Geometry-Topology-Physics Aligned Building Energy Modeling

Accurate estimation of building energy use is essential for achieving carbon neutral and sustainable buildings. To better understand the influence of design decisions on building energy use and calibrate machine learning models that can give architects and engineers rapid design feedback, large-scale datasets are needed that explicitly map building geometry to performance. We present ArchEGraph, a large-scale benchmark dataset that represents buildings as heterogeneous graphs with aligned geometry, topology, weather, and zone-level thermal loads. The dataset contains 5,481 buildings and 49,326 validated building-weather simulation cases. In total, it includes over 133,000 space nodes and 1.44 million face nodes, reflecting substantial geometric and topological complexity. Based on ArchEGraph, we define two benchmark tasks: (i) graph reconstruction from polygonal meshes, aiming to recover topological structure from geometric representations; and (ii) topology-informed load prediction, which leverages graph structure and temporal weather conditions to forecast zone-level response time series. We further introduce standardized evaluation protocols for both tasks and conduct cross-building and cross-climate generalization experiments to assess model robustness. ArchEGraph provides a unified testbed for studying geometry-topology-physics coupling in building energy modeling, enabling the development and evaluation of scalable and generalizable surrogate models.

Agentic Bayesian Optimization through Surrogate-Augmented Autoresearch

Bayesian optimization (BO) has become the standard tool for sample-efficient optimization and owes its efficiency to uncertainty-aware search driven by generic statistical priors. Richer domain priors can improve BO in principle, but encoding them through tailored kernels or problem structure is difficult and rarely done in practice. LLMs can help sidestep this difficulty by making informal priors from natural language, code, and documentation directly available to the optimizer. However, existing LLM-based BO methods either insert the LLM into a fixed role (surrogate, acquisition proxy, or configuration interface) or hand it broad control, sacrificing the systematic exploration that makes BO reliable. We introduce agentic Bayesian optimization: a paradigm in which an LLM agent is the central decision maker in the BO loop while a Bayesian backend provides the uncertainty-aware optimization substrate. The agent configures the problem, queries the backend, selects and commits evaluations, and can revise the optimization strategy during the run by tightening bounds, switching acquisition functions, proposing targeted evaluations, or even reframing the problem following new instructions or observed evidence. We instantiate this idea in Sara, a surrogate-augmented autoresearch agent, and lenz, a modular BoTorch-based backend that the agent can inspect and modify through a structured interface. Across synthetic and real-world benchmarks, Sara preserves the reliability of state-of-the-art BO without prior knowledge, outperforms LLM-based baselines, and uses natural-language priors to improve beyond standard BO. We further demonstrate the practical value of agentic BO in dynamic settings, where Sara reconfigures the full optimization problem on the fly as requirements change, a capability not previously available in standard BO.

Frugal Bayesian Optimization: Scalable Surrogates for Data- and Resource-Limited Discovery

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.

Surrogate assisted diversity estimation in neural ensemble search

Ensembles are a standard way to improve the performance and robustness of deep neural networks, but their effectiveness crucially depends on both the quality and the diversity of individual models. Most neural architecture search (NAS) methods are computationally expensive. Extending them to neural ensemble search (NES), which requires joint optimization of individual architectures and their ensemble composition, leads to an exponential growth of the search space and makes the problem computationally intractable. To address this, we introduce a dual-objective surrogate-guided ensemble search: candidate architectures are represented as directed acyclic graphs, and two surrogate models are trained independently to estimate predictive accuracy and diversity potential. Their combined estimates guide an NES framework that efficiently identifies architectures that are both individually strong and collectively diverse. Our final ensemble achieves competitive or superior performance compared to standard baselines such as Deep Ensembles and Random Search on FashionMNIST, CIFAR-10, and CIFAR-100.

Optimization with Dynamic Constraint Learning (DCL)

We propose Dynamic Constraint Learning (DCL), a data-driven framework for constrained optimization when constraint functions are unknown and cannot be queried during optimization. At each iteration, the method learns a local surrogate from nearby data and solves a subproblem within a data-supported trust region. Compared with offline global constraint learning, the approach uses local surrogates that adapt to the data distribution during optimization and can achieve solution quality comparable to that of global models while using simpler local models and smaller optimization subproblems. We demonstrate the performance of DCL on a synthetic test problem and two case studies from the literature.

Uncertainty quantification in mechanics: A unified Bayesian perspective

Uncertainty quantification (UQ) is essential to experimental mechanics, but has become particularly relevant in computational mechanics, manifesting in two fundamental problem types: forward and inverse problems. The former addresses how input uncertainties propagate to the quantities of interest, whereas the latter aims to infer unknown parameters from experimental observations or simulations. Since efficient propagation typically requires a prohibitive number of evaluations to compute marginal output distributions, the development of fast, data-driven surrogate models becomes necessary. Thus, we can distinguish between two inverse tasks: (i) the identification and calibration of input uncertainties, and (ii) the construction of surrogates, a methodology collectively referred to as surrogate-based UQ. Building on probabilistic reasoning and the concept of partial belief, we demonstrate that Bayesian probability theory provides a unified theoretical framework for addressing both problem types. We further show that Bayesian inference allows for the seamless incorporation of essential subproblems, including model selection for identifying the most probable model specifications and experimental design for optimizing data collection by identifying experiments or simulations that maximize expected information gain about parameters, among others such as connections to sensitivity analysis or the use of special priors like random fields. While this theoretical framework is presented for general mechanical problems, particular emphasis is placed on biomechanics, where variability and uncertainty is especially pronounced due to inherent biological heterogeneity, patient-specific variability, and noisy data.

Gradient-Free Topology Adaptation for Power Flow Surrogates via In-Context Whitening

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.

Physics-Audited Agentic Discovery in Scientific Machine Learning

In agentic scientific machine learning (SciML), large language model (LLM) agents can discover surrogate models and select one by an automated score, typically an error metric. A low error, however, does not establish that the predicted fields satisfy the physics that matter for mechanics, such as boundary conditions, superposition, stiffness scaling, or causality. We introduce Physics-Audited Agentic SciML (PA-SciML), a verification-first workflow for agentic SciML discovery. The workflow fixes a scoring evaluator before search, derives reviewable machine-checkable physics requirements, checks each trained candidate on its outputs, and separately searches prescribed input ranges or measured load-history spans for high-violation cases without reference solution fields. A surrogate is reported as verified only under the stated checks. When enabled, the workflow also adds advisory numerical probes before training and tests one modeling change at a time to record which isolated edits are associated with score gains before reuse. In the reported computational-solid-mechanics numerical examples, the static elasticity run selects a surrogate with lower validation error than the error-only baseline while both selected models pass the common linear-elastic checks. In the transient elastodynamics run, an error-only baseline with similar mean error fails a stricter causality check by responding to future parts of the loading history, while the selected surrogate passes the stated checks. The main distinction is per-candidate physics evidence on predicted fields, not a richer aggregate score.

Constrained Bayesian Optimisation with Multiple Information Sources

Bayesian Optimisation (BO) under unknown constraints is particularly challenging when feasible regions are small. In such settings, existing methods that typically rely solely on evaluations of the true objective and constraints struggle to efficiently explore the design space. However, many real-world applications offer auxiliary data sources (e.g. surrogate models or simplified simulations) that can support early exploration. Despite this potential, their integration into constrained BO remains largely unexplored. We propose a general multi-source framework that extends constrained Max-value Entropy Search, capturing inter-source correlation while balancing evaluation cost and information gain. Experiments on both synthetic and physics-based benchmarks show that our method efficiently identifies feasible and optimal solutions, even when auxiliary data are only weakly correlated. The proposed approach consistently outperforms existing methods, particularly in early-stage exploration.

Uncertainty Quantification for AI-Driven Crash Simulation Surrogates: A Comparative Study of Monte Carlo Dropout and Deep Ensemble on Open-Source Bumper Beam Benchmark

Machine learning surrogate models are increasingly being explored in engineering product development to augment simulation-driven design, offering near-instantaneous predictions that complement computationally expensive high-fidelity analyses. However, a critical gap limits their adoption in safety-critical workflows: a point prediction without an accompanying uncertainty estimate cannot tell an engineer when the model should not be trusted. This work presents a systematic, head-to-head comparison of two widely used uncertainty quantification approaches -- Monte Carlo Dropout and Deep Ensembles -- applied to an open-source surrogate pipeline built on NVIDIA PhysicsNeMo. A key contribution is the use of concrete dropout, a built-in PhysicsNeMo capability that eliminates the dropout rate as a manual hyperparameter by learning it end-to-end during training, directly addressing the most common criticism of Monte Carlo Dropout-based uncertainty quantification. Automotive crash simulation is used as the application domain, with a steel bumper beam impact problem serving as the benchmark. Both methods are evaluated on identical held-out simulations and compared on point accuracy, uncertainty band calibration, and computational cost. The results reveal a fundamental trade-off between accuracy and calibration that challenges the common assumption that deep ensembles are the default gold standard for surrogate uncertainty quantification. The findings demonstrate that well-calibrated, hyperparameter-free uncertainty estimates are achievable within a fully open-source engineering workflow at a fraction of the computational cost of ensemble approaches.

Surrogate Fidelity: When Can Open LLMs Explain Closed Ones?

Mechanistic interpretability (MI) requires full access to model internals, yet the APIs for most widely deployed language models at best expose log-probabilities over output tokens. This creates a surrogate problem: when do measurements made on open models allow us to make claims about a closed model? We evaluate surrogate fidelity at the prediction, attribution, and representation levels. For binary classification tasks, log-odds provide an API-compatible scalar readout of the model's representation space, and leave-one-out attributions provide insight into model behavior. Across eleven models spanning four families (Llama, Qwen, GPT, and Gemini), we find that prediction fidelity substantially overstates attribution fidelity: models that agree on what the answer is often disagree on why. We document an access-validity inversion: white-box signals like attention patterns and perturbation magnitudes are highly stable across models but only weakly predictive of causal attributions, which black-box input ablations capture by design. Mechanistic insight does not automatically transfer to closed targets, and prediction-level agreement is insufficient to warrant such transfer. Code and results are available at https://github.com/facebookresearch/surrogate.

RECAST: Model Reconstruction via Counterfactual-Aware Wasserstein Geometry under Limited Data

Counterfactual explanations (CFs) help understand machine learning models by identifying minimal input changes that would lead to alternative model outcomes. Recent work demonstrates their utility for reconstructing black-box models, enabling third-party auditing of opaque decision systems for fairness and accountability. Still, CF-based reconstruction may suffer from decision boundary shifts, overfitting, and restrictive assumptions requiring online query access to target platforms. We propose REconstruction via Counterfactual-Aware waSserstein opTimization (RECAST) under limited data and restricted access, a behavioral surrogate model based on Wasserstein barycentric prototypes. Our approach addresses decision boundary shifts by incorporating CFs as informative, though less representative, samples for both classes, maintaining high surrogate fidelity in low-sample regimes without requiring online access during reconstruction. To enhance fairness auditing, our method enables systematic group fairness diagnostics. Experiments on real-world datasets and various setups show that RECAST effectively achieves high fidelity and query efficiency, as well as stable results even when the access is limited and noisy.

BASIL: Bayesian Application for Scientific Iteration and Learning

We introduce BASIL, a user-friendly desktop application for process optimization. BASIL employs a Bayesian approach, incorporating special acquisition functions that can be used to solve both single and multi-objective optimization problems. It provides a graphical interface that enables users to input their experimental parameters, optimization objectives, and legacy data. This is then used to build surrogate models, which are coupled with acquisition functions to guide and optimize a process towards a desired objective. To facilitate model building, BASIL provides a variety of predefined surrogate model templates. BASIL can be used to optimize any arbitrary experiment or process with known, user-defined input variables, optimization objectives, and defined output.

AK-MCS-C2 : Active Kriging Monte Carlo Simulation method with conformal certification for failure probability estimation

We introduce a novel active-learning framework for failure probability estimation in structural reliability analysis that integrates Active Kriging Monte Carlo simulation with conformal prediction. The proposed approach employs an adaptive cross-conformal strategy specifically designed for small-sample settings and kriging surrogate models using the J+GP conformal estimator. Unlike standard AK-MCS methods, the proposed framework provides distribution-free guarantees on prediction errors, leading to more reliable classification of samples near the limit-state surface. This improved uncertainty quantification enhances both the accuracy and robustness of failure probability estimates, especially for rare-event regimes where such efficiency is crucial. Reproducible numerical results illustrate the effectiveness of the method and also compare it to classical approaches on well-established benchmarks.

Advances in Scientific Machine Learning for Coupled Fluid Flow and Transport

This chapter reviews recent advances in Scientific Machine Learning (SciML) for modeling coupled fluid flow and transport phenomena governed by the incompressible Navier-Stokes and scalar transport equations. Such systems, found in applications like turbidity currents and thermal convection, feature strong nonlinear coupling and multiscale behavior that make high-fidelity simulations computationally expensive. To address this, the chapter surveys state-of-the-art SciML methods for building efficient surrogate models, including linear reduced-order techniques based on Singular Value Decomposition (such as Dynamic Mode Decomposition) and nonlinear neural network approaches like Physics-Informed Neural Networks (PINNs) and $β$-Variational Autoencoders ($β$-VAEs). It first covers the authors' work combining these models with High Performance Computing strategies, including Adaptive Mesh Refinement/Coarsening (AMR/C) and scientific floating-point data compression. It then presents two new contributions: surrogate modeling of turbidity currents via PINNs, and the extraction of disentangled nonlinear modes from thermal flows using $β$-VAEs. Governing equations and representative benchmarks, including lock-exchange flows and Rayleigh-Bénard convection, illustrate these methodologies. The chapter is intentionally long, covering both the mathematical and physical foundations of coupled fluid flow and the computational aspects of state-of-the-art modeling. Overall, it demonstrates how SciML enables fast, accurate approximations of complex coupled systems within the specific data regimes and modeling assumptions considered, while substantially reducing computational cost relative to full-order simulations. Broader capabilities such as real-time prediction and uncertainty quantification remain active research directions whose feasibility depends strongly on the problem at hand.

Optimal scenario design for climate emulation

As deep learning for physical systems continues to grow in popularity, efforts to improve generalizability have primarily focused on designing architectures that embed physical constraints. However, for machine-learning surrogate climate models (emulators), we show that the low structural diversity in existing scenarios commonly used to generate training data places a ceiling on predictive skill. Here, we examine whether training datasets themselves can be optimized to improve generalization. We introduce a method to create datasets that produce emulators capable of generalizing to new, structurally different scenarios absent from the training data. We use a differentiable Simple Climate Model (SCM) to calculate the sensitivity of emulator loss to perturbations in the training data, iteratively updating the training data to maximize emulator skill. For an SCM, training on one scenario optimized in this fashion outperforms an emulator trained on six standard ScenarioMIP pathways. We achieve this higher predictive skill despite training on a smaller dataset, finding that our emulator successfully isolates distinct physical behaviors of different climate forcing agents (e.g., greenhouse gases vs. aerosols) without single-forcing runs. We then demonstrate that scenarios optimized using an SCM, when used to drive an intermediate-complexity climate model, produce a training dataset that yields a more skillful emulator than training on ScenarioMIP outputs. Our results suggest that, in the compute-constrained environment of running full-scale climate models, generating a small number of dynamically rich scenarios provides greater marginal value for emulation and characterizing system responses than expanding the suite of traditional emissions pathways.

Domain-Validity-Gated Metamorphic Testing of Scientific ML Surrogates

Scientific machine-learning (SciML) surrogates approximate expensive simulations, but exact expected outputs for arbitrary inputs are unavailable (the oracle problem). Metamorphic testing checks relations across executions, yet a candidate relation is not automatically valid: its preconditions, output mapping, and the numerical floor of the scoring operator determine whether a violation is meaningful. We study how candidate metamorphic relations (MRs) can be screened for domain validity and turned into executable, oracle-free test assets for SciML surrogates. We propose (i) a domain-validity rubric that admits a candidate only when its tolerance dominates the operator's numerical floor and its preconditions hold; (ii) an MR-card executable-asset format recording source cases, transformations, metrics, tolerances, and typed relation-level verdicts; and (iii) a case-study protocol on MeshGraphNets cylinder-flow surrogates, with a claim ledger binding every result to a tracked artifact. On a MeshGraphNets checkpoint, node permutation holds to machine precision, mirror-y is a bounded out-of-distribution stress finding rather than an exact symmetry, and absolute conservation stays deferred while a reference-relative guard passes. The same readings hold across held-out trajectories, a checkpoint roster, three further architectures, and PhysicsNeMo. On a second CFD task (compressible airfoil) the predicate instead rejects incompressible continuity on physical grounds, showing it reasons about domain validity rather than running a fixed checklist. On a second PDE family, FNO Burgers and heat surrogates run full admit/reject/execute verdicts. The evidence spans two CFD tasks and a second PDE family, supporting a validity-aware bridge from candidate MRs to auditable SciML test assets that separates model-level violations from out-of-domain applications.

Uncertainty Quantification of Engineering Structures by Polynomial Chaos Expansion and Multivariate Active Learning

In many engineering applications, a single high-fidelity model produces multiple quantities of interest (QoIs) under the same input parameters, e.g. finite element models of complex physical systems. To alleviate the high computational cost of direct model evaluations, surrogate models are widely used to construct efficient approximations of model responses. Naturally, the accuracy of surrogates strongly depends on the quality of the experimental design (ED). However, a single ED may not provide an adequate representation for all outputs simultaneously, especially when different outputs exhibit varying sensitivities to the input variables. A straightforward solution is to perform separate sampling for each output, but this results in increased sampling complexity and computational cost. From a statistical perspective, such an approach also ignores potential correlations among all outputs and may compromise data consistency. To address this issue, an adaptive sequential sampling method for constructing polynomial chaos expansion surrogate models is generalized for vector valued QoIs. The method sequentially selects new samples from a candidate pool based on their local contribution to the output variance, while balancing distance-based exploration of the input space and exploitation of aggregated variance information across all outputs. Its performance is compared with non-sequential Latin Hypercube Sampling through several numerical examples from engineering problems. Numerical results demonstrate that the proposed strategy improves both surrogate accuracy and stability, and provides a more reliable estimation of second-order statistics.

Model Stealing Through the Lens of Model Multiplicity

Model stealing attacks, where adversaries create high-fidelity surrogate models, are a significant threat to the intellectual property of machine learning services. Conventional wisdom suggests these surrogates could provide adversaries with economic leverage comparable to the original service providers. This paper challenges this assumption by evaluating model stealing attacks beyond mere fidelity to the target model. Because query-based extraction provides only partial supervision of the target's input-output behavior, the surrogate is not uniquely identified: many near-optimal surrogates can achieve comparable fidelity while differing in deployment-relevant properties. Instead of performing a classic learning-based model stealing attack, we compute the Rashomon Set (i.e., the set of almost-equally-accurate models) of surrogate models, and evaluate its diversity using multiplicity metrics (ambiguity, discrepancy, and Rashomon Capacity) and group fairness metrics. Across tabular, medical imaging, and NLP tasks, our experiments on real-world datasets reveal that despite exhibiting similar fidelity to the target model, surrogate models can display significant variances in other critical performance metrics. These findings cast doubt on the presumed equivalence between high-fidelity surrogates and the target model in practical deployment scenarios.

Physics-conforming Latent Twins

Surrogate models are central to scientific machine learning, where they enable fast prediction, simulation, inference, and control for complex physical systems. For time-dependent problems, however, accurate interpolation of training trajectories is not sufficient: reliable surrogates should also respect the conservation laws, invariants, admissibility conditions, and dissipative structures that give those trajectories physical meaning. We introduce Physics-conforming Latent Twins, a framework for learning latent surrogate solution operators whose dynamics satisfy selected physical principles by design. The method builds on the Latent Twin formulation by jointly learning an encoder, a decoder, and a latent flow map between arbitrary time-indexed states, while constraining the latent dynamics to preserve or dissipate prescribed structural quantities. We develop a constraint-transfer viewpoint that connects physical structure in the original state space with compatible constraints in latent space, and prove structure-preservation bounds showing how latent enforcement improves control of physical defects after decoding. We also derive algebraic conditions for latent flow maps that preserve linear and quadratic invariants or enforce dissipative inequalities. Numerical experiments on representative ODE and PDE benchmarks demonstrate improved constraint satisfaction, structural fidelity, and qualitative long-time behavior while maintaining accurate surrogate prediction.

Input-schema identifiability limits in physics-informed surrogates for mechanics-governed flow

Physics-informed and data-driven surrogates are increasingly used to approximate mechanics-governed flow fields, but the target quantities assigned to such models are not always identifiable from the input variables available at prediction time. We introduce an input-schema identifiability certificate for computational surrogates. Starting from a reduced physical model, the certificate decomposes a target field into components that are measurable from geometry, components that require boundary-condition information, and components identifiable only up to a symmetry quotient. This yields a pre-training audit: it predicts which oracle-channel interventions should reduce error, which should fail, and which ambiguity cannot be removed by changing the architecture, loss, optimizer, or sample size. We instantiate the framework for incompressible tubular flow using a Cosserat-rod reduction, where lumen velocity separates into a mesh-measurable tangent direction, a boundary-condition-dependent magnitude, and a signed-orientation ambiguity. Controlled experiments on patient-specific aortic CFD geometries, analytic Womersley flows, and an advection-diffusion transfer problem confirm the predicted pattern: supplying signed direction collapses angular error to the oracle regime, whereas supplying magnitude without orientation leaves the predicted sign ambiguity and yields 16-33 percent per-node sign flips. The results provide a mechanics-based diagnostic for deciding whether a surrogate modelling task is physically identifiable before training, and expose failure modes that aggregate error metrics can hide.

SAILS: Surrogate-based Analysis of Interactions via Local Effect Smooths

Feature interactions drive much of the predictive power of machine learning models, yet existing explanation methods only detect and quantify interactions without revealing their functional form, or visualize only restricted interaction types. We propose Surrogate-based Analysis of Interactions via Local effect Smooths (SAILS), a model-agnostic framework that analyzes pairwise interactions through interpretable generalized additive model (GAM) surrogates fitted to the local effects of a black-box model. For each interval of a feature of interest, the surrogate smooth terms isolate the interaction components on derivative level, enabling (i) interaction detection through a heuristic derived from significance tests on smooth terms, (ii) interaction form categorization into linear, product-separable, and non-product-separable types, and (iii) tailored, interpretable visualizations for each interaction type. We empirically validate the framework through controlled simulations and a real-world task, demonstrating its effectiveness for pairwise interactions, with limitations under strong feature correlations and higher-order interactions. SAILS fills a notable gap in the XAI toolbox, going beyond detection of interactions alone to characterizing their functional form.

Amortized Neural Optimization for Pre-Layout Signal Integrity Design Space Exploration using Differentiable Surrogates

Pre-layout design space exploration (DSE) for high-speed signal integrity (SI) analysis is often limited by the computational cost of simulations and iterative optimization algorithms within modern electronic design automation (EDA) workflows. While machine learning surrogate models accelerate the simulation step, optimizing designs still requires utilizing iterative black-box search methods. This iterative nature scales poorly, making multi-corner sweeps computationally expensive. As a solution, this paper proposes amortized neural optimization (ANO) for pre-layout SI design. ANO entirely eliminates iterative black-box inference by utilizing fully differentiable neural network surrogate models. ANO extracts analytical gradients from the surrogate to train a global optimization policy. Instead of solving the optimization problem repeatedly at inference, the optimization process is learned offline and therefore amortized. Once the ANO policy is trained, it maps different channel contexts directly to near-optimal design parameters in a single deterministic forward pass. The efficiency and accuracy of the ANO framework are demonstrated based on three complex SI design scenarios, including DDR5 decision feedback equalization (DFE), 9-dimensional SerDes Tx/Rx co-equalization, and DDR3 DQS differential pair routing to optimize eye diagram metrics under intra-pair skew constraints. By trading roughly 10% in optimality compared to instance-specific black-box algorithms, it realizes speedups of three to four orders of magnitude. For a large-scale 320,000-instance multi-corner SerDes sweep optimization, ANO collapses what would have taken days of computation using iterative search algorithms into a single batched forward pass that completes in milliseconds. This transforms computationally expensive SI optimization into real-time and interactive pre-layout DSE.

Decision-Aware Evaluation of Physics-Informed Surrogates

Physics-informed machine learning is often assessed by curve error, although engineering use depends on downstream decisions: ranking candidates, avoiding infeasible designs and limiting regret. We introduce pinn-gym, an open benchmark for material-conditioned lattice design that couples a transparent reduced-order crush-and-impact oracle with five printable polymer cards, dimensionless force-response targets and a protocol spanning curve fidelity, physical admissibility, top-k retrieval and mass regret. Across per-material, pooled and cross-material settings, low nRMSE is frequently insufficient to identify useful design selections. Physics-informed losses alter trade-offs rather than monotonically improving all metrics, and dimensionless conditioning improves comparability without making transfer symmetric. The benchmark is not a certified material model; within the released oracle, candidate generator and material cards, pinn-gym provides a reproducible testbed for evaluating PIML surrogates as decision systems rather than curve predictors alone.

Validation-Gated Multi-Agent Governance for Online Adaptation of Thermal-Hydraulic Surrogate Models under Operating-Regime Shift

Artificial-intelligence surrogates can support second-by-second thermal-hydraulic forecasting, but models selected and frozen offline may become condition-locked once deployed outside their pretraining envelope. This study develops a guarded continual-adaptation framework for experimental thermal-hydraulic loop data in which role-separated agents - Monitor, Diagnosis, Adaptation, Safety-Auditor, and Orchestrator - diagnose error signatures, prioritize candidate model families, and review promotions, while deterministic champion-challenger gates and background shadow learning retain final authority over model replacement. Seven surrogate families were screened by blocked three-fold cross-validation, and a temporal Fourier neural operator was selected as the initial champion for 60-s-history-to-10-s-trajectory forecasting on two held-out transients, with three seeds per adaptive mode. Static deployment gave a channel-averaged MAE of 7.06 and a 56.8% warning-exceedance ratio; rule-based adaptation reduced MAE to 6.54, whereas shadow refresh alone remained close to Static. The MA-Full mode, in which the role-separated multi-agent council reviews every evaluated stream step, achieved the lowest mean error, 5.72, and 35.8% exceedance, corresponding to a 19.0% improvement over Static. Paired bootstrap intervals against Static excluded zero, although intervals among adaptive modes overlapped and the six paired units limit broad statistical claims. Validated promotions from the neural operator to Transformer and graph neural network indicate that logged, gate-controlled adaptation can support auditable surrogate evolution while deterministic gates retain deployment authority.

On the Generalization in Topology Optimization via Sensitivity-Conditioned Bernoulli Flow Matching

Surrogate models for topology optimization (TO) exhibit highly variable out-of-distribution (OOD) generalization under distribution shifts such as changing loads or boundary conditions, yet the source of this variability remains unclear. We hypothesize that OOD performance is governed by how much information the conditioning signal preserves about the adjoint sensitivity (reduced gradient) that drives classical TO. Modeling the TO pipeline as a causal Markov chain, the Data Processing Inequality establishes that, under this abstraction, the sensitivity field is an information-theoretically optimal conditioning signal for topology prediction. However, computing exact adjoint sensitivities can be expensive or unavailable in practice; we observe that certain physical fields can approximate sensitivities through monotone transformations. To formalize this, we introduce \textbf{pseudo-sensitivities} to characterize which fields enable generalization versus those that are information-poor. We then show that a sensitivity-conditioned Bernoulli flow-matching generator empirically confirms these predictions: conditioning on sensitivities yields state-of-the-art OOD performance, while increasingly distant physical fields degrade toward raw parameter conditioning. Results hold across structural TO benchmarks under load shifts and our new CFD-TO dataset under boundary-condition shifts such as multi-outlet configurations. Code and datasets are available at https://tum-pbs.github.io/topotransformer/ .

ShapeBench: A Scalable Benchmark and Diagnostic Suite for Standardized Evaluation in Aerodynamic Shape Optimization

Rapid progress in aerodynamic shape optimization (ASO) has outpaced currently-available standardized evaluation frameworks. Fair comparison requires a unified benchmark spanning diverse shape classes, objective formulations, and matched-budget state-of-the-art baselines. We introduce ShapeBench, an open-source ASO benchmark with a unified API spanning 103 tasks across eight shape categories and multiple optimization regimes. Each ShapeBench task includes a validated surrogate for fast search; when feasible, a high-fidelity Computational Fluid Dynamics (CFD) pipeline for final verification is available, enabling systematic fidelity-gap analysis. ShapeBench provides a reproducible protocol with well-configured baselines to compare fairly using a consistent budget metric, allowing for comparison among both classical and LLM-driven methods, including general-purpose optimizers and a new domain-specialized evolutionary LLM baseline, ShapeEvolve. Results on ShapeBench demonstrate substantial variance in optimizer rankings across shape categories and problem formulations, with mean pairwise Spearman $ρ= 0.013$, so single-task conclusions do not reliably generalize across problem classes. The benchmark is also far from saturation; classical methods are rarely applicable across all shape categories and tasks, further highlighting the need for more general-purpose approaches.