engineering design teams

Abstract: Machine learning (ML) architectures are being developed for fast emulation of numerical simulators to accelerate both scientific discovery and engineering design. While these approaches are well-tested on popular PDE (partial differential equation) benchmarks, it is necessary to evaluate their performance on datasets that more accurately reflect industrial and engineering applications. We evaluate several computer vision-based architectures trained as surrogate models on a challenging computational physics task involving multiple materials, revealing significant implementation challenges for adapting certain pre-trained models, including transformer-based architectures. For such multi-physics multi-material datasets, our results underscore the importance of learning algorithms designed for sparse and imbalanced data, techniques for adapting spatial encodings and physical consistency metrics, in addition to methods for reducing the cost of generating sufficient training data.

Abstract: Many decision-making tasks are inherently multi-objective. Interactive evolutionary multi-objective optimization algorithms (iEMOAs) are particularly well-suited to help the decision-maker find their most preferred solution. However, many of these algorithms employ black-box preference models. For high-stakes decision-making tasks, like healthcare and defense, a high level of transparency is needed, for instance to support accountability. We propose an interpretable iEMOA which uses active learning to efficiently learn a tree-based preference model directly from pairwise comparisons. The survival operator of NSGA-II and NSGA-III is extended with the learned preference model to guide the algorithm towards the region of interest. An extensive experimental study compares the proposed method to a state-of-the-art black-box model and a state-of-the-art interpretable model. Results indicate that our proposed model outperforms the alternatives in terms of finding the most preferred solution at the cost of a slightly worse average final population. Finally, a case study on a real-life engineering problem illustrates how inspecting the learned model reveals which objectives drive the decision-maker's preferences.

Abstract: Complex objects such as engineering designs and proteins are often difficult to optimise because their design spaces exhibit high-dimensional structure and objective evaluations are expensive. Generative models provide continuous latent representations, but their latent spaces can have thousands to tens of thousands of dimensions, creating a regime where the latent dimension $D$ greatly exceeds the evaluation budget. We introduce SABLE, a Bayesian optimisation method for high-dimensional latent spaces with an isotropic distribution and limited budget. SABLE uses a Bayesian affine surrogate for prediction and acquisition, treating higher-order structure as surrogate discrepancy. After $N$ observations, the slope update has dimension at most $N-1$, yielding a decomposition of each query into an in-span component optimised by expected improvement (EI) in at most $N$ dimensions and an off-span component governed by a scalar norm. We show that the off-span norm implicitly selected by affine EI can lead to underexploration, and SABLE instead prescribes it using a finite-horizon schedule, without restricting search to a learned subspace. A recompression scheme reduces information to $\mathcal O(M)$ pseudo-observations, bounding refitting cost by $\mathcal O(M^2D+M^3)$ while keeping parameter inference, prediction, and acquisition decisions to tens of milliseconds. Across synthetic benchmarks and latent-space optimisation tasks, SABLE achieves high sample efficiency and reduces decision time by several orders of magnitude at large budgets.

Abstract: Scientific discovery often requires identifying a small number of high-performing designs in vast, constrained search spaces. This is difficult when evaluations are costly, feasible solutions are sparse, parameters are strongly coupled, and physical constraints are strict. Recent AI for AI methods can automatically improve algorithms and optimization procedures. However, general purpose approaches are not designed around scientific priors, physical constraints, and limited evaluation budgets. We introduce ADAPT for Science, a multi-agent framework that treats scientific optimization as two coupled decisions: where to search and how to search. ADAPT uses historical designs to identify promising and diverse initial conditions, progressively concentrates computation on favorable search directions, and evolves the optimization procedure from execution feedback. We evaluate ADAPT on the design of gravitational wave detectors using a differentiable physics simulator and eight unseen detector topologies. Under matched scientific evaluation budgets, ADAPT achieves a mean loss of 0.204 +/- 0.101, reducing loss by 54.9% relative to the best classical optimizer and by 62.2% relative to the best general purpose agentic evolution baseline. ADAPT achieves the lowest loss on all unseen topologies among the evaluated baselines. ADAPT provides a step toward scientific optimization systems that continuously learn from prior experience and their own search outcomes.

Abstract: How can language models learn to optimize physical designs through experience? We introduce FracLearn, an experience-abstraction-generalization framework evaluated through a deliberately unfamiliar, Tetris-inspired fracture game. The model first proposes architectures and examines simulated fracture responses to accumulate experience. Abstraction organizes these observations into conditional principles linking reinforcement placement, crack evolution and load transfer, with supporting evidence and failure conditions. Generalization challenges the model to combine these principles in new architectures and surpass the earlier design record. Campaigns demonstrate progressive refinement and recovery through hypothesis revision, yielding a best composite score 11.0% above the experience-stage record. Fracture analyses connect improved performance to crack deflection and temporary trapping as toughening mechanisms, alongside greater residual load capacity. Learning occurs through external knowledge and decisions, without model-weight updates. This approach offers a route to scientific agents that turn computational experiments into reusable physical knowledge for materials discovery and engineering design.

Abstract: In many engineering design problems, the objective and constraints depend on the state: the solution of a PDE determined by the design parameters. We consider improving a design while holding selected state observables near trusted values, which we call state preservation constraints. Constrained Bayesian optimisation handles these with a learnt feasibility model, but struggles with this problem's highly anisotropic feasible set. Our central idea is to pre-compute the set of controls whose linearised constraint response stays within tolerance, thereby pulling back the state-space constraint into design space. This linearisation defines an ellipsoid from which we can efficiently draw a large number of well-spread candidates. The underlying linear response map is refined online, and the ellipsoid is rebuilt accordingly. We demonstrate the method end-to-end on our key application - Tokamak divertor optimisation under plasma-boundary preservation.

Abstract: Autoresearch agents tackle open-ended problems by repeatedly proposing candidate solutions, evaluating them, and using feedback to guide subsequent experiments. We show that independent runs of the same agent on the same task often plateau at substantially different scores, with gaps that persist even after considerable additional compute. Embedding their candidate artifacts by functional similarity provides further evidence that trajectories remain in localized regions of the solution space, which we call idea basins. To help agents escape these basins, we study a simple periodic intervention, fork-and-flush. Our method forks the agent into parallel trajectories, each inheriting the accumulated workspace but starting with a fresh chat context. After running each trajectory for a fixed horizon, the agent continues from the highest-scoring one. Across 13 long-horizon research and engineering tasks, with individual agent runs lasting up to several days, fork-and-flush outperformed the single-run and best-of-N baselines by a relative improvement of 66.0% and 44.4%, respectively, on the min-max normalized average score under an equal compute budget.

Abstract: Planar graphs are central to applications across science and engineering, yet existing generators provide limited support for goal-directed generation under hard structural and geometric feasibility constraints. We propose a dataset-free method for generating planar graph embeddings by combining parametric graph grammars with safe reinforcement learning to optimize generic task-specific objectives while satisfying constraints during construction. We formulate the generation process as a constrained Markov decision process, where the graph grammar defines the state and action spaces. We further introduce an action projection that maps sampled actions toward state-dependent safe sets, improving constraint satisfaction during training. In contrast to classical graph generators and deep generative models, which typically offer limited goal-directed control or rely on weak constraint satisfaction, our method constructs feasible planar graph embeddings directly during generation. We also introduce a benchmark suite for constrained and goal-directed planar graph generation, together with classical and deep generative baselines. Across all benchmark tasks, our method consistently outperforms baselines while satisfying the formulated constraints.

Abstract: Structural diagrams are widely used to represent complex systems and relational information across scientific, engineering, procedural, and spatial domains. Recent vision-language models (VLMs) have become increasingly capable of recognizing diagram elements and reasoning about their content, while complete diagram topology extraction remains comparatively underexplored. In this paper, we study diagram-to-graph topology extraction: extracting all diagram entities and the complete relations among them. To enable large-scale supervised training and systematic evaluation of this task, we introduce Knossos, a benchmark of 19,200 diagrams across six diverse domains, with 245,179 nodes and 439,740 edges. Its symbolic generation process provides exact alignment between rendered diagrams and annotations of complete topology, relation types, and connector geometry. To address the modeling challenge of complete topology extraction, we also present Ariadne, a structured framework that decomposes the task into node inventory extraction and source-conditioned edge prediction. Extensive experiments show that training on Knossos substantially improves complete topology extraction in smaller open-source VLMs. Ariadne further improves over one-step extraction under matched supervision, demonstrating the additional benefit of structured decomposition. It achieves the highest average Edge F1 among the evaluated methods on Knossos, while both backbone variants also improve over their unadapted counterparts on the real-world external benchmark. Code and benchmark are available at https://github.com/bangwayne/knossos_Ariadne_Public.

Abstract: Differentiable programming connects scientific computation with gradient-based inference, learning and design. Extending these capabilities across a heterogeneous software ecosystem requires specialized effort to implement derivatives, integrate interfaces and evaluate quality. AI coding agents can accelerate this transformation, but translating their capabilities into useful scientific software requires identifying research needs and evaluating how well implementations meet them. We present an environment for agent-driven evolution of differentiable scientific software that connects demand identification, development and quality evaluation. A unified differentiation interface exposes reusable derivative rules alongside existing numerical routines, allowing research tasks to share these capabilities. Research requirements guide development, with implementations assessed through independent derivative checks, workflow tests and performance evaluation. Validated software, research programs and tests become shared resources for subsequent studies. We construct and validate automatic differentiation extensions across 20 packages spanning physical, chemical and biological modeling, with research workflows demonstrating reuse across tasks. Benchmarks demonstrate computational savings over finite differences in gradient evaluation and complete parameter estimation. Research-driven revisions make previously unsupported workflows differentiable, correct derivatives of scientific observables and eliminate redundant computation. Quantum-control and thermal-design studies revise objectives in response to physical evaluation, improving designs while reusing existing derivatives. This work provides a practical approach to expanding differentiable programming across established scientific software and organizing AI agents around the recursive improvement of a shared computational ecosystem.

Abstract: Applications such as engineering design often require us to optimize a black-box function, i.e., a system whose inner processing is not analytically known and whose gradients are not available. Practitioners often have a fixed budget for the number of function evaluations and the performance of an optimization algorithm is measured by its simple regret. In this paper, we study the class of "Optimistic Optimization" algorithms for black-box optimization that use a partitioning scheme for the domain. We develop algorithms that learn a good partitioning scheme and use flexible surrogate models such as neural networks in the optimization procedure. For multi-index functions on an $m$-dimensional subspace within $d$ dimensions, our algorithm attains $\tilde{O}(n^{-β/ d})$ regret, where $β= 1 + \frac{d-m}{2m-1}$, as opposed to $\tilde{O}(n^{-1/d})$ for SequOOL, a state-of-the-art optimistic optimization algorithm. We use our approach to improve the quality of Activation-aware Weight Quantization (AWQ) of the OPT-1.3B model, achieving $\sim10\%$ improvement in performance relative to the best possible unquantized model.

Abstract: Quantum-inspired evolutionary optimization (QIEO) represents design variables as a set of qubits and searches a continuous, multi-dimensional landscape through rotation of the qubit's amplitude pair. Every generation rotates those amplitudes toward a single elite, which corresponds to that generation's best. The update is cheap, almost parameter-free, and well-suited for massive parallel implementation, which has encouraged its adoption in engineering, design, and planning applications. However, there are critical issues with this formulation, principally, the treatment of design variables as independent probability components which make it incapable of exploiting local curvature, anisotropy, or variable coupling. Despite this, QIEO is believed to hold promise, and has been used extensively to solve real-world problems, with significant qualitative and computational advantage over its classical counterpart, Genetic Algorithm (GA). A collection of 256 (actually 508; 256 unshifted + 252 shifted, 4 could not be shifted) continuous function are selected from the prior works, in such a way that they represent eleven landscape characteristics, namely continuity, differentiability, separability, scalability, modality, convexity, conditioning, symmetry, maximum dimensionality, dimension dependency, and the coupling pattern of the design variables. These functions are then solved by three QIEO variants, two GA encodings and Hansen's Covariance Matrix Adaptation Evolution Strategy (CMA-ES). The results are evaluated in terms of computational cost, solution precision, and specialization across landscape characteristics. They identify the conditions under which QIEO provides competitive performance, clarify where its independent-variable representation becomes limiting, and establish whether particular QIEO variants offer advantages for specific landscape characteristics.

Abstract: Multi-Fidelity optimization (MFO) has received extensive attentions in engineering design, which resorts to augmenting the small number of expensive high-fidelity (HF) samples by a large number of low-fidelity (LF) but cheap samples to improve the optimization performance. A key factor that influences the effectiveness of MFO is how to adaptively assign samples for HF and LF simulations in the iteration process. To address such sample assignment issue in MFO, we propose a new infill criterion named as Filter-GEI, which imposes an adaptive filter function on top of the generalized expected improvement (GEI) acquisition function. In particular, by taking the correlations between HF and LF models into account, the Filter-GEI can efficiently allocate HF and LF samples to achieve a good balance in between the local and global search. Furthermore, considering parallel computing, the Filter-GEI infills multiple HF and LF samples in each iteration, which can further improve its efficiency as computing power increases. Through tests on five mathematical toy problems and one engineering problem for the turbine blade design, the effectiveness of the proposed algorithm has been well demonstrated.

Abstract: The problem of multiobjective optimization under uncertainties is often approached by taking the expectation of each objective. In this work, we propose instead to formulate this as a Bayesian decision problem and to rely on the expected value of the hypervolume, which is to be maximized with respect to a finite set of input points. We show that this can be performed using methods based on gradients in a stochastic optimization framework, provided that care is taken with respect to dominated points. Moreover, in the absence of readily available differentiable code, we propose to use Gaussian Processes as differentiable surrogate models, in order to perform the optimization. An additional contribution in this work are some active learning strategies, through acquisition functions which helps construct a surrogate model well-designed for the multiobjective optimization problem at stake. These strategies are compared on simple analytical problems to assess their performances.

Abstract: Surrogate-assisted evolutionary algorithms (SAEAs) are effective methods for solving expensive optimization problems (EOPs), where surrogate models replace most expensive evaluations and critically influence the final optimization results. In recent years, tabular foundation models have advanced rapidly, and the Tabular Prior-data Fitted Network (TabPFN) has been adopted as a surrogate model for EOPs due to its strong predictive capability, demonstrating promising performance. Motivated by its potential as a surrogate model in SAEAs, this work conducts a comprehensive study that combines extensive experiments with in-depth theoretical analysis to investigate the effectiveness of TabPFN. Specifically, we perform experiments across both offline and online SAEA settings, covering diverse problem scenarios such as single-objective, multi-objective, constrained, combinatorial, mixed-variable, and engineering optimization problems. In addition, we further analyze the advantages and limitations of TabPFN within SAEAs and provide practical guidelines for its application in different optimization settings. Results show that the effectiveness of TabPFN is highly problem dependent, and it cannot replace conventional surrogates universally. Overall, TabPFN should be adopted selectively according to data availability, landscape complexity, search space characteristics, and its role within the algorithm. Customized model management strategies and role-specific algorithm design are necessary to fully exploit its advantages and avoid its pitfalls.

Abstract: The DIRECT algorithm is a deterministic global optimization method known for its versatility and balanced exploration-exploitation strategy. However, DIRECT-type algorithms are primarily effective for low-dimensional problems and often exhibit slow convergence as dimensionality increases, limiting their applicability to more complex optimization tasks. To address this limitation, this paper introduces X-DTC-GL, a novel DIRECT-type algorithm that incorporates dynamic partitioning and hybridization techniques. The dynamic partitioning approach adaptively refines the search space based on local one-dimensional surrogate models, enabling rapid subdivision of promising hyper-rectangles. The hybridization strategy selectively employs a hill-climbing method to exploit promising regions identified by the surrogate models. Extensive experiments on four diverse benchmark suites demonstrate that X-DTC-GL significantly outperforms existing DIRECT-type baselines, achieving improvements of ~12% in solvability and ~27% in solution quality. Performance-profile analyses indicate the fastest convergence on up to ~40% of instances, the best runtime performance on ~17% of problems, and competitive overall execution times. By improving performance within the partition-based framework, these advances strengthen the algorithm's competitiveness in state-of-the-art black-box optimization.

Abstract: Discrete black-box optimization is often addressed using approaches such as Sequential Model-Based Optimization (SMBO), which aims to improve sample efficiency by fitting surrogate models that approximate a costly objective function over a discrete search space. In many real-world problems, the set of feasible inputs is often given by logical constraints known in advance. However, existing surrogate modeling techniques generally fail to capture the symbolic rules governing feasibility in discrete input spaces. In this paper, we propose a surrogate modeling approach based on tensor decomposition that captures the structure of discrete search spaces while directly integrating feasibility information. To implement this approach, we formulate surrogate model training as a constrained polynomial optimization problem and solve a relaxed formulation using a differentiable penalty term derived from T-norms. Our experiments on both synthetic and real-world benchmarks, including a pressure vessel design task, demonstrate that the proposed method improves sample efficiency by effectively guiding the search away from infeasible regions.

Abstract: Every data-driven equation discovery method assumes (implicitly and without verification) that the target system obeys a single governing law ($K{=}1$). Here we show that this assumption is the primary bottleneck limiting scientific discovery in multi-mechanism systems, and introduce Physical Law Ecology, a framework that makes $K^*$ (the number of coexisting independent mechanisms) itself the first quantity to be determined from data. The framework automatically mines a pool of topologically distinct candidate equations, constructs a continuous dominance weight field across parameter space, and discovers analytic evolution laws governing mechanism succession---with optional monotonicity constraints encoding irreversible physics. Across four unrelated systems (elastomer mechanics, pool boiling, galactic dynamics, and droplet evaporation), BIC consistently identifies $K^*{=}3$ independent governing topologies. Applied to 163 SPARC galaxies (3,269 spatially resolved measurements), the framework autonomously recovers three gravitational laws whose coexistence provides evidence against the single-universal-acceleration hypothesis of MOND ($p<10^{-34}$). In engineering applications, multi-law weighted prediction reduces error by 67-72\% over single-equation baselines while retaining full interpretability. By establishing the determination of $K^*$ as the zeroth step of scientific discovery-prior to and independent of equation search---this work opens a direction orthogonal to existing symbolic regression: not finding better equations, but mapping the ecology of mechanisms that govern complex systems.

Abstract: Offline multi-objective optimization requires not only moving the objective vectors of candidate designs toward the Pareto front, but also distributing them effectively along it. Generative methods have recently emerged as a natural approach because they learn a distribution over feasible designs while allowing generation to be steered toward promising designs. Existing methods, however, largely retain classical sample-wise guidance strategies, leaving the distribution-level modeling capability of generative methods underused. We propose ParetoTransport, a training-free guidance method for pre-trained flow-matching models that explicitly specifies and refines a population-level distribution in objective space. ParetoTransport guides a flow-matching sampler to iteratively transport the empirical offline distribution toward the Pareto front, with Wasserstein matching to intermediate proxy distributions. This directly controls distributional displacement and mass allocation along the front. We establish a convergence result and demonstrate state-of-the-art performance on standard offline MOO benchmarks, extending recent evaluations beyond hypervolume to generational distance, inverted generational distance, and Wasserstein distance.