aerospace engineers

Abstract: The curse of dimensionality associated with solving the Hamilton-Jacobi-Bellman equation for the value function remains a key obstacle for real-time optimal feedback control of high-dimensional nonlinear dynamical systems. This is especially severe in aerospace applications such as relaminarizing unsteady turbulent flows and recovering from aerodynamic stall where nonlinear dynamics play a significant role. We introduce Balanced Active Subspaces for Optimal Control (BASOC), a model reduction framework which seeks to find directions in state space along which the value function is most sensitive, and the distribution of states exhibits maximum variance along optimal trajectories. BASOC leverages trajectory optimization and the Pontryagin minimum principle to obtain state and co-state (value function gradient) data along locally optimal trajectories for constructing state and gradient covariance matrices. Balancing these matrices provides an oblique projection for approximating the value function, which can also be used to construct reduced-order models and surrogate feedback control laws. We show that for linear-quadratic optimal control problems, BASOC becomes equivalent to a snapshot method for initial condition balancing of the optimally controlled closed-loop realization. The framework is demonstrated on a nonlinear three-dimensional system where POD and balanced truncation are known to perform poorly, and on the nonlinear complex Ginzburg-Landau equation to demonstrate feasibility for larger-scale systems.

Abstract: Computational Fluid Dynamics (CFD) is essential in contemporary engineering design, yet it remains expensive to compute and can take thousands of CPU/GPU hours or more for a single high-fidelity simulation. Recent developments in machine learning for scientific modeling have led to powerful surrogate frameworks that can approximate flow fields and physical quantities by using a fraction of the computational cost. However, most of these methods require largescale homogeneous datasets or simple geometries, exhibiting severe generalization gaps when applied to complex and data-scarce configurations. To address this, we propose the Factorized Geometry Convolutional Neural Operator (FG-ConvNO) for robust geometry-aware propeller pressure prediction under limited training data. We introduce geometryaware encoding, efficient interpolation-based decoding, and auxiliary global quantity supervision. In addition, we incorporate DISCO blocks that use discrete continuous convolutions to make the model discretization agnostic. In our experiments, FG-ConvNO achieves the highest accuracy for both surface pressure and global thrust prediction on a procedurally generated propeller CFD dataset. Geometry-aware encoding and architectural simplification improve stability, while random vertex subsampling enhances robustness. Overall, adding geometric priors to grid-based convolutional operators reduces overfitting on complex propeller geometries and improves generalization in low-data regimes.

Abstract: Deep reinforcement learning (DRL) is challenging long-held assumptions in active flow control. By learning directly from interaction with a flow, DRL agents can find actuation strategies for nonlinear, unsteady flows without explicit models, often exploiting mechanisms that classical control would not anticipate. High-speed flows are a demanding test of this promise: shocks, shock/boundary-layer interactions, transition, aerothermal loading and microsecond-scale dynamics strain both algorithms and hardware. Yet most demonstrations remain idealized, low-speed simulations with limited evidence of robustness, interpretability, transferability or experimental deployment. In this perspective, we examine what constrains DRL-based high-speed flow control, including compressible simulation cost and fidelity, data efficiency, sensing in extreme environments, reward design, explainability, and generalization across Mach and Reynolds number. We argue that these limits reflect a tension between data-driven optimization and the structured physics, constraints and uncertainties of real flows. We then highlight where DRL may go beyond conventional approaches: adaptive control of shock-induced separation and turbulent boundary layers, coordination of distributed actuators, and discovery of unconventional flow-manipulation mechanisms.The central challenge, however, is translating these capabilities into reliable technology, which will require validated compressible simulation environments, physics- and constraint-aware learning, robustness to off-design conditions and sensor degradation, real-time operation, hardware-in-the-loop and wind-tunnel validation, and credible pathways to safety and certification.

Abstract: We introduce a conformal prediction framework for regression with Grassmann-valued responses. The proposed method constructs prediction regions in the form of metric balls directly on the Grassmann manifold, using basis-invariant geometric distances as non-conformity measures and scaling the corresponding non-conformity scores through a learned prediction difficulty estimator. This yields locally adaptive, input-dependent prediction regions that respect the underlying manifold geometry, while retaining the finite-sample marginal coverage guarantee of split conformal prediction under exchangeability. We evaluate several Grassmannian distance metrics and compare their prediction-region efficiency on synthetic benchmarks and an airfoil inverse shape-design problem. The results highlight the advantages of geometry-aware non-conformity scores, while local adaptation improves empirical coverage uniformity across prediction difficulty levels and, in strongly heteroscedastic settings, can substantially reduce prediction-region size while maintaining the target coverage.

Abstract: Cage-based deformation (CBD) parametrises 3D geometry through a small set of control handles, effectively enabling a variety of tasks from animation and interactive modelling to tool-based co-design, neural deformation transfer, and aerodynamic shape optimization. Many optimization approaches relying on CBD employ regularisation strategies to reduce the distortion of the deformed mesh by encouraging smooth, regular cage deformations. These techniques offer soft guidance to an optimization algorithm towards desirable deformations, but compete with the task objective rather than changing the deformation parameterization itself. In this work we introduce Structural Affinity for CBD, an explicit regularisation method which enables smooth deformations through control cages by exploiting a two-cage structure to couple cage-handle motion directly. Structural Affinity precomputes an affinity matrix using mean-value coordinates, binding the inner control-cage to a coarser outer-cage. This matrix defines how much a cage handle displacement propagates to neighbouring handles which substantially decreases and often eliminates cage self-intersections, reduces mesh distortion, and adds linear overhead at deformation time. Across robotic control--morphology co-design, source-to-target neural deformation transfer, and aerodynamic wing shape optimization, Structural Affinity produces more regular deformations and substantially reduces reliance on hand-designed structural loss terms. We report consistent gains on three complementary diagnostics: the cotangent Laplacian, a proxy for surface smoothness; cage distortion, capturing whether control handles move coherently; and surface roughness, which measures undesirable oscillation in wing geometry.

Abstract: Designing the stacking sequence of a composite laminate is a discrete optimisation problem: each ply takes one of a few orientations, each evaluation may cost a finite-element solve, and the design must obey manufacturing rules and design guidelines, which optimisers enforce by penalty, repair or rejection. We describe the admissible set exactly. The two manufacturing rules forbid a finite set of factors, so the sequences they admit form a regular language, recognised by an automaton that tracks the last orientation and the length of its run; balance and the ten per cent rule constrain the Parikh vector and are carried by a dynamic program over automaton state and counters. One table, polynomial in N, counts the admissible sequences without producing them, draws them uniformly, and tells whether a partial sequence can still be completed. We give pseudocode, exact counts for three orientation sets, closed-form ceilings on the composition, and four of the five single-rule entries a published table left uncomputed. At 48 plies, 99.8% of the nodes of a layer-wise search tree checking the rules locally have no admissible completion on eight orientations; the completion test removes them. A one-point crossover that cuts two admissible parents only where they share an automaton state and their child closes the counters returns admissible children by construction.

Abstract: Projection-based model order reduction mitigates the computational cost of high-fidelity parametric simulations but can suffer from the "snapping phenomenon", whereby a projection-based reduced-order model (PROM) rigidly latches onto a training snapshot, impairing parametric interpolation. Standard methods also struggle to enforce parameter-dependent boundary conditions without costly constraints or penalty schemes. This work proposes a tripartite taxonomy of snapping, distinguishing intrinsic, extrinsic, and numerical mechanisms. Focusing on intrinsic and numerical snapping, we introduce a unified framework based on a parameter-dependent shift vector. By embedding spatial transport into the state ansatz, the method enforces boundary conditions exactly, restores continuous parametric sensitivity, and eliminates snapshot latching in affine and regression-augmented PROMs without increasing online complexity. We establish the framework's mathematical foundations in the linear regime, showing how it overcomes test-space orthogonality blind spots. In nonlinear computational fluid dynamics, we identify the roles of boundary conditions, mesh grading, and discrete equation scaling in numerical snapping. We also show that formulation-toggling is an unreliable heuristic that can compromise near-field accuracy. Finally, we develop a field-theoretic realization using a spatially varying shift vector governed by a scaled Laplace equation. The approach is validated on structural and aerodynamic benchmarks, including viscous flow around a NACA airfoil and a three-dimensional NASA Common Research Model.

Abstract: Bayesian optimisation is the natural tool for shape design when objectives are expensive and non-differentiable, but it needs a compact yet expressive parameterisation of the search space. Hand-crafting one is a complex endeavour requiring domain expertise, and often yields implicit infeasible regions, artificial bounds, and coupled, unordered coordinates. We instead learn the parameterisation from a collection of existing designs, applying principal component analysis to the deformations between shapes. The result is a linear, interpretable search space in which the number of components explicitly trades expressivity against dimensionality. Across aerofoils, wings, and radio-frequency cavities, spanning 2D geometry to 3D aerodynamics and electromagnetics, we show improved sample efficiency and the ability to explore beyond the confines of hand-crafted baselines.

Abstract: AutoCFD5 Case 2 compares the participants' CFD results with wind tunnel measurements of surface pressure, velocity profiles and force coefficients. To place each run on a diagram of error against computational cost, these quantities must be combined into one number. This note defines that number, the joint error. Following the practice of interlaboratory proficiency testing (ISO 13528), every deviation from the experiment is expressed in units of the spread of the participants' results at that point, estimated robustly with the standard's Algorithm A. The point-wise spreads are pooled into one scale per component, so that every measurement point carries equal weight within its component. The joint error is a fixed weighted sum of five component errors. The scales are computed once from all AutoCFD5 submissions received by 5 October 2026 and then frozen, so that scores are reproducible and comparable across workshops.

Abstract: Joint-Embedding Predictive Architectures (JEPAs) provide a framework for learning compact representations without directly reconstructing high-dimensional observations. However, in parameterized physical systems, learned representations can entangle geometry with operating conditions and task-specific physical responses, limiting their reuse across prediction tasks. We introduce D-JEPA (Design-recoverable JEPA), a geometry-centric JEPA that computes a compact representation from geometry alone and reuses it across operating conditions and physical response spaces through lightweight physics-specific decoders. An explicit design-recoverability objective encourages the geometry latent to preserve information about the underlying design variables, enabling the representation to support design analysis and optimization. We further identify a case-level collapse failure mode in which target representations become nearly invariant across distinct geometries despite low reconstruction error, and mitigate it using case-level variation constraints and auxiliary target reconstruction. Across four 3D aerodynamic, hydrodynamic, and structural benchmarks, D-JEPA maintains or improves full-field prediction accuracy while achieving near-perfect linear recoverability of design parameters. The frozen geometry representation can be reused at held-out operating conditions and transferred to a structural response task with fewer trainable parameters. Finally, the representation supports differentiable design optimization, with designs validated using high-fidelity CFD, preserving the predicted ranking of candidate designs. These results demonstrate that separating a reusable geometry representation from physics-specific prediction provides a practical representation for scientific surrogate modeling and design.

Abstract: Multidisciplinary Design Optimization (MDO) enables the application of optimization algorithms to complex engineered systems, ranging from aerospace and automotive to robotics and microelectronics. Such multi-component systems typically consist of coupled subsystems, each characterized by its own design variables, constraints and objectives. Without adequate coordination of these couplings, subsystems may be optimal in isolation while the overall system remains suboptimal or even infeasible. Distributed design optimization coordinates coupled subsystem optimization problems while allowing them to retain control over their local design variables. Although promising coordination methods exist, their application is hindered by the lack of a comprehensive software framework which supports intuitive problem definition, provides suitable distributed coordination algorithms, is modular and extensible, enables interactive (post-)processing, and supports the distributed computation of subsystem executions. This work derives requirements for such software, assesses existing frameworks against them, and introduces DistributedDesignOptimizer, an open-source Python framework to fill this gap.

Abstract: A piezoelectric transducer embedded in a pitch-plunge aerofoil with a finite-mass trailingedge flap converts the limit-cycle oscillation that follows flutter into electrical power. The design findings for such a harvester have so far been obtained with incompressible strip theory, whose aerodynamic state is a handful of lag variables. Here the same section, the same transducer and the same test cases are coupled instead to the two-dimensional compressible Euler equations, giving a full-order model of twelve thousand states, and the two aerodynamic models are placed side by side on the flutter boundary, on the limit cycle and on the harvested power, with the strip-theory results compared against higher fidelity aerodynamic modelling provided by CFD. The degree of freedom carrying the transducer remains the first-order design variable, and the ranking of the mountings is unchanged and wider, while strip theory is found to under-predict the harvested power of the compressible section and to overstate the effect of the transducer on stability where the electrical time constant meets the flutter frequency. A nonlinear reduced model of four states, built on eigenvectors of the coupled Jacobian at the velocity of interest, reproduces the frequency of the cycle, its pitch amplitude, the transducer voltage and the mean power, and misstates the proportion of plunge to pitch in the orbit and its phase. That error is shown to be independent of the amplitude of the cycle and to survive enlargement of the basis, which places it in the retained subspace rather than in the order of the expansion, and suggests that such models should be judged on the shape of the orbit rather than on a single amplitude.

Abstract: Long-horizon scientific discovery requires agents to alternate between exploration, disciplined execution, and critical reassessment as evidence changes. Current language models are trained primarily on the products of science and optimized using outcome-level signals, providing limited supervision for these process-level shifts in scientific judgment. We investigate whether such judgment can be recovered from scientist interaction traces and used to control the internal computation of a frozen frontier model. Using contrastive interventions collected during real scientific research, we identify a coordinated, low-dimensional control structure within Kimi 2.6, a trillion-parameter mixture-of-experts model. Residual analysis, attention-weight subspace alignment, and cross-layer singular value decomposition converge on a mid-depth control surface spanning key layers. We introduce Metacognitive Steering, an inference-time controller that reads the model's cognitive regime and dynamically composes layer-specific interventions for exploration, procedural convergence, or critical reassessment without modifying model parameters. Behavioral analyses show that this control produces more sustained exploration, explicit pruning, and evidence-responsive synthesis. We operationalize the method in Columbus-1, an autonomous research system that identified eight independently reproduced, attacker-reachable vulnerabilities in BlueZ and directed the design, simulation, and fabrication of a ten-foot rocket intended to land propulsively using non-throttleable solid motors. Together, these results show that process-level scientific judgment can provide supervision for interpretable, dynamic control over a model's reasoning strategy.

Abstract: Assigning reduced coordinates to states near an attracting limit cycle requires the correct invariant-fibre geometry. The classical first-order phase-isostable chart obtained from adjoint Floquet modes projects along the strong-stable quotient fibre, whereas a metric-orthogonal complement of the retained slow bundle generally does not. We prove locally that a chart satisfying the linearised semiconjugacy relation leaves an O(delta^2) invariance residual, while projection along a non-invariant complement generically leaves an O(delta) term. For a nonlinear aeroelastic limit cycle, the metric-normal and strong-stable directions differ by 48.5 to 71.7 degrees, and metric-normal perturbations contain first-order retained phase and slow-amplitude components. Replacing the metric normal by the strong-stable fibre changes the measured residual scaling from delta^1.01 to delta^1.87 without fitted parameters. We then test learned higher-order corrections whose linearisation is pinned to the adjoint-Floquet chart, whose symmetry is exact, and whose reduced flow is fixed. Although they reduce the registered fixed-normalisation latent residual, post-hoc amplitude recalibration and adjoint-Floquet-targeted future consistency move or reverse the ranking. Because the learned maps already share the baseline's first-order gauge and the future target is supplied by the baseline chart, these diagnostics establish neither an independent positive nor negative higher-order result. Correct first-order Floquet geometry is therefore necessary in this benchmark, while the additional predictive value of the learned correction remains unidentified by the available representation-dependent diagnostics.

Abstract: Aeroelastic ?utter is normally a failure mode to be designed against, yet the limit-cycle oscillations (LCOs) that follow it convert flow energy into sustained structural motion that a piezoelectric transducer can turn into electrical power. A transducer is embedded in a three-degree-of-freedom pitch-plunge aerofoil with a finite-mass trailing-edge flap and unsteady strip-theory aerodynamics, giving a fifteen-state electro-aeroelastic system with a cubic hardening pitch spring, and the system is reduced by biorthonormal projection of the Taylor-expanded residual onto eigenvectors of the coupled Jacobian. The testbed is deliberately low order, so that every reduced prediction can be checked against the full-order system it replaces. The degree of freedom that carries the transducer is a first-order design variable, since it sets both the sign of the shift in the flutter boundary and the magnitude of the harvested power. The error of the reduced model is dominated not by the size of the retained basis but by how the reduced operator is made to depend on low speed. Expanding the retained eigenvalues leaves the reduced operator block-diagonal, with no coupling between the retained modes at any order of the expansion, whereas re-projecting the exact Jacobian onto the same frozen basis supplies that coupling and restores the structural response without enlarging the basis. It is found that the error that remains lies in the harvested voltage, which the equilibrium eigenvectors carry in a fixed proportion to the motion, and this is not removed by adding the electrical modes to the basis, whereas the flap detection, which the same basis also misses, is recovered by retaining the flap modes. The accuracy of a harvester reduced-order model must therefore be reported on the harvested quantity itself.

Abstract: Turbomachinery design optimization involves expensive black-box problems. Sample-efficient multi-fidelity optimization (MFO) offers an efficient solution. By utilizing multi-fidelity surrogates (MFS), the MFO algorithm can use fewer high-fidelity samples aided by low-fidelity samples to establish an accurate surrogate model. However, when MFS is used in sequential sampling optimization, it has been observed that the final optimal solution obtained by single-fidelity optimization (SFO) is better than that of MFO, even though MFO performs better at the early stages. This can be attributed to the assumption of an even and nested distribution of samples, which is incorrect when using a sequential adding strategy. To address these issues, we propose a novel algorithm called multi-single-fidelity optimization (MSFO) to overcome the limitations of the conventional MFO procedures. In the surrogate establishment of MSFO, we use the density-based spatial clustering of applications with noise (DBSCAN) method to detect local areas where low-fidelity samples are no longer effective. A combination of both global MFS and local single-fidelity surrogate model, built using high-fidelity samples alone, is used to establish an ensemble, which improves the anti-interference ability of the algorithm against misleading low-fidelity data. The effectiveness of the MSFO algorithm is verified first on numerical benchmark functions. Then, the algorithm is used to optimize the aerodynamic profile of a turbine and the film cooling layout design of a turbine endwall. Here, high-fidelity sample sources are obtained from fine-mesh CFD simulations, whereas low-fidelity sample sources are obtained from the same simulations run on a coarser mesh. The results demonstrate that our MSFO algorithm performs significantly better than the conventional SFO and MFO processes, with a higher level of robustness.

Abstract: Graph-based surrogate models offer a promising route to accelerate computational fluid dynamics (CFD) simulations on unstructured meshes. However, their development is limited by the scarcity of benchmark datasets spanning multiple flow regimes and standardized protocols for long-horizon autoregressive prediction. We introduce ONECYL (ONE CYLinder), a new benchmark for unsteady flow past a circular cylinder across laminar, transitional, and high-Reynolds-number regimes. The benchmark comprises 450 high-fidelity Variational Multiscale finite-element simulations (270,000 flow snapshots) with randomized cylinder geometries, providing time-resolved velocity and pressure fields together with mesh connectivity, geometric descriptors, Reynolds numbers, and integrated aerodynamic quantities. Beyond the dataset, ONECYL establishes a unified evaluation framework combining full-field rollout errors, virtual probes, and drag and lift predictions to assess numerical accuracy and physical fidelity. To accompany the benchmark, we develop a Graph Transformer as a reference baseline predicting velocity and pressure fields autoregressively on unstructured meshes. Using ONECYL, we investigate geometric representations and physics-based regularization across the three Reynolds-number regimes. The results show that explicitly encoding the cylinder geometry through a level-set representation consistently improves long-horizon prediction accuracy and generalization to unseen geometries, while divergence-based regularization becomes increasingly beneficial as flow complexity increases. The ONECYL benchmark and its Graph Transformer baseline provide a reproducible framework for evaluating graph-based surrogate models and establish a foundation for future research on long-horizon prediction of unsteady bluff-body flows.