arXiv subjects

Joaquim R. R. A. Martins

Publications and source records attributed to Joaquim R. R. A. Martins.

13 recordsLinked to original sources

arXiv2026

Buffet Alleviation via Linear Stability Adjoint

Transonic buffet, self--sustained shock and shear--layer oscillations, imposes hard limits on the cruise envelope of modern transport aircraft, and avoiding it is a primary design driver. State-of-the-art buffet-onset criteria used in design, such as the $Δα= 0.1^\circ$ criterion and separation--sensor methods, are empirical surrogates rather than first--principle predictors, and can yield either overly conservative or unsafe designs. Linear stability analysis (LST) predicts buffet onset directly from the spectrum of the linearized operator about the steady base flow, but using it as an aerodynamic shape optimization constraint has been bottlenecked by the cost of differentiating an eigenvalue with respect to many design variables. In this paper, we develop a coupled adjoint method that efficiently computes the sensitivity of the dominant LST eigenvalue with respect to a large number of shape design variables, by reusing the steady CFD adjoint within a top and bottom level decomposition of the eigenproblem. We verify the eigensolver and adjoint against the canonical cylinder vortex--shedding benchmark, then verify the LST predictions on the OAT15A supercritical airfoil at $M=0.73$, $Re=3.2\times 10^{6}$ against published eigenspectra and against the linear growth phase of a URANS run. Using the resulting gradients, a single-point buffet-constrained drag minimization of the OAT15A achieves a $22.4\%$ drag reduction while satisfying the LST-based buffet constraint. Finally, we present preliminary three-dimensional results on the wing only NASA common research model (CRM) at $M=0.85$, $Re=5\times 10^{6}$, recovering buffet onset at $α\approx 4.0^\circ$ from a sweep of warm--started URANS runs and providing a stepping stone toward three-dimensional buffet-constrained wing optimization with the present adjoint.

physics.flu-dyn↗

arXiv2026

Efficient Adjoint-based Design Optimization with Optimal Control

Multidisciplinary engineering system design typically employs a sequential process, progressing from system dynamics to design variables and control. However, this process is inefficient and may lead to a suboptimal design. We propose formulating the optimal control and multidisciplinary design optimization (MDO) problems as a single problem with linear quadratic regulator (LQR) control. We use the coupled adjoint method to compute the design variable derivatives, which are critical for gradient-based design optimization. The computational cost of the derivative computation using the adjoint method is independent of the number of design variables, making it suitable for large-scale problems. We show that the coupled adjoint can be solved indirectly and more efficiently by solving three smaller adjoint equations that leverage the feedforward structure of the problem. We demonstrate this new approach on two test problems: design optimization of a classic cart-pole problem and the aerodynamic shape of a quadrotor blade. For the quadrotor blade design problem, we reduce the control cost by 10% by optimizing the blade for a specific control task with a slight penalty in steady hovering power consumption.

math.OC↗

arXiv2025

Adjoint-based Hopf-bifurcation Instability Suppression via First Lyapunov Coefficient

Many physical systems exhibit limit cycle oscillations induced by Hopf bifurcations. In aerospace engineering, limit cycle oscillations arise from undesirable Hopf bifurcation phenomena such as aeroelastic flutter and transonic buffet. In some cases, the resulting limit cycle oscillations can themselves be unstable, leading to amplitude divergence or hysteretic transitions that threaten structural integrity and performance. Avoiding such phenomena when performing gradient based design optimization requires a constraint that quantifies the stability of the bifurcations and the derivative of that constraint with respect to the design variables. To capture the local stability of bifurcations, we leverage the first Lyapunov coefficient, which predicts whether the resulting limit cycle oscillation is stable or unstable. We develop an accurate and efficient method for computing derivatives of the first Lyapunov coefficient. We leverage the adjoint method and reverse algorithmic differentiation to efficiently compute the derivative of the first Lyapunov coefficient. We demonstrate the efficacy of the proposed adjoint method in three design optimization problems that suppress unstable bifurcation: an algebraic Hopf bifurcation model, an aeroelastic model of a typical section, and a nonlinear problem based on the complex Ginzburg-Landau partial differential equation. While the current formulation addresses only a single bifurcation mode, the proposed adjoint shows great potential for efficiently handling Hopf bifurcation constraints in large scale nonlinear problems governed by partial differential equations. Its accuracy, versatility and scalability make it a promising tool for aeroelastic and aerodynamic design optimization as well as other engineering problems involving Hopf bifurcation instabilities.

math.DS↗

arXiv2025

Accelerating Bayesian Inference via Multi-Fidelity Transport Map Coupling

Mathematical models in computational physics contain uncertain parameters that impact prediction accuracy. In turbulence modeling, this challenge is especially significant: Reynolds averaged Navier-Stokes (RANS) models, such as the Spalart-Allmaras (SA) model, are widely used for their speed and robustness but often suffer from inaccuracies and associated uncertainties due to imperfect model parameters. Reliable quantification of these uncertainties is becoming increasingly important in aircraft certification by analysis, where predictive credibility is critical. Bayesian inference provides a framework to estimate these parameters and quantify output uncertainty, but traditional methods are prohibitively expensive, especially when relying on high-fidelity simulations. We address the challenge of expensive Bayesian parameter estimation by developing a multi-fidelity framework that combines Markov chain Monte Carlo (MCMC) methods with multilevel Monte Carlo (MLMC) estimators to efficiently solve inverse problems. The MLMC approach requires correlated samples across different fidelity levels, achieved through a novel transport map-based coupling algorithm. We demonstrate a 50% reduction in inference cost compared to traditional single-fidelity methods on the challenging NACA0012 airfoil at high angles of attack near stall, while delivering realistic uncertainty bounds for model predictions in complex separated flow regimes. These results demonstrate that multi-fidelity approaches significantly improve turbulence parameter calibration, paving the way for more accurate and efficient aircraft certification by analysis.

stat.ME↗

arXiv2025

Verification and Validation for Trustworthy Scientific Machine Learning

Scientific machine learning (SciML) models are transforming many scientific disciplines. However, the development of good modeling practices to increase the trustworthiness of SciML has lagged behind its application, limiting its potential impact. The goal of this paper is to start a discussion on establishing consensus-based good practices for predictive SciML. We identify key challenges in applying existing computational science and engineering guidelines, such as verification and validation protocols, and provide recommendations to address these challenges. Our discussion focuses on predictive SciML, which uses machine learning models to learn, improve, and accelerate numerical simulations of physical systems. While centered on predictive applications, our 16 recommendations aim to help researchers conduct and document their modeling processes rigorously across all SciML domains.

cs.LG↗

arXiv2024

CFD-based design optimization of a 5 kW ducted hydrokinetic turbine with practical constraints

Ducted hydrokinetic turbines enhance energy-harvesting efficiency by better conditioning the flow to the blades, which may yield higher power output than conventional freestream turbines for the same reference area. In this work, we present a ducted hydrokinetic turbine design obtained by simultaneously optimizing the duct, blade, and hub geometries. Our optimization framework combines a CFD solver, an adjoint solver, and a gradient-based optimizer to efficiently explore a large design space, together with a feature-based parameterization method to handle the complex geometry. Practical geometrical constraints ensure the manufacturability of the duct in terms of a minimum thickness and the housing of a 5 kW generator within the hub. The optimization converges to a short, thin duct with a rounded leading edge and an elongated hub protruding the duct inlet. The optimized ducted turbine achieves up to 50% efficiency when evaluated by RANS/URANS solvers despite a bulky hub, outperforming the 45% efficiency of the freestream Bahaj turbine featuring the same hub. This work showcases the effectiveness of CFD-based optimization in advancing ducted turbine designs and demonstrates the hydrodynamic benefits of a ducted configuration, paving the way for future research and real-world applications.

physics.flu-dyn↗

arXiv2024

SMT 2.0: A Surrogate Modeling Toolbox with a focus on Hierarchical and Mixed Variables Gaussian Processes

The Surrogate Modeling Toolbox (SMT) is an open-source Python package that offers a collection of surrogate modeling methods, sampling techniques, and a set of sample problems. This paper presents SMT 2.0, a major new release of SMT that introduces significant upgrades and new features to the toolbox. This release adds the capability to handle mixed-variable surrogate models and hierarchical variables. These types of variables are becoming increasingly important in several surrogate modeling applications. SMT 2.0 also improves SMT by extending sampling methods, adding new surrogate models, and computing variance and kernel derivatives for Kriging. This release also includes new functions to handle noisy and use multifidelity data. To the best of our knowledge, SMT 2.0 is the first open-source surrogate library to propose surrogate models for hierarchical and mixed inputs. This open-source software is distributed under the New BSD license.

cs.LG↗

arXiv2023

CFD-based Design Optimization of Ducted Hydrokinetic Turbines

Hydrokinetic turbines extract kinetic energy from moving water to generate renewable electricity, thus contributing to sustainable energy production and reducing reliance on fossil fuels. It has been hypothesized that a duct can accelerate and condition the fluid flow passing the turbine blades, improving the overall energy extraction efficiency. However, no substantial evidence has been provided so far for hydrokinetic turbines. To investigate this problem, we perform a CFD-based optimization study with a blade-resolved Reynolds-averaged Navier--Stokes (RANS) solver to explore the design of a ducted hydrokinetic turbine that maximizes the efficiency of energy extraction. To handle the high-dimensional design space of the blade and duct geometry, we use a gradient-based optimization approach where the gradients are computed using the adjoint method. The final design is re-evaluated through higher-fidelity unsteady RANS (URANS) simulations. Our optimized ducted turbine achieves an efficiency of about 54% over a range of operating conditions, higher than the typical 46% efficiency of unducted turbines such as the well-known Bahaj model.

physics.flu-dyn↗

arXiv2023

Control Co-design of a Hydrokinetic Turbine: A Comparative Study of Open-loop Optimal Control and Feedback Control

Control co-design (CCD) explores physical and control design spaces simultaneously to optimize a system's performance. A commonly used CCD framework aims to achieve open-loop optimal control (OLOC) trajectory while optimizing the physical design variables subject to constraints on control and design parameters. In this study, in contrast with the conventional CCD methods based on OLOC schemes, we present a CCD formulation that explicitly considers a feedback controller. In the formulation, we consider two control laws based on proportional linear and quadratic state feedback, where the control gain is optimized. The simulation results show that the OLOC trajectory could be approximated by a feedback controller. While the total energy generated from the CCD with a feedback controller is slightly lower than that of the CCD with OLOC, it results in a much simpler control structure and more robust performance in the presence of uncertainties and disturbances, making it suitable for real-time control. The study in this paper investigates the performance of optimal hydrokinetic turbine design with a feedback controller in the presence of uncertainties and disturbances to demonstrate the benefits and highlight challenges associated with incorporating the feedback controller explicitly in the CCD stage.

eess.SY↗

arXiv2022

Machine Learning in Aerodynamic Shape Optimization

Machine learning (ML) has been increasingly used to aid aerodynamic shape optimization (ASO), thanks to the availability of aerodynamic data and continued developments in deep learning. We review the applications of ML in ASO to date and provide a perspective on the state-of-the-art and future directions. We first introduce conventional ASO and current challenges. Next, we introduce ML fundamentals and detail ML algorithms that have been successful in ASO. Then, we review ML applications to ASO addressing three aspects: compact geometric design space, fast aerodynamic analysis, and efficient optimization architecture. In addition to providing a comprehensive summary of the research, we comment on the practicality and effectiveness of the developed methods. We show how cutting-edge ML approaches can benefit ASO and address challenging demands, such as interactive design optimization. Practical large-scale design optimizations remain a challenge because of the high cost of ML training. Further research on coupling ML model construction with prior experience and knowledge, such as physics-informed ML, is recommended to solve large-scale ASO problems.

cs.LG↗

arXiv2022

Learning High-Dimensional Parametric Maps via Reduced Basis Adaptive Residual Networks

We propose a scalable framework for the learning of high-dimensional parametric maps via adaptively constructed residual network (ResNet) maps between reduced bases of the inputs and outputs. When just few training data are available, it is beneficial to have a compact parametrization in order to ameliorate the ill-posedness of the neural network training problem. By linearly restricting high-dimensional maps to informed reduced bases of the inputs, one can compress high-dimensional maps in a constructive way that can be used to detect appropriate basis ranks, equipped with rigorous error estimates. A scalable neural network learning framework is thus to learn the nonlinear compressed reduced basis mapping. Unlike the reduced basis construction, however, neural network constructions are not guaranteed to reduce errors by adding representation power, making it difficult to achieve good practical performance. Inspired by recent approximation theory that connects ResNets to sequential minimizing flows, we present an adaptive ResNet construction algorithm. This algorithm allows for depth-wise enrichment of the neural network approximation, in a manner that can achieve good practical performance by first training a shallow network and then adapting. We prove universal approximation of the associated neural network class for $L^2_ν$ functions on compact sets. Our overall framework allows for constructive means to detect appropriate breadth and depth, and related compact parametrizations of neural networks, significantly reducing the need for architectural hyperparameter tuning. Numerical experiments for parametric PDE problems and a 3D CFD wing design optimization parametric map demonstrate that the proposed methodology can achieve remarkably high accuracy for limited training data, and outperformed other neural network strategies we compared against.

cs.LG↗

arXiv2022

Control Co-design of a Hydrokinetic Turbine with Open-loop Optimal Control

This paper introduces a control co-design (CCD) framework to simultaneously explore the physical parameters and control spaces for a hydro-kinetic turbine (HKT) rotor optimization. The optimization formulation incorporates a coupled dynamic-hydrodynamic model to maximize the rotor power efficiency for various time-variant flow profiles. The open-loop optimal control is applied for maximum power tracking, and the blade element momentum theory (BEMT) is used to model the hydrodynamics. Case studies with different control constraints are investigated for CCD. Sensitivity analyses were conducted with respect to different flow profiles and initial geometries. Comparisons are made between CCD and the sequential process, with physical design followed by a control design process under the same conditions. The results demonstrate the benefits of CCD and reveal that, with control constraints, CCD leads to increased energy production compared to the design obtained from the sequential design process.

eess.SY↗

arXiv2017

Gradient-enhanced kriging for high-dimensional problems

Surrogate models provide a low computational cost alternative to evaluating expensive functions. The construction of accurate surrogate models with large numbers of independent variables is currently prohibitive because it requires a large number of function evaluations. Gradient-enhanced kriging has the potential to reduce the number of function evaluations for the desired accuracy when efficient gradient computation, such as an adjoint method, is available. However, current gradient-enhanced kriging methods do not scale well with the number of sampling points due to the rapid growth in the size of the correlation matrix where new information is added for each sampling point in each direction of the design space. They do not scale well with the number of independent variables either due to the increase in the number of hyperparameters that needs to be estimated. To address this issue, we develop a new gradient-enhanced surrogate model approach that drastically reduced the number of hyperparameters through the use of the partial-least squares method that maintains accuracy. In addition, this method is able to control the size of the correlation matrix by adding only relevant points defined through the information provided by the partial-least squares method. To validate our method, we compare the global accuracy of the proposed method with conventional kriging surrogate models on two analytic functions with up to 100 dimensions, as well as engineering problems of varied complexity with up to 15 dimensions. We show that the proposed method requires fewer sampling points than conventional methods to obtain the desired accuracy, or provides more accuracy for a fixed budget of sampling points. In some cases, we get over 3 times more accurate models than a bench of surrogate models from the literature, and also over 3200 times faster than standard gradient-enhanced kriging models.

cs.LG↗