arXiv subjects

Ashwin Renganathan

Publications and source records attributed to Ashwin Renganathan.

7 recordsLinked to original sources

arXiv2026

A Bayesian latent Gaussian process framework for aerodynamic uncertainty quantification

Predicting the aerodynamic performance (e.g. lift, drag, and moment coefficients) of an aircraft is challenging -- computational models are biased and direct simulations are prohibitive. A pragmatic way to overcome this limitation is by calibrating low-fidelity computational predictions with experimental measurements. This, however, requires calibrating against \emph{sparse} measurements contaminated with \emph{uncertainty} in both the control inputs and the measured aerodynamic response. We develop a methodology to address this problem based on Gaussian process surrogates and the classical Kennedy-O'Hagan calibration. A surrogate model learned on abundant-but-cheap low-fidelity data is calibrated with a sparse set of measurement data. Crucialy, we develop a Bayesian latent Gaussian process based approach that marginalizes the calibrated surrogate model over the input uncertainty, while also matching the marginal mean and variance of the measured output uncertainty. Once calibrated, our surrogate model predicts the uncertainty in aerodynamic coefficients with very high accuracy, including at extrapolative input settings. We validate our calibrated surrogate model predictions against measurement data with \emph{true} uncertainty intervals to demonstrate that the model places $94.2-95.8\%$ of its predictive samples inside the released $95\%$ truth intervals, with endpoint cumulative probabilities very close to the nominal 0.025 and 0.975 levels.

stat.ML↗

arXiv2026

REMAL: Residual Equilibrium Manifold Active Learning for Surrogate-Based Multidisciplinary Design Analysis

Multidisciplinary design analysis of coupled engineering systems requires the computation of equilibrium states in which all disciplinary coupling variables are mutually consistent. Conventional fixed-point iteration resolves this consistency problem separately at each design point, which can become expensive when disciplinary evaluations are costly and many analyses are required in outer-loop tasks such as multidisciplinary design optimization, uncertainty quantification, or digital twin updating. This paper introduces REMAL, a residual manifold surrogate modeling framework for coupled systems. Instead of approximating each discipline independently or directly learning converged coupling variables, the proposed method learns a surrogate model of the joint residual manifold via multitask Gaussian process models. An entropy-based active learning strategy selects additional residual evaluations near uncertain zero-contour regions, and equilibrium states for new design inputs are recovered by solving a nonlinear least squares optimization problem using only the trained surrogate. The method is evaluated on four engineering coupled system benchmarks: a satellite model, an aerostructural model, a finite-element gas-turbine heat-transfer and economics model, and a modified turbine model with added feedback coupling. Across these cases, REMAL consistently demonstrates the cost effectiveness when repeated evaluations of the fixed point across the design space are necessary. Theoretically, we show that, under mild assumptions, REMAL's predictive fixed point error is bounded.

physics.comp-ph↗

arXiv2026

Derivative-free optimization is competitive for aerodynamic design optimization in moderate dimensions

Aerodynamic design optimization is an important problem in aircraft design that depends on the interplay between a numerical optimizer and a high-fidelity flow physics solver. Derivative-based, first and (quasi) second order, optimization techniques are the de facto choice, particularly given the availability of the adjoint method and its ability to efficiently compute gradients at the cost of just one solution of the forward problem. However, implementation of the adjoint method requires careful mathematical treatment, and its sensitivity to changes in mesh quality limits widespread applicability. Derivative-free approaches are often overlooked for large scale optimization, citing their lack of scalability in higher dimensions and/or the lack of practical interest in globally optimal solutions that they often target. However, breaking free from an adjoint solver can be paradigm-shifting in broadening the applicability of aerodynamic design optimization. We provide a systematic benchmarking of a select sample of widely used derivative-based and derivative-free optimization algorithms on the design optimization of three canonical aerodynamic bodies, namely, the NACA0012 and RAE2822 airfoils, and the ONERAM6 wing. Our results demonstrate that derivative-free methods are competitive with derivative-based methods, while outperforming them consistently in the high-dimensional setting. These findings highlight the practical competitiveness of modern derivative-free strategies, offering a scalable and robust alternative for aerodynamic design optimization when adjoint-based gradients are unavailable or unreliable.

math.OC↗

arXiv2026

Surrogate-Guided Adaptive Importance Sampling for Failure Probability Estimation

We consider the sample efficient estimation of failure probabilities from expensive oracle evaluations of a limit state function via importance sampling (IS). In contrast to conventional ``two stage'' approaches, which first train a surrogate model for the limit state and then construct an IS proposal to estimate failure probability using separate oracle evaluations, we propose a \emph{single stage} approach where a Gaussian process surrogate and a surrogate for the optimal (zero-variance) IS density are trained from shared evaluations of the oracle, making better use of a limited budget. With such an approach, small failure probabilities can be learned with relatively few oracle evaluations. We propose \emph{kernel density estimation adaptive importance sampling} (\texttt{KDE-AIS}), which combines Gaussian process surrogates with kernel density estimation to adaptively construct the IS proposal density, leading to sample efficient estimation of failure probabilities. We show that \texttt{KDE-AIS} density asymptotically converges to the optimal zero-variance IS density in total variation. Empirically, \texttt{KDE-AIS} enables accurate and sample efficient estimation of failure probabilities compared to the state of the art, including previous work on Gaussian process based adaptive importance sampling.

stat.CO↗

arXiv2025

Multiobjective Aerodynamic Design Optimization of the NASA Common Research Model

Aircraft aerodynamic design optimization must account for the varying operating conditions along the cruise segment as opposed to designing at one fixed operating condition, to arrive at more realistic designs. Conventional approaches address this by performing a ``multi-point'' optimization that assumes a weighted average of the objectives at a set of sub-segments along the cruise segment. We argue that since such multi-point approaches are, inevitably, biased by the specification of the weights, they can lead to sub-optimal designs. Instead, we propose to optimize the aircraft design at multiple sub-segments simultaneously -- that is, via multiobjective optimization that leads to a set of Pareto optimal solutions. However, existing work in multiobjective optimization suffers from (i) lack of sample efficiency (that is, keeping the number of function evaluations to convergence minimal), (ii) scalability {in the absence of derivative information}, and (iii) the ability to generate a batch of iterates for synchronous parallel evaluations. To overcome these limitations, we {apply} a novel multiobjective Bayesian optimization methodology {for aerodynamic design optimization} that demonstrates improved sample efficiency and accuracy compared to the state of the art. Inspired by Thompson sampling, our approach leverages Gaussian process surrogates and Bayesian decision theory to generate a sequence of iterates according to the probability that they are Pareto optimal. Our approach, named batch Pareto optimal Thompson sampling (\qpots)\footnote{Here, $q$ stands for selecting a batch of $q$ iterates at every step.}, demonstrates superior empirical performance on a variety of synthetic experiments as well as a $24$ dimensional two-objective aerodynamic design optimization of the NASA common research model. We also provide open-source software of our methodology {and experiments}.

math.OC↗

arXiv2025

$\texttt{CRLS}$: Convolutional Regularized Least Squares Framework for Reduced Order Modeling of Transonic Flows

We develop a convolutional regularized least squares ($\texttt{CRLS}$) framework for reduced-order modeling of transonic flows with shocks. Conventional proper orthogonal decomposition (POD) based reduced models are attractive because of their optimality and low online cost; however, but they perform poorly when snapshots contain parameter-dependent discontinuities, leading to smeared shocks, stair-stepping, or non-physical oscillations. In $\texttt{CRLS}$, we first map each full-order snapshot to a smoother representation by applying a one-dimensional Gaussian convolution with reflect padding along the flow field coordinates. The convolution hyperparameters (kernel width and support) are selected automatically by Bayesian optimization on a held-out set of snapshots. POD bases are then extracted from the smoothed data, and the parametric dependence of the POD coefficients is learned via radial basis function interpolation. To recover sharp shock structures, we introduce an efficient deconvolution step formulated as a regularized least squares problem, where the regularization centers the reconstruction around a nearest-neighbor reference snapshot in parameter space. The resulting $\texttt{CRLS}$ surrogate is evaluated on inviscid transonic flow over the RAE2822 airfoil, modeled by the steady compressible Euler equations solved with SU2 over a Latin hypercube sample of Mach number and angle of attack. Compared with standard POD and smoothed-POD baselines, $\texttt{CRLS}$ yields markedly improved shock location and strength, lower surface-pressure and field-level errors, and a $42$\% reduction in the number of POD modes required to capture a fixed fraction of snapshot energy. These results demonstrate that $\texttt{CRLS}$ provides an accurate, data-efficient, and largely automated route to shock-aware reduced order models for high-speed aerodynamic design.

physics.flu-dyn↗

arXiv2025

qPOTS: Efficient batch multiobjective Bayesian optimization via Pareto optimal Thompson sampling

Classical evolutionary approaches for multiobjective optimization are quite accurate but incur a lot of queries to the objectives; this can be prohibitive when objectives are expensive oracles. A sample-efficient approach to solving multiobjective optimization is via Gaussian process (GP) surrogates and Bayesian optimization (BO). Multiobjective Bayesian optimization (MOBO) involves the construction of an acquisition function which is optimized to acquire new observation candidates sequentially. This ``inner'' optimization can be hard due to various reasons: acquisition functions being nonconvex, nondifferentiable and/or unavailable in analytical form; batch sampling usually exacerbates these problems and the success of MOBO heavily relies on this inner optimization. This, ultimately, affects their sample efficiency. To overcome these challenges, we propose a Thompson sampling (TS) based approach ($q\texttt{POTS}$). Whereas TS chooses candidates according to the probability that they are optimal, $q\texttt{POTS}$ chooses candidates according to the probability that they are Pareto optimal. Instead of a hard acquisition function optimization, $q\texttt{POTS}~$ solves a cheap multiobjective optimization on the GP posteriors with evolutionary approaches. This way we get the best of both worlds: accuracy of evolutionary approaches and sample-efficiency of MOBO. New candidates are chosen on the posterior GP Pareto frontier according to a maximin distance criterion. $q\texttt{POTS}~$ is endowed with theoretical guarantees, a natural exploration-exploitation trade-off, and superior empirical performance.

math.OC↗