A Novel and Fully Automated Domain Transformation Scheme for Near Optimal Surrogate Construction

Recent developments in surrogate construction predominantly focused on two strategies to improve surrogate accuracy. Firstly, component-wise domain scaling informed by cross-validation. Secondly, regression to construct response surfaces using additional information in the form of additional function-values sampled from multi-fidelity models and gradients. Component-wise domain scaling reliably improves the surrogate quality at low dimensions but has been shown to suffer from high computational costs for higher dimensional problems. The second strategy, adding gradients to train surrogates, typically results in regression surrogates. Counter-intuitively, these gradient-enhanced regression-based surrogates do not exhibit improved accuracy compared to surrogates only interpolating function values. This study empirically establishes three main findings. Firstly, constructing the surrogate in poorly scaled domains is the predominant cause of deteriorating response surfaces when regressing with additional gradient information. Secondly, surrogate accuracy improves if the surrogates are constructed in a fully transformed domain, by scaling and rotating the original domain, not just simply scaling the domain. The domain transformation scheme should be based on the local curvature of the approximation surface and not its global curvature. Thirdly, the main benefit of gradient information is to efficiently determine the (near) optimal domain in which to construct the surrogate. This study proposes a foundational transformation algorithm that performs near-optimal transformations for lower dimensional problems. The algorithm consistently outperforms cross-validation-based component-wise domain scaling for higher dimensional problems. A carefully selected test problem set that varies between 2 and 16-dimensional problems is used to clearly demonstrate the three main findings of this study.Comment: 20 pages, 28 figure

Challenges and solutions to arc-length controlled structural shape design problems

This paper presents a general and reliable shape optimization scheme for snap-through structures to match a target load-deflection curve. The simulation of the snap-through structures typically requires the Arc Length Control (ALC) method. The adaptive stepping in ALC creates unavoidable discontinuities in the objective function. A discontinuous objective function is often handled by zero-order methods. However, we opt to solve the optimization problems using gradient-only optimization. Numerical examples demonstrate that function value based methods can misinterpret discontinuities as minima and terminate prematurely. In contrast, gradient-only algorithms are demonstrated to be insensitive to numerical discontinuities, and locate the correct solutions reliably.https://www.tandfonline.com/loi/lmbd20hj2023Mechanical and Aeronautical Engineerin

A novel and fully automated coordinate system transformation scheme for near optimal surrogate construction

DATA AVAILABILITY : No data was used for the research described in the article.This work develops a novel coordinate system transformation scheme to improve the performance of common radial basis function surrogate models. This coordinate system transformation scheme is based on the fact that commonly used basis functions are isotropic. Three main empirical findings are established in this study. Firstly, in general isotropic functions are inadequate to describe anisotropic data manifolds due to a mismatch between the functional form and the form of the data manifold resulting in poor generative performance. Counter-intuitively, utilising additional gradients during surrogate training often worsens the generative capability. Secondly, component-wise scaling of isotropic model forms during cross-validation is inadequate to enhance the functional form of the data manifold form as anisotropic coupling in the data manifold remains coupled. Improving the match between the functional form and the data manifold form requires both rotation and scaling. Thirdly, the coordinate system transformation scheme should predominantly be based on a collection of local curvature estimations and not on global curvature approximations. Gradients are critical to estimating the local curvature for identifying a near-optimal reference frame for surrogate construction, which then translates to additional benefits of gradients in gradient-enhanced surrogates. Based on the above observations, this paper proposes an isotropic transformation for the data coordinate system that performs near-optimal transformations on lower dimensional data without requiring any cross-validation. The method is compared against commonly applied component-wise cross-validation data coordinate system scaling as well as the more modern Active Subspace Method on a carefully crafted decomposable test problem, which has a known optimal coordinate system, that varies between 2 and 16 dimensions. The paper concludes after demonstrating that the developed transformation scheme, as well as the other common methods, will offer little benefit on non-decompose problems and offers some suggestions on future work to create a more general isotropic transformation.http://www.elsevier.com/locate/cma2025-11-24hj2024Mechanical and Aeronautical EngineeringNon

Spatio-Temporal Gradient Enhanced Surrogate Modeling Strategies

This research compares the performance of space-time surrogate models (STSMs) and network surrogate models (NSMs). Specifically, when the system response varies over time (or pseudo-time), the surrogates must predict the system response. A surrogate model is used to approximate the response of computationally expensive spatial and temporal fields resulting from some computational mechanics simulations. Within a design context, a surrogate takes a vector of design variables that describe a current design and returns an approximation of the design’s response through a pseudo-time variable. To compare various radial basis function (RBF) surrogate modeling approaches, the prediction of a load displacement path of a snap-through structure is used as an example numerical problem. This work specifically considers the scenario where analytical sensitivities are available directly from the computational mechanics’ solver and therefore gradient enhanced surrogates are constructed. In addition, the gradients are used to perform a domain transformation preprocessing step to construct surrogate models in a more isotropic domain, which is conducive to RBFs. This work demonstrates that although the gradient-based domain transformation scheme offers a significant improvement to the performance of the space-time surrogate models (STSMs), the network surrogate model (NSM) is far more robust. This research offers explanations for the improved performance of NSMs over STSMs and recommends future research to improve the performance of STSMs

Prednisone augmentation in treatment‐resistant depression with fatigue and hypocortisolaemia: A case series

Abnormalities of the hypothalamic‐pituitary‐adrenal (HPA) axis have long been implicated in major depression with hypercortisolaemia reported in typical depression and hypocortisolaemia in some studies of atypical depression. We report on the use of prednisone in treatment‐resistant depressed patients with reduced plasma cortisol concentrations. Six patients with treatment‐resistant major depression were found to complain of severe fatigue, consistent with major depression, atypical subtype, and to demonstrate low plasma cortisol levels. Prednisone 7.5 mg daily was added to the antidepressant regime. Five of six patients demonstrated significant improvement in depression on prednisone augmentation of antidepressant therapy. Although hypercortisolaemia has been implicated in some patients with depression, our findings suggest that hypocortisolaemia may also play a role in some subtypes of this disorder. In treatment‐resistant depressed patients with fatigue and hypocortisolaemia, prednisone augmentation may be useful. Depression and Anxiety 12:44–50, 2000. © 2000 Wiley‐Liss, Inc