Explicitly accounting for uncertainties is paramount to the safety of engineering structures. Optimization which is often carried out at the early stage of the structural design offers an ideal framework for this task. When the uncertainties are mainly affecting the objective function, robust design optimization is traditionally considered. This work further assumes the existence of multiple and competing objective functions that need to be dealt with simultaneously. The optimization problem is formulated by considering quantiles of the objective functions which allows for the combination of both optimality and robustness in a single metric. By introducing the concept of common random numbers, the resulting nested optimization problem may be solved using a general-purpose solver, herein the non-dominated sorting genetic algorithm (NSGA-II). The computational cost of such an approach is however a serious hurdle to its application in real-world problems. We therefore propose a surrogate-assisted approach using Kriging as an inexpensive approximation of the associated computational model. The proposed approach consists of sequentially carrying out NSGA-II while using an adaptively built Kriging model to estimate the quantiles. Finally, the methodology is adapted to account for mixed categorical-continuous parameters as the applications involve the selection of qualitative design parameters as well. The methodology is first applied to two analytical examples showing its efficiency. The third application relates to the selection of optimal renovation scenarios of a building considering both its life cycle cost and environmental impact. It shows that when it comes to renovation, the heating system replacement should be the priority.
Deep generative models have demonstrated effectiveness in learning compact and expressive design representations that significantly improve geometric design optimization. However, these models do not consider the uncertainty introduced by manufacturing or fabrication. Past work that quantifies such uncertainty often makes simplifying assumptions on geometric variations, while the "real-world", "free-form" uncertainty and its impact on design performance are difficult to quantify due to the high dimensionality. To address this issue, we propose a Generative Adversarial Network-based Design under Uncertainty Framework (GAN-DUF), which contains a deep generative model that simultaneously learns a compact representation of nominal (ideal) designs and the conditional distribution of fabricated designs given any nominal design. This opens up new possibilities of 1)~building a universal uncertainty quantification model compatible with both shape and topological designs, 2)~modeling free-form geometric uncertainties without the need to make any assumptions on the distribution of geometric variability, and 3)~allowing fast prediction of uncertainties for new nominal designs. We can combine the proposed deep generative model with robust design optimization or reliability-based design optimization for design under uncertainty. We demonstrated the framework on two real-world engineering design examples and showed its capability of finding the solution that possesses better performances after fabrication.
This study considers the Joint Transmit/Reflect Beamforming and Power Splitting (JTRBPS) optimization problem in a spectrum underlay setting, such that the transmit sum-energy of the intelligent reflecting surface (IRS)-aided secondary transmitter (ST) is minimized subject to the quality-of-service requirements of the PS-simultaneous wireless information and power transfer (SWIPT) secondary receivers and the interference constraints of the primary receivers (PR). The interference at the PRs caused by the reception of IRS-reflected signals sent by the primary transmitter is taken into account. A coordinated channel state information (CSI) acquisition protocol is proposed. Next, assuming availability at the ST of perfect CSI for all direct and IRS-cascaded transmitter--receiver channels, two penalty-based iterative algorithms are developed: an alternating minimization algorithm that involves semi-definite relaxation in JTBPS design and successive convex approximation in RB optimization, and a block coordinate descent algorithm that employs the Riemannian conjugate gradient algorithm in RB updates. Finally, an outage-constrained robust design under imperfect CSI is devised. Numerical simulations highlight the performance gains of the proposed strategies over benchmarks, corroborate the benefits of using an IRS, and provide valuable insights.
Deep learning (DL) inverse techniques have increased the speed of artificial electromagnetic material (AEM) design and improved the quality of resulting devices. Many DL inverse techniques have succeeded on a number of AEM design tasks, but to compare, contrast, and evaluate assorted techniques it is critical to clarify the underlying ill-posedness of inverse problems. Here we review state-of-the-art approaches and present a comprehensive survey of deep learning inverse methods and invertible and conditional invertible neural networks to AEM design. We produce easily accessible and rapidly implementable AEM design benchmarks, which offers a methodology to efficiently determine the DL technique best suited to solving different design challenges. Our methodology is guided by constraints on repeated simulation and an easily integrated metric, which we propose expresses the relative ill-posedness of any AEM design problem. We show that as the problem becomes increasingly ill-posed, the neural adjoint with boundary loss (NA) generates better solutions faster, regardless of simulation constraints. On simpler AEM design tasks, direct neural networks (NN) fare better when simulations are limited, while geometries predicted by mixture density networks (MDN) and conditional variational auto-encoders (VAE) can improve with continued sampling and re-simulation.
From an engineering perspective, a design should not only perform well in an ideal condition, but should also resist noises. Such a design methodology, namely robust design, has been widely implemented in the industry for product quality control. However, classic robust design requires a lot of evaluations for a single design target, while the results of these evaluations could not be reused for a new target. To achieve a data-efficient robust design, we propose Robust Inverse Design under Noise (RID-Noise), which can utilize existing noisy data to train a conditional invertible neural network (cINN). Specifically, we estimate the robustness of a design parameter by its predictability, measured by the prediction error of a forward neural network. We also define a sample-wise weight, which can be used in the maximum weighted likelihood estimation of an inverse model based on a cINN. With the visual results from experiments, we clearly justify how RID-Noise works by learning the distribution and robustness from data. Further experiments on several real-world benchmark tasks with noises confirm that our method is more effective than other state-of-the-art inverse design methods. Code and supplementary is publicly available at https://github.com/ThyrixYang/rid-noise-aaai22
Genetic circuit design is a well-studied problem in synthetic biology. Ever since the first genetic circuits -- the repressilator and the toggle switch -- were designed and implemented, many advances have been made in this area of research. The current review systematically organizes a number of key works in this domain by employing the versatile framework of generalized morphological analysis. Literature in the area has been mapped based on (a) the design methodologies used, ranging from brute-force searches to control-theoretic approaches, (b) the modelling techniques employed, (c) various circuit functionalities implemented, (d) key design characteristics, and (e) the strategies used for the robust design of genetic circuits. We conclude our review with an outlook on multiple exciting areas for future research, based on the systematic assessment of key research gaps that have been readily unravelled by our analysis framework.
In this paper, state and noise covariance estimation problems for linear system with unknown multiplicative noise are considered. The measurement likelihood is modelled as a mixture of two Gaussian distributions and a Student's t distribution, respectively. The unknown covariance of multiplicative noise is modelled as an inverse Gamma/Wishart distribution and the initial condition is formulated as the nominal covariance. By using robust design and choosing hierarchical priors, two variational Bayesian based robust Kalman filters are proposed. Stability and covergence of the proposed filters, the covariance parameters, the VB inference, and the estimation error dynamics are analyzed. The lower and upper bounds are also provided to guarantee the performance of the proposed filters. A target tracking simulation is provided to validate the effectiveness of the proposed filters.
Optimizing the reliability and the robustness of a design is important but often unaffordable due to high sample requirements. Surrogate models based on statistical and machine learning methods are used to increase the sample efficiency. However, for higher dimensional or multi-modal systems, surrogate models may also require a large amount of samples to achieve good results. We propose a sequential sampling strategy for the surrogate based solution of multi-objective reliability based robust design optimization problems. Proposed local Latin hypercube refinement (LoLHR) strategy is model-agnostic and can be combined with any surrogate model because there is no free lunch but possibly a budget one. The proposed method is compared to stationary sampling as well as other proposed strategies from the literature. Gaussian process and support vector regression are both used as surrogate models. Empirical evidence is presented, showing that LoLHR achieves on average better results compared to other surrogate based strategies on the tested examples.
Robust topology optimization (RTO), as a class of topology optimization problems, identifies a design with the best average performance while reducing the response sensitivity to input uncertainties, e.g. load uncertainty. Solving RTO is computationally challenging as it requires repetitive finite element solutions for different candidate designs and different samples of random inputs. To address this challenge, a neural network method is proposed that offers computational efficiency because (1) it builds and explores a low dimensional search space which is parameterized using deterministically optimal designs corresponding to different realizations of random inputs, and (2) the probabilistic performance measure for each design candidate is predicted by a neural network surrogate. This method bypasses the numerous finite element response evaluations that are needed in the standard RTO approaches and with minimal training can produce optimal designs with better performance measures compared to those observed in the training set. Moreover, a multi-fidelity framework is incorporated to the proposed approach to further improve the computational efficiency. Numerical application of the method is shown on the robust design of L-bracket structure with single point load as well as multiple point loads.
Parametric variability is inevitable in actual energy harvesters. It can significantly affect crucial aspects of the system performance, especially in harvesting systems that present geometric parameters, material properties, or excitation conditions that are susceptible to small perturbations. This work aims to develop an investigation to identify the most critical parameters in the dynamic behavior of asymmetric bistable energy harvesters with nonlinear piezoelectric coupling, considering the variability of their physical and excitation properties. For this purpose, a global sensitivity analysis based on orthogonal variance decomposition, employing Sobol indices, is performed to quantify the effect of the harvester parameters on the variance of the recovered power. This technique quantifies the variance concerning each parameter individually and collectively regarding the total variation of the model. The results indicate that the frequency and amplitude of excitation, asymmetric terms and electrical proprieties of the piezoelectric coupling are the most critical parameters that affect the mean power harvested. It is also shown that the order of importance of the parameters can change according to the stability of the harvester's dynamic response. In this way, a better understanding of the system under analysis is obtained since the study allows the identification of vital parameters that rule the change of dynamic behavior and therefore constitutes a powerful tool in the robust design, optimization, and response prediction of nonlinear harvesters.
The architectures of deep artificial neural networks (DANNs) are routinely studied to improve their predictive performance. However, the relationship between the architecture of a DANN and its robustness to noise and adversarial attacks is less explored. We investigate how the robustness of DANNs relates to their underlying graph architectures or structures. This study: (1) starts by exploring the design space of architectures of DANNs using graph-theoretic robustness measures; (2) transforms the graphs to DANN architectures to train/validate/test on various image classification tasks; (3) explores the relationship between the robustness of trained DANNs against noise and adversarial attacks and the robustness of their underlying architectures estimated via graph-theoretic measures. We show that the topological entropy and Olivier-Ricci curvature of the underlying graphs can quantify the robustness performance of DANNs. The said relationship is stronger for complex tasks and large DANNs. Our work will allow autoML and neural architecture search community to explore design spaces of robust and accurate DANNs.
We consider the problem of spatial signal design for multipath-assisted mmWave positioning under limited prior knowledge on the user's location and clock bias. We propose an optimal robust design and, based on the low-dimensional precoder structure under perfect prior knowledge, a codebook-based heuristic design with optimized beam power allocation. Through numerical results, we characterize different position-error-bound (PEB) regimes with respect to clock bias uncertainty and show that the proposed low-complexity codebook-based designs outperform the conventional directional beam codebook and achieve near-optimal PEB performance for both analog and digital architectures.
Probabilistic models such as Gaussian processes (GPs) are powerful tools to learn unknown dynamical systems from data for subsequent use in control design. While learning-based control has the potential to yield superior performance in demanding applications, robustness to uncertainty remains an important challenge. Since Bayesian methods quantify uncertainty of the learning results, it is natural to incorporate these uncertainties into a robust design. In contrast to most state-of-the-art approaches that consider worst-case estimates, we leverage the learning method's posterior distribution in the controller synthesis. The result is a more informed and, thus, more efficient trade-off between performance and robustness. We present a novel controller synthesis for linearized GP dynamics that yields robust controllers with respect to a probabilistic stability margin. The formulation is based on a recently proposed algorithm for linear quadratic control synthesis, which we extend by giving probabilistic robustness guarantees in the form of credibility bounds for the system's stability.Comparisons to existing methods based on worst-case and certainty-equivalence designs reveal superior performance and robustness properties of the proposed method.
Recent advances on Vision Transformer (ViT) and its improved variants have shown that self-attention-based networks surpass traditional Convolutional Neural Networks (CNNs) in most vision tasks. However, existing ViTs focus on the standard accuracy and computation cost, lacking the investigation of the intrinsic influence on model robustness and generalization. In this work, we conduct systematic evaluation on components of ViTs in terms of their impact on robustness to adversarial examples, common corruptions and distribution shifts. We find some components can be harmful to robustness. By using and combining robust components as building blocks of ViTs, we propose Robust Vision Transformer (RVT), which is a new vision transformer and has superior performance with strong robustness. We further propose two new plug-and-play techniques called position-aware attention scaling and patch-wise augmentation to augment our RVT, which we abbreviate as RVT*. The experimental results on ImageNet and six robustness benchmarks show the advanced robustness and generalization ability of RVT compared with previous ViTs and state-of-the-art CNNs. Furthermore, RVT-S* also achieves Top-1 rank on multiple robustness leaderboards including ImageNet-C and ImageNet-Sketch. The code will be available at \url{https://github.com/alibaba/easyrobust}.
This paper investigates the combined benefits of full-duplex (FD) and cell-free massive multiple-input multipleoutput (CF-mMIMO), where a large number of distributed access points (APs) having FD capability simultaneously serve numerous uplink and downlink user equipments (UEs) on the same time-frequency resources. To enable the incorporation of FD technology in CF-mMIMO systems, we propose a novel heapbased pilot assignment algorithm, which not only can mitigate the effects of pilot contamination but also reduce the involved computational complexity. Then, we formulate a robust design problem for spectral efficiency (SE) maximization in which the power control and AP-UE association are jointly optimized, resulting in a difficult mixed-integer nonconvex programming. To solve this problem, we derive a more tractable problem before developing a very simple iterative algorithm based on inner approximation method with polynomial computational complexity. Numerical results show that our proposed methods with realistic parameters significantly outperform the existing approaches in terms of the quality of channel estimate and SE.
Industry 4.0 anticipates massive interconnectivity of industrial devices (e.g., sensors, actuators) to support factory automation and production. Due to the rigidity of wired connections to harmonize with automation, wireless information transfer has attracted substantial attention. However, existing solutions for the manufacturing sector face critical issues in coping with the key performance demands: ultra-low latency, high throughput, and high reliability. Besides, recent advancements in wireless millimeter-wave technology advocates hybrid precoding with affordable hardware and outstanding spatial multiplexing performance. Thus, we present HYDRAWAVE -- a new paradigm that contemplates the joint design of group scheduling and hybrid precoding for multi-group multicasting to support ubiquitous low-latency communications. Our hybrid precoder, based on semidefinite relaxation and Cholesky matrix factorization, facilitates the robust design of the constant-modulus phase shifts rendering formidable performance at a fraction of the power required by fully-digital precoders. Further, our novel group scheduling formulation minimizes the number of scheduling windows while accounting for the channel correlation of the co-scheduled multicast receivers. Compared to exhaustive search, which renders the optimal scheduling at high overhead, HYDRAWAVE incurs only 9.5% more delay. Notoriously, HYDRAWAVE attains up to 102% gain when compared to the other benchmarked schemes.
The paper focuses on the a posteriori tuning of a generative model in order to favor the generation of good instances in the sense of some external differentiable criterion. The proposed approach, called Boltzmann Tuning of Generative Models (BTGM), applies to a wide range of applications. It covers conditional generative modelling as a particular case, and offers an affordable alternative to rejection sampling. The contribution of the paper is twofold. Firstly, the objective is formalized and tackled as a well-posed optimization problem; a practical methodology is proposed to choose among the candidate criteria representing the same goal, the one best suited to efficiently learn a tuned generative model. Secondly, the merits of the approach are demonstrated on a real-world application, in the context of robust design for energy policies, showing the ability of BTGM to sample the extreme regions of the considered criteria.
Heterologous gene expression draws resources from host cells. These resources include vital components to sustain growth and replication, and the resulting cellular burden is a widely recognised bottleneck in the design of robust circuits. In this tutorial we discuss the use of computational models that integrate gene circuits and the physiology of host cells. Through various use cases, we illustrate the power of host-circuit models to predict the impact of design parameters on both burden and circuit functionality. Our approach relies on a new generation of computational models for microbial growth that can flexibly accommodate resource bottlenecks encountered in gene circuit design. Adoption of this modelling paradigm can facilitate fast and robust design cycles in synthetic biology.
An approach to the time-accurate prediction of chaotic solutions is by learning temporal patterns from data. Echo State Networks (ESNs), which are a class of Reservoir Computing, can accurately predict the chaotic dynamics well beyond the predictability time. Existing studies, however, also showed that small changes in the hyperparameters may markedly affect the network's performance. The aim of this paper is to assess and improve the robustness of Echo State Networks for the time-accurate prediction of chaotic solutions. The goal is three-fold. First, we investigate the robustness of routinely used validation strategies. Second, we propose the Recycle Validation, and the chaotic versions of existing validation strategies, to specifically tackle the forecasting of chaotic systems. Third, we compare Bayesian optimization with the traditional Grid Search for optimal hyperparameter selection. Numerical tests are performed on two prototypical nonlinear systems that have both chaotic and quasiperiodic solutions. Both model-free and model-informed Echo State Networks are analysed. By comparing the network's robustness in learning chaotic versus quasiperiodic solutions, we highlight fundamental challenges in learning chaotic solutions. The proposed validation strategies, which are based on the dynamical systems properties of chaotic time series, are shown to outperform the state-of-the-art validation strategies. Because the strategies are principled-they are based on chaos theory such as the Lyapunov time-they can be applied to other Recurrent Neural Networks architectures with little modification. This work opens up new possibilities for the robust design and application of Echo State Networks, and Recurrent Neural Networks, to the time-accurate prediction of chaotic systems.
Robust design of autonomous systems under uncertainty is an important yet challenging problem. This work proposes a robust controller that consists of a state estimator and a tube based predictive control law. The class of linear systems under ellipsoidal uncertainty is considered. In contrast to existing approaches based on polytopic sets, the constraint tightening is directly computed from the ellipsoidal sets of disturbances without over-approximation, thus leading to less conservative bounds. Conditions to guarantee robust constraint satisfaction and robust stability are presented. Further, by avoiding the usage of Minkowski sum in set computation, the proposed approach can also scale up to high-dimensional systems. The results are illustrated by examples.