Physics simulations like computational fluid dynamics (CFD) are a computational bottleneck in computer-aided design (CAD) optimization processes. To overcome this bottleneck, one requires either an optimization framework that is highly sample-efficient, or a fast data-driven proxy (surrogate model) for long-running simulations. Both approaches have benefits and limitations. Bayesian optimization is often used for sample efficiency, but it solves one specific problem and struggles with transferability; alternatively, surrogate models can offer fast and often more generalizable solutions for CFD problems, but gathering data for and training such models can be computationally demanding. In this work, we leverage recent advances in optimization and artificial intelligence (AI) to explore both of these potential approaches, in the context of designing an optimal unmanned underwater vehicle (UUV) hull. Our study finds that the Bayesian Optimization-Lower Condition Bound (BO-LCB) algorithm is the most sample-efficient optimization framework and has the best convergence behavior of those considered. Subsequently, we show that our DNN-based surrogate model predicts drag force on test data in tight agreement with CFD simulations, with a mean absolute percentage error (MAPE) of 1.85%. Combining these results, we demonstrate a two-orders-of-magnitude speedup (with comparable accuracy) for the design optimization process when the surrogate model is used. To our knowledge, this is the first study applying Bayesian optimization and DNN-based surrogate modeling to the problem of UUV design optimization, and we share our developments as open-source software.
Recent advances have extended the scope of Bayesian optimization (BO) to expensive-to-evaluate black-box functions with dozens of dimensions, aspiring to unlock impactful applications, for example, in the life sciences, neural architecture search, and robotics. However, a closer examination reveals that the state-of-the-art methods for high-dimensional Bayesian optimization (HDBO) suffer from degrading performance as the number of dimensions increases or even risk failure if certain unverifiable assumptions are not met. This paper proposes BAxUS that leverages a novel family of nested random subspaces to adapt the space it optimizes over to the problem. This ensures high performance while removing the risk of failure, which we assert via theoretical guarantees. A comprehensive evaluation demonstrates that BAxUS achieves better results than the state-of-the-art methods for a broad set of applications.
Gaussian processes are the model of choice in Bayesian optimization and active learning. Yet, they are highly dependent on cleverly chosen hyperparameters to reach their full potential, and little effort is devoted to finding good hyperparameters in the literature. We demonstrate the impact of selecting good hyperparameters for GPs and present two acquisition functions that explicitly prioritize hyperparameter learning. Statistical distance-based Active Learning (SAL) considers the average disagreement between samples from the posterior, as measured by a statistical distance. SAL outperforms the state-of-the-art in Bayesian active learning on several test functions. We then introduce Self-Correcting Bayesian Optimization (SCoreBO), which extends SAL to perform Bayesian optimization and active learning simultaneously. SCoreBO learns the model hyperparameters at improved rates compared to vanilla BO, while outperforming the latest Bayesian optimization methods on traditional benchmarks. Moreover, we demonstrate the importance of self-correction on atypical Bayesian optimization tasks.
Recent advances in many domains require more and more complicated experiment design. Such complicated experiments often have many parameters, which necessitate parameter tuning. Tree-structured Parzen estimator (TPE), a Bayesian optimization method, is widely used in recent parameter tuning frameworks. Despite its popularity, the roles of each control parameter and the algorithm intuition have not been discussed so far. In this tutorial, we will identify the roles of each control parameter and their impacts on hyperparameter optimization using a diverse set of benchmarks. We compare our recommended setting drawn from the ablation study with baseline methods and demonstrate that our recommended setting improves the performance of TPE. Our TPE implementation is available at https://github.com/nabenabe0928/tpe/tree/single-opt.
Automated augmentation is an emerging and effective technique to search for data augmentation policies to improve generalizability of deep neural network training. Most existing work focuses on constructing a unified policy applicable to all data samples in a given dataset, without considering sample or class variations. In this paper, we propose a novel two-stage data augmentation algorithm, named Label-Aware AutoAugment (LA3), which takes advantage of the label information, and learns augmentation policies separately for samples of different labels. LA3 consists of two learning stages, where in the first stage, individual augmentation methods are evaluated and ranked for each label via Bayesian Optimization aided by a neural predictor, which allows us to identify effective augmentation techniques for each label under a low search cost. And in the second stage, a composite augmentation policy is constructed out of a selection of effective as well as complementary augmentations, which produces significant performance boost and can be easily deployed in typical model training. Extensive experiments demonstrate that LA3 achieves excellent performance matching or surpassing existing methods on CIFAR-10 and CIFAR-100, and achieves a new state-of-the-art ImageNet accuracy of 79.97% on ResNet-50 among auto-augmentation methods, while maintaining a low computational cost.
Deep learning models have become increasingly popular for flood prediction due to their superior accuracy and efficiency compared to traditional methods. However, current machine learning methods often rely on separate spatial or temporal feature analysis and have limitations on the types, number, and dimensions of input data. This study presented a CNN-RNN hybrid feature fusion modelling approach for urban flood prediction, which integrated the strengths of CNNs in processing spatial features and RNNs in analyzing different dimensions of time sequences. This approach allowed for both static and dynamic flood predictions. Bayesian optimization was applied to identify the seven most influential flood-driven factors and determine the best combination strategy. By combining four CNNs (FCN, UNet, SegNet, DeepLabv3+) and three RNNs (LSTM, BiLSTM, GRU), the optimal hybrid model was identified as LSTM-DeepLabv3+. This model achieved the highest prediction accuracy (MAE, RMSE, NSE, and KGE were 0.007, 0.025, 0.973 and 0.755, respectively) under various rainfall input conditions. Additionally, the processing speed was significantly improved, with an inference time of 1.158s (approximately 1/125 of the traditional computation time) compared to the physically-based models.
We apply Bayesian optimization and reinforcement learning to a problem in topology: the question of when a knot bounds a ribbon disk. This question is relevant in an approach to disproving the four-dimensional smooth Poincar\'e conjecture; using our programs, we rule out many potential counterexamples to the conjecture. We also show that the programs are successful in detecting many ribbon knots in the range of up to 70 crossings.
Manufacturing advanced materials and products with a specific property or combination of properties is often warranted. To achieve that it is crucial to find out the optimum recipe or processing conditions that can generate the ideal combination of these properties. Most of the time, a sufficient number of experiments are needed to generate a Pareto front. However, manufacturing experiments are usually costly and even conducting a single experiment can be a time-consuming process. So, it's critical to determine the optimal location for data collection to gain the most comprehensive understanding of the process. Sequential learning is a promising approach to actively learn from the ongoing experiments, iteratively update the underlying optimization routine, and adapt the data collection process on the go. This paper presents a novel data-driven Bayesian optimization framework that utilizes sequential learning to efficiently optimize complex systems with multiple conflicting objectives. Additionally, this paper proposes a novel metric for evaluating multi-objective data-driven optimization approaches. This metric considers both the quality of the Pareto front and the amount of data used to generate it. The proposed framework is particularly beneficial in practical applications where acquiring data can be expensive and resource intensive. To demonstrate the effectiveness of the proposed algorithm and metric, the algorithm is evaluated on a manufacturing dataset. The results indicate that the proposed algorithm can achieve the actual Pareto front while processing significantly less data. It implies that the proposed data-driven framework can lead to similar manufacturing decisions with reduced costs and time.
The linearized-Laplace approximation (LLA) has been shown to be effective and efficient in constructing Bayesian neural networks. It is theoretically compelling since it can be seen as a Gaussian process posterior with the mean function given by the neural network's maximum-a-posteriori predictive function and the covariance function induced by the empirical neural tangent kernel. However, while its efficacy has been studied in large-scale tasks like image classification, it has not been studied in sequential decision-making problems like Bayesian optimization where Gaussian processes -- with simple mean functions and kernels such as the radial basis function -- are the de-facto surrogate models. In this work, we study the usefulness of the LLA in Bayesian optimization and highlight its strong performance and flexibility. However, we also present some pitfalls that might arise and a potential problem with the LLA when the search space is unbounded.
This paper studies the problem of online performance optimization of constrained closed-loop control systems, where both the objective and the constraints are unknown black-box functions affected by exogenous time-varying contextual disturbances. A primal-dual contextual Bayesian optimization algorithm is proposed that achieves sublinear cumulative regret with respect to the dynamic optimal solution under certain regularity conditions. Furthermore, the algorithm achieves zero time-average constraint violation, ensuring that the average value of the constraint function satisfies the desired constraint. The method is applied to both sampled instances from Gaussian processes and a continuous stirred tank reactor parameter tuning problem; simulation results show that the method simultaneously provides close-to-optimal performance and maintains constraint feasibility on average. This contrasts current state-of-the-art methods, which either suffer from large cumulative regret or severe constraint violations for the case studies presented.
Large language models (LLMs) can perform accurate classification with zero or few examples through in-context learning. We extend this capability to regression with uncertainty estimation using frozen LLMs (e.g., GPT-3.5, Gemini), enabling Bayesian optimization (BO) in natural language without explicit model training or feature engineering. We apply this to materials discovery by representing experimental catalyst synthesis and testing procedures as natural language prompts. A key challenge in materials discovery is the need to characterize suboptimal candidates, which slows progress. While BO is effective for navigating large design spaces, standard surrogate models like Gaussian processes assume smoothness and continuity, an assumption that fails in highly non-linear domains such as heterogeneous catalysis. Our task-agnostic BO workflow overcomes this by operating directly in language space, producing interpretable and actionable predictions without requiring structural or electronic descriptors. On benchmarks like aqueous solubility and oxidative coupling of methane (OCM), BO-ICL matches or outperforms Gaussian processes. In live experiments on the reverse water-gas shift (RWGS) reaction, BO-ICL identifies near-optimal multi-metallic catalysts within six iterations from a pool of 3,700 candidates. Our method redefines materials representation and accelerates discovery, with broad applications across catalysis, materials science, and AI. Code: https://github.com/ur-whitelab/BO-ICL.
Fast charging has attracted increasing attention from the battery community for electrical vehicles (EVs) to alleviate range anxiety and reduce charging time for EVs. However, inappropriate charging strategies would cause severe degradation of batteries or even hazardous accidents. To optimize fast-charging strategies under various constraints, particularly safety limits, we propose a novel deep Bayesian optimization (BO) approach that utilizes Bayesian recurrent neural network (BRNN) as the surrogate model, given its capability in handling sequential data. In addition, a combined acquisition function of expected improvement (EI) and upper confidence bound (UCB) is developed to better balance the exploitation and exploration. The effectiveness of the proposed approach is demonstrated on the PETLION, a porous electrode theory-based battery simulator. Our method is also compared with the state-of-the-art BO methods that use Gaussian process (GP) and non-recurrent network as surrogate models. The results verify the superior performance of the proposed fast charging approaches, which mainly results from that: (i) the BRNN-based surrogate model provides a more precise prediction of battery lifetime than that based on GP or non-recurrent network; and (ii) the combined acquisition function outperforms traditional EI or UCB criteria in exploring the optimal charging protocol that maintains the longest battery lifetime.
The indeterminate nature of human motion requires trajectory prediction systems to use a probabilistic model to formulate the multi-modality phenomenon and infer a finite set of future trajectories. However, the inference processes of most existing methods rely on Monte Carlo random sampling, which is insufficient to cover the realistic paths with finite samples, due to the long tail effect of the predicted distribution. To promote the sampling process of stochastic prediction, we propose a novel method, called BOsampler, to adaptively mine potential paths with Bayesian optimization in an unsupervised manner, as a sequential design strategy in which new prediction is dependent on the previously drawn samples. Specifically, we model the trajectory sampling as a Gaussian process and construct an acquisition function to measure the potential sampling value. This acquisition function applies the original distribution as prior and encourages exploring paths in the long-tail region. This sampling method can be integrated with existing stochastic predictive models without retraining. Experimental results on various baseline methods demonstrate the effectiveness of our method.
In the literature on deep neural networks, there is considerable interest in developing activation functions that can enhance neural network performance. In recent years, there has been renewed scientific interest in proposing activation functions that can be trained throughout the learning process, as they appear to improve network performance, especially by reducing overfitting. In this paper, we propose a trainable activation function whose parameters need to be estimated. A fully Bayesian model is developed to automatically estimate from the learning data both the model weights and activation function parameters. An MCMC-based optimization scheme is developed to build the inference. The proposed method aims to solve the aforementioned problems and improve convergence time by using an efficient sampling scheme that guarantees convergence to the global maximum. The proposed scheme is tested on three datasets with three different CNNs. Promising results demonstrate the usefulness of our proposed approach in improving model accuracy due to the proposed activation function and Bayesian estimation of the parameters.
Stakeholders in electricity delivery infrastructure are amassing data about their system demand, use, and operations. Still, they are reluctant to share them, as even sharing aggregated or anonymized electric grid data risks the disclosure of sensitive information. This paper highlights how applying differential privacy to distributed energy resource production data can preserve the usefulness of that data for operations, planning, and research purposes without violating privacy constraints. Differentially private mechanisms can be optimized for queries of interest in the energy sector, with provable privacy and accuracy trade-offs, and can help design differentially private databases for further analysis and research. In this paper, we consider the problem of inference and publication of solar photovoltaic systems' metadata. Metadata such as nameplate capacity, surface azimuth and surface tilt may reveal personally identifiable information regarding the installation behind-the-meter. We describe a methodology to infer the metadata and propose a mechanism based on Bayesian optimization to publish the inferred metadata in a differentially private manner. The proposed mechanism is numerically validated using real-world solar power generation data.
The performance of navigation algorithms significantly determines the trajectory tracking accuracy of the guidance, navigation, and control (GNC) system of an autonomous underwater vehicle (AUV). In closed-loop operation, the interaction among path planning, control, and navigation plays a crucial role in the tracking accuracy of the overall GNC system. A Doppler velocity log (DVL) is often used for AUVs to measure velocity over the ground, positively affecting the closed-loop tracking error. However, a DVL may not be installed in miniaturized AUVs due to limited space and energy. In this paper, a navigation filter for an underactuated miniature AUV (nanoAUV) is considered that is mainly based on acoustic localization using a novel highly-miniaturized ultra-short baseline (USBL) system and a depth pressure sensor. The nanoAUV is being developed for subglacial lake exploration. We compare two unscented Kalman filters (UKF) with different prediction models - the classical strapdown inertial navigation systems (SINS) model and a hydrodynamic motion model (HMM). To enable a fair comparison, filter parameters are auto-tuned with Bayesian optimization (BO) for open and closed-loop performance, which is novel in AUV navigation. The results indicate that BO performs similarly to particle swarm optimization (PSO) regarding sample efficiency for the proposed problem. To quantify the GNC tracking performance, we use extensive Monte Carlo simulations. Results suggest that with BO-tuned navigation filter parameters, the median tracking error is reduced by up to 50% compared to default parametrization.
Early degradation prediction of lithium-ion batteries is crucial for ensuring safety and preventing unexpected failure in manufacturing and diagnostic processes. Long-term capacity trajectory predictions can fail due to cumulative errors and noise. To address this issue, this study proposes a data-centric method that uses early single-cycle data to predict the capacity degradation trajectory of lithium-ion cells. The method involves predicting a few knots at specific retention levels using a deep learning-based model and interpolating them to reconstruct the trajectory. Two approaches are used to identify the retention levels of two to four knots: uniformly dividing the retention up to the end of life and finding optimal locations using Bayesian optimization. The proposed model is validated with experimental data from 169 cells using five-fold cross-validation. The results show that mean absolute percentage errors in trajectory prediction are less than 1.60% for all cases of knots. By predicting only the cycle numbers of at least two knots based on early single-cycle charge and discharge data, the model can directly estimate the overall capacity degradation trajectory. Further experiments suggest using three-cycle input data to achieve robust and efficient predictions, even in the presence of noise. The method is then applied to predict various shapes of capacity degradation patterns using additional experimental data from 82 cells. The study demonstrates that collecting only the cycle information of a few knots during model training and a few early cycle data points for predictions is sufficient for predicting capacity degradation. This can help establish appropriate warranties or replacement cycles in battery manufacturing and diagnosis processes.
Symbolic regression searches for analytic expressions that accurately describe studied phenomena. The main attraction of this approach is that it returns an interpretable model that can be insightful to users. Historically, the majority of algorithms for symbolic regression have been based on evolutionary algorithms. However, there has been a recent surge of new proposals that instead utilize approaches such as enumeration algorithms, mixed linear integer programming, neural networks, and Bayesian optimization. In order to assess how well these new approaches behave on a set of common challenges often faced in real-world data, we hosted a competition at the 2022 Genetic and Evolutionary Computation Conference consisting of different synthetic and real-world datasets which were blind to entrants. For the real-world track, we assessed interpretability in a realistic way by using a domain expert to judge the trustworthiness of candidate models.We present an in-depth analysis of the results obtained in this competition, discuss current challenges of symbolic regression algorithms and highlight possible improvements for future competitions.
This study aims to comprehensively investigate the deep ensemble approach, an approximate Bayesian inference, in the multi-output regression task for predicting the aerodynamic performance of a missile configuration. To this end, the effect of the number of neural networks used in the ensemble, which has been blindly adopted in previous studies, is scrutinized. As a result, an obvious trend towards underestimation of uncertainty as it increases is observed for the first time, and in this context, we propose the deep ensemble framework that applies the post-hoc calibration method to improve its uncertainty quantification performance. It is compared with Gaussian process regression and is shown to have superior performance in terms of regression accuracy ($\uparrow55\sim56\%$), reliability of estimated uncertainty ($\uparrow38\sim77\%$), and training efficiency ($\uparrow78\%$). Finally, the potential impact of the suggested framework on the Bayesian optimization is briefly examined, indicating that deep ensemble without calibration may lead to unintended exploratory behavior. This UQ framework can be seamlessly applied and extended to any regression task, as no special assumptions have been made for the specific problem used in this study.
As we enter the exascale computing era, efficiently utilizing power and optimizing the performance of scientific applications under power and energy constraints has become critical and challenging. We propose a low-overhead autotuning framework to autotune performance and energy for various hybrid MPI/OpenMP scientific applications at large scales and to explore the tradeoffs between application runtime and power/energy for energy efficient application execution, then use this framework to autotune four ECP proxy applications -- XSBench, AMG, SWFFT, and SW4lite. Our approach uses Bayesian optimization with a Random Forest surrogate model to effectively search parameter spaces with up to 6 million different configurations on two large-scale production systems, Theta at Argonne National Laboratory and Summit at Oak Ridge National Laboratory. The experimental results show that our autotuning framework at large scales has low overhead and achieves good scalability. Using the proposed autotuning framework to identify the best configurations, we achieve up to 91.59% performance improvement, up to 21.2% energy savings, and up to 37.84% EDP improvement on up to 4,096 nodes.