Batch Bayesian active learning for feasible region identification by local penalization

Identifying all designs satisfying a set of constraints is an important part of the engineering design process. With physics-based simulation codes, evaluating the constraints becomes considerable expensive. Active learning can provide an elegant approach to efficiently characterize the feasible region, i.e., the set of feasible designs. Although active learning strategies have been proposed for this task, most of them are dealing with adding just one sample per iteration as opposed to selecting multiple samples per iteration, also known as batch active learning. While this is efficient with respect to the amount of information gained per iteration, it neglects available computation resources. We propose a batch Bayesian active learning technique for feasible region identification by assuming that the constraint function is Lipschitz continuous. In addition, we extend current state-of-the-art batch methods to also handle feasible region identification. Experiments show better performance of the proposed method than the extended batch methods

Bayesian active learning for multi-objective feasible region identification in microwave devices

In microwave device and circuit design, many simulations are often needed to find a set of designs that satisfy one or multiple specifications chosen by the designer upfront: the feasible region. A novel Bayesian active learning framework is presented to accurately identify the feasible region with a low number of simulations. The technique leverages on a stochastic model to obtain an efficient and automated procedure. A suitable application example validates the proposed technique and shows its effectiveness to rapidly obtain many suitable designs

Trieste: Efficiently Exploring The Depths of Black-box Functions with TensorFlow

We present Trieste, an open-source Python package for Bayesian optimization and active learning benefiting from the scalability and efficiency of TensorFlow. Our library enables the plug-and-play of popular TensorFlow-based models within sequential decision-making loops, e.g. Gaussian processes from GPflow or GPflux, or neural networks from Keras. This modular mindset is central to the package and extends to our acquisition functions and the internal dynamics of the decision-making loop, both of which can be tailored and extended by researchers or engineers when tackling custom use cases. Trieste is a research-friendly and production-ready toolkit backed by a comprehensive test suite, extensive documentation, and available at https://github.com/secondmind-labs/trieste

Spectral representation of robustness measures for optimization under input uncertainty

We study the inference of mean-variance robustness measures to quantify input uncertainty under the Gaussian Process (GP) framework. These measures are widely used in applications where the robustness of the solution is of interest, for example, in engineering design. While the variance is commonly used to characterize the robustness, Bayesian inference of the variance using GPs is known to be challenging. In this paper, we propose a Spectral Representation of Robustness Measures based on the GP's spectral representation, i.e., an analytical approach to approximately infer both robustness measures for normal and uniform input uncertainty distributions. We present two approximations based on different Fourier features and compare their accuracy numerically. To demonstrate their utility and efficacy in robust Bayesian Optimization, we integrate the analytical robustness measures in three standard acquisition functions for various robust optimization formulations. We show their competitive performance on numerical benchmarks and real-life applications

A robust multi-objective Bayesian optimization framework considering input uncertainty

Bayesian optimization is a popular tool for optimizing time-consuming objective functions with a limited number of function evaluations. In real-life applications like engineering design, the designer often wants to take multiple objectives as well as input uncertainty into account to find a set of robust solutions. While this is an active topic in single-objective Bayesian optimization, it is less investigated in the multi-objective case. We introduce a novel Bayesian optimization framework to perform multi-objective optimization considering input uncertainty. We propose a robust Gaussian Process model to infer the Bayes risk criterion to quantify robustness, and we develop a two-stage Bayesian optimization process to search for a robust Pareto frontier, i.e., solutions that have good average performance under input uncertainty. The complete framework supports various distributions of the input uncertainty and takes full advantage of parallel computing. We demonstrate the effectiveness of the framework through numerical benchmarks

Arbuscular Mycorrhizal Fungi and Microbes Interaction in Rice Mycorrhizosphere

Rice (Oryza sativa L.) is the most widely consumed staple crop for approximately half of the world’s population. Many interactions take place in paddy soil, particularly in the rice mycorrhizosphere region. Arbuscular mycorrhizal fungi (AMF) and soil microbe interactions are among the most important and influential processes that occur, as they significantly influence the plant growth and soil structure properties. Their interactions may be of crucial importance to the sustainable, low-input productivity of paddy ecosystems. In this study, we summarize the major groups of microbial communities interacting with arbuscular mycorrhizal fungi in the rice mycorrhizosphere, and discuss the mechanisms involved in these arbuscular mycorrhizal fungi and microbe interactions. We further highlight the potential application of arbuscular mycorrhizal mutualism in paddy fields, which will be helpful for the production of bioinoculants in the future

Adaptive sampling with automatic stopping for feasible region identification in engineering design

Engineering design is a complex process to find a suitable trade-off among different, and sometimes conflicting, design specifications. In reality, these requirements can be often considered as constraints of the design problem, that can be defined in terms of performance measures or geometrical characteristics of the device under study. In this paper, a new design space exploration methodology is presented for discovering feasible regions in the design space, where the term feasible region indicates the set of all design configurations satisfying all constraints of the design problem. The proposed method is based on Gaussian process metamodels to estimate the feasible region and leverages a information-based adaptive sampling technique to sequentially refine the prediction accuracy, which is applicable for multiple constraints problems. To efficiently stop the adaptive sampling process, a novel framework to estimate the metamodel's prediction accuracy is proposed. The efficiency, accuracy and robustness of the proposed approach are compared with state-of-art techniques on suitable benchmark problems and practical engineering examples

Arbuscular Mycorrhizal Fungi and Microbes Interaction in Rice Mycorrhizosphere

Rice (Oryza sativa L.) is the most widely consumed staple crop for approximately half of the world’s population. Many interactions take place in paddy soil, particularly in the rice mycorrhizosphere region. Arbuscular mycorrhizal fungi (AMF) and soil microbe interactions are among the most important and influential processes that occur, as they significantly influence the plant growth and soil structure properties. Their interactions may be of crucial importance to the sustainable, low-input productivity of paddy ecosystems. In this study, we summarize the major groups of microbial communities interacting with arbuscular mycorrhizal fungi in the rice mycorrhizosphere, and discuss the mechanisms involved in these arbuscular mycorrhizal fungi and microbe interactions. We further highlight the potential application of arbuscular mycorrhizal mutualism in paddy fields, which will be helpful for the production of bioinoculants in the future

Finding knees in Bayesian multi-objective optimization

Multi-objective optimization requires many evaluations to identify a sufficiently dense approximation of the Pareto front. Especially for a higher number of objectives, extracting the Pareto front might not be easy nor cheap. On the other hand, the Decision-Maker is not always interested in the entire Pareto front, and might prefer a solution where there is a desirable trade-off between different objectives. An example of an attractive solution is the knee point of the Pareto front, although the current literature differs on the definition of a knee. In this work, we propose to detect knee solutions in a data-efficient manner (i.e., with a limited number of time-consuming evaluations), according to two definitions of knees. In particular, we propose several novel acquisition functions in the Bayesian Optimization framework for detecting these knees, which allows for scaling to many objectives. The suggested acquisition functions are evaluated on various benchmarks with promising results