Related papers: Composite Bayesian Optimization In Function Spaces…

Operator learning refers to the application of ideas from machine learning to approximate (typically nonlinear) operators mapping between Banach spaces of functions. Such operators often arise from physical models expressed in terms of…

Neural operators (NOs) are a class of deep learning models designed to simultaneously solve infinitely many related problems by casting them into an infinite-dimensional space, whereon these NOs operate. A significant gap remains between…

The Deep Operator Network (DeepONet) is a powerful neural operator architecture that uses two neural networks to map between infinite-dimensional function spaces. This architecture allows for the evaluation of the solution field at any…

Modern deep learning tools are remarkably effective in addressing intricate problems. However, their operation as black-box models introduces increased uncertainty in predictions. Additionally, they contend with various challenges,…

Bayesian Optimization (BO) is a powerful framework for optimizing noisy, expensive-to-evaluate black-box functions. When the objective exhibits invariances under a group action, exploiting these symmetries can substantially improve BO…

Neural Operators (NOs) are machine learning models designed to solve partial differential equations (PDEs) by learning to map between function spaces. Neural Operators such as the Deep Operator Network (DeepONet) and the Fourier Neural…

Bayesian Neural Networks (BNNs) offer a principled and natural framework for proper uncertainty quantification in the context of deep learning. They address the typical challenges associated with conventional deep learning methods, such as…

Neural Ordinary Differential Equations (N-ODEs) are a powerful building block for learning systems, which extend residual networks to a continuous-time dynamical system. We propose a Bayesian version of N-ODEs that enables well-calibrated…

This paper analyzes DONE, an online optimization algorithm that iteratively minimizes an unknown function based on costly and noisy measurements. The algorithm maintains a surrogate of the unknown function in the form of a random Fourier…

Bayesian optimization (BO) is a widely-used sequential method for zeroth-order optimization of complex and expensive-to-compute black-box functions. The existing BO methods assume that the function evaluation (feedback) is available to the…

Bayesian Optimization is the state of the art technique for the optimization of black boxes, i.e., functions where we do not have access to their analytical expression nor its gradients, they are expensive to evaluate and its evaluation is…

Bayesian optimization (BO) has become an effective approach for black-box function optimization problems when function evaluations are expensive and the optimum can be achieved within a relatively small number of queries. However, many…

By learning the mappings between infinite function spaces using carefully designed neural networks, the operator learning methodology has exhibited significantly more efficiency than traditional methods in solving complex problems such as…

While Bayesian Optimization (BO) is a very popular method for optimizing expensive black-box functions, it fails to leverage the experience of domain experts. This causes BO to waste function evaluations on bad design choices (e.g., machine…

Existing architectures for operator learning require that the number and locations of sensors (where the input functions are evaluated) remain the same across all training and test samples, significantly restricting the range of their…

Bayesian optimization has been successfully applied to optimize black-box functions where the number of evaluations is severely limited. However, in many real-world applications, it is hard or impossible to know in advance which designs are…

User response prediction makes a crucial contribution to the rapid development of online advertising system and recommendation system. The importance of learning feature interactions has been emphasized by many works. Many deep models are…

In-context operator networks (ICON) are a class of operator learning methods based on the novel architectures of foundation models. Trained on a diverse set of datasets of initial and boundary conditions paired with corresponding solutions…

Learning robot controllers by minimizing a black-box objective cost using Bayesian optimization (BO) can be time-consuming and challenging. It is very often the case that some roll-outs result in failure behaviors, causing premature…

Bayesian optimization (BO) is a widely used method for data-driven optimization that generally relies on zeroth-order data of objective function to construct probabilistic surrogate models. These surrogates guide the…