Related papers: Some Best Practices in Operator Learning

DeepONets and Koopman autoencoders are two prevalent neural operator architectures. These architectures are autoencoders. An adversarial addition to an autoencoder have improved performance of autoencoders in various areas of machine…

Fast and accurate predictions for complex physical dynamics are a significant challenge across various applications. Real-time prediction on resource-constrained hardware is even more crucial in real-world problems. The deep operator…

We construct and compare three operator learning architectures, DeepONet, Fourier Neural Operator, and Wavelet Neural Operator, in order to learn the operator mapping a time-dependent applied current to the transmembrane potential of the…

The deep operator networks (DeepONet), a class of neural operators that learn mappings between function spaces, have recently been developed as surrogate models for parametric partial differential equations (PDEs). In this work we propose a…

Learning algorithms related to artificial neural networks and in particular for Deep Learning may seem to involve many bells and whistles, called hyper-parameters. This chapter is meant as a practical guide with recommendations for some of…

Deep Operator Networks (DeepONets) are among the most prominent frameworks for operator learning, grounded in the universal approximation theorem for operators. However, training DeepONets typically requires significant computational…

Koopman operator theory, a powerful framework for discovering the underlying dynamics of nonlinear dynamical systems, was recently shown to be intimately connected with neural network training. In this work, we take the first steps in…

When training deep learning models, the performance depends largely on the selected hyperparameters. However, hyperparameter optimization (HPO) is often one of the most expensive parts of model design. Classical HPO methods treat this as a…

Since deep neural networks were developed, they have made huge contributions to everyday lives. Machine learning provides more rational advice than humans are capable of in almost every aspect of daily life. However, despite this…

Most machine learning algorithms are configured by one or several hyperparameters that must be carefully chosen and often considerably impact performance. To avoid a time consuming and unreproducible manual trial-and-error process to find…

Deep Operator Networks (DeepONets) have recently emerged as powerful data-driven frameworks for learning nonlinear operators, particularly suited for approximating solutions to partial differential equations. Despite their promising…

Operator learning aims to discover properties of an underlying dynamical system or partial differential equation (PDE) from data. Here, we present a step-by-step guide to operator learning. We explain the types of problems and PDEs amenable…

Deep learning is revolutionizing weather forecasting, with new data-driven models achieving accuracy on par with operational physical models for medium-term predictions. However, these models often lack interpretability, making their…

Over the last few years, several works have proposed deep learning architectures to learn dynamical systems from observation data with no or little knowledge of the underlying physics. A line of work relies on learning representations where…

Training an effective deep learning model to learn ocean processes involves careful choices of various hyperparameters. We leverage the advanced search algorithms for multiobjective optimization in DeepHyper, a scalable hyperparameter…

Deep neural networks are an attractive alternative for simulating complex dynamical systems, as in comparison to traditional scientific computing methods, they offer reduced computational costs during inference and can be trained directly…

Operator learning provides methods to approximate mappings between infinite-dimensional function spaces. Deep operator networks (DeepONets) are a notable architecture in this field. Recently, an extension of DeepONet based on model…

The Koopman operator has recently garnered much attention for its value in dynamical systems analysis and data-driven model discovery. However, its application has been hindered by the computational complexity of extended dynamic mode…

The Koopman operator provides a principled framework for analyzing nonlinear dynamical systems through linear operator theory. Recent advances in dynamic mode decomposition (DMD) have shown that trajectory data can be used to identify…

Deep neural operators can learn nonlinear mappings between infinite-dimensional function spaces via deep neural networks. As promising surrogate solvers of partial differential equations (PDEs) for real-time prediction, deep neural…