Zobrazeno 1 - 10
of 120
pro vyhledávání: '"Schaeffer, Hayden"'
Single-operator learning involves training a deep neural network to learn a specific operator, whereas recent work in multi-operator learning uses an operator embedding structure to train a single neural network on data from multiple operators. Thus,
Externí odkaz:
http://arxiv.org/abs/2408.16168
Foundation models, such as large language models, have demonstrated success in addressing various language and image processing tasks. In this work, we introduce a multi-modal foundation model for scientific problems, named PROSE-PDE. Our model, desi
Externí odkaz:
http://arxiv.org/abs/2404.12355
Neural operators have been applied in various scientific fields, such as solving parametric partial differential equations, dynamical systems with control, and inverse problems. However, challenges arise when dealing with input functions that exhibit
Externí odkaz:
http://arxiv.org/abs/2310.18888
Approximating nonlinear differential equations using a neural network provides a robust and efficient tool for various scientific computing tasks, including real-time predictions, inverse problems, optimal controls, and surrogate modeling. Previous w
Externí odkaz:
http://arxiv.org/abs/2309.16816
We present a new framework for computing fine-scale solutions of multiscale Partial Differential Equations (PDEs) using operator learning tools. Obtaining fine-scale solutions of multiscale PDEs can be challenging, but there are many inexpensive comp
Externí odkaz:
http://arxiv.org/abs/2308.14188
We present a generalized version of the discretization-invariant neural operator and prove that the network is a universal approximation in the operator sense. Moreover, by incorporating additional terms in the architecture, we establish a connection
Externí odkaz:
http://arxiv.org/abs/2307.09738
Operator learning trains a neural network to map functions to functions. An ideal operator learning framework should be mesh-free in the sense that the training does not require a particular choice of discretization for the input functions, allows fo
Externí odkaz:
http://arxiv.org/abs/2212.07336
Particle dynamics and multi-agent systems provide accurate dynamical models for studying and forecasting the behavior of complex interacting systems. They often take the form of a high-dimensional system of differential equations parameterized by an
Externí odkaz:
http://arxiv.org/abs/2212.05591
The spectra of random feature matrices provide essential information on the conditioning of the linear system used in random feature regression problems and are thus connected to the consistency and generalization of random feature models. Random fea
Externí odkaz:
http://arxiv.org/abs/2204.06935
Signal decomposition and multiscale signal analysis provide many useful tools for time-frequency analysis. We proposed a random feature method for analyzing time-series data by constructing a sparse approximation to the spectrogram. The randomization
Externí odkaz:
http://arxiv.org/abs/2204.06108