Related papers: Discretization-independent multifidelity operator …

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…

The predictive accuracy of operator learning frameworks depends on the quality and quantity of available training data (input-output function pairs), often requiring substantial amounts of high-fidelity data, which can be challenging to…

Recent years have witnessed the promise of coupling machine learning methods and physical domain-specific insights for solving scientific problems based on partial differential equations (PDEs). However, being data-intensive, these methods…

We propose a novel fine-tuning method to achieve multi-operator learning through training a distributed neural operator with diverse function data and then zero-shot fine-tuning the neural network using physics-informed losses for…

Time-dependent partial differential equations are ubiquitous in physics-based modeling, but they remain computationally intensive in many-query scenarios, such as real-time forecasting, optimal control, and uncertainty quantification.…

Operator learning frameworks, because of their ability to learn nonlinear maps between two infinite dimensional functional spaces and utilization of neural networks in doing so, have recently emerged as one of the more pertinent areas in…

Neural operators have emerged as a powerful, discretization-invariant framework for solving partial differential equations (PDEs). Although established approaches like the Deep Operator Network (DeepONet) have successfully achieved…

A kernel-based approach for the learning of the solution operator of general nonhomogeneous partial differential equations (PDEs) is proposed. The method incorporates physical priors, typically encoded through the PDE operator, into a…

Operator learning has emerged as a powerful tool in scientific computing for approximating mappings between infinite-dimensional function spaces. A primary application of operator learning is the development of surrogate models for the…

Deep neural operators can learn operators mapping between infinite-dimensional function spaces via deep neural networks and have become an emerging paradigm of scientific machine learning. However, training neural operators usually requires…

We present a new scientific machine learning method that learns from data a computationally inexpensive surrogate model for predicting the evolution of a system governed by a time-dependent nonlinear partial differential equation (PDE), an…

We introduce the technique of adaptive discretization to design an efficient model-based episodic reinforcement learning algorithm in large (potentially continuous) state-action spaces. Our algorithm is based on optimistic one-step value…

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,…

Transfer learning (TL) enables the transfer of knowledge gained in learning to perform one task (source) to a related but different task (target), hence addressing the expense of data acquisition and labeling, potential computational power…

The numerical solution of partial differential equations (PDEs) is challenging because of the need to resolve spatiotemporal features over wide length and timescales. Often, it is computationally intractable to resolve the finest features…

An important application of neural networks to scientific computing has been the learning of non-linear operators. In this framework, a neural network is trained to fit a non-linear map between two infinite dimensional spaces, for example,…

Traditional, numerical discretization-based solvers of partial differential equations (PDEs) are fundamentally agnostic to domains, boundary conditions and coefficients. In contrast, machine learnt solvers have a limited generalizability…

We develop and evaluate a method for learning solution operators to nonlinear problems governed by partial differential equations (PDEs). The approach is based on a finite element discretization and aims at representing the solution…

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…

Operator learning is a variant of machine learning that is designed to approximate maps between function spaces from data. The Fourier Neural Operator (FNO) is one of the main model architectures used for operator learning. The FNO combines…