Papers Operator learning
“Operator learning” 태그가 달린 논문 347편 · 필터 해제
Neural Operators Meet Energy-based Theory: Operator Learning for Hamiltonian and Dissipative PDEs
The operator learning has received significant attention in recent years, with the aim of learning a mapping between function spaces. Prior works have proposed deep neural networks (DNNs) for learning such a mapping, ena…
Operator learningSuper-ResolutionParametric Learning of Time-Advancement Operators for Unstable Flame Evolution
This study investigates the application of machine learning, specifically Fourier Neural Operator (FNO) and Convolutional Neural Network (CNN), to learn time-advancement operators for parametric partial differential equa…
Operator learningLearning time-dependent PDE via graph neural networks and deep operator network for robust accuracy on irregular grids
Scientific computing using deep learning has seen significant advancements in recent years. There has been growing interest in models that learn the operator from the parameters of a partial differential equation (PDE) t…
Operator learningDIMON: Learning Solution Operators of Partial Differential Equations on a Diffeomorphic Family of Domains
The solution of a PDE over varying initial/boundary conditions on multiple domains is needed in a wide variety of applications, but it is computationally expensive if the solution is computed de novo whenever the initial…
Operator learningAn operator learning perspective on parameter-to-observable maps
Computationally efficient surrogates for parametrized physical models play a crucial role in science and engineering. Operator learning provides data-driven surrogates that map between function spaces. However, instead o…
Operator learningLearning Operators with Stochastic Gradient Descent in General Hilbert Spaces
This study investigates leveraging stochastic gradient descent (SGD) to learn operators between general Hilbert spaces. We propose weak and strong regularity conditions for the target operator to depict its intrinsic str…
Operator learningvalidFunctional SDE approximation inspired by a deep operator network architecture
A novel approach to approximate solutions of Stochastic Differential Equations (SDEs) by Deep Neural Networks is derived and analysed. The architecture is inspired by the notion of Deep Operator Networks (DeepONets), whi…
Operator learningUncertainty QuantificationCalibrated Uncertainty Quantification for Operator Learning via Conformal Prediction
Operator learning has been increasingly adopted in scientific and engineering applications, many of which require calibrated uncertainty quantification. Since the output of operator learning is a continuous function, qua…
Conformal PredictionOperator learningPredictionUncertainty QuantificationOperator learning without the adjoint
There is a mystery at the heart of operator learning: how can one recover a non-self-adjoint operator from data without probing the adjoint? Current practical approaches suggest that one can accurately recover an operato…
Operator learningUnsupervised Solution Operator Learning for Mean-Field Games via Sampling-Invariant Parametrizations
Recent advances in deep learning has witnessed many innovative frameworks that solve high dimensional mean-field games (MFG) accurately and efficiently. These methods, however, are restricted to solving single-instance M…
Operator learningGeneralization Error Guaranteed Auto-Encoder-Based Nonlinear Model Reduction for Operator Learning
Many physical processes in science and engineering are naturally represented by operators between infinite-dimensional function spaces. The problem of operator learning, in this context, seeks to extract these physical p…
Operator learningEquivariant Graph Neural Operator for Modeling 3D Dynamics
Modeling the complex three-dimensional (3D) dynamics of relational systems is an important problem in the natural sciences, with applications ranging from molecular simulations to particle mechanics. Machine learning met…
Operator learningPDE Generalization of In-Context Operator Networks: A Study on 1D Scalar Nonlinear Conservation Laws
Can we build a single large model for a wide range of PDE-related scientific learning tasks? Can this model generalize to new PDEs, even of new forms, without any fine-tuning? In-context operator learning and the corresp…
Operator learningIntegration of physics-informed operator learning and finite element method for parametric learning of partial differential equations
We present a method that employs physics-informed deep learning techniques for parametrically solving partial differential equations. The focus is on the steady-state heat equations within heterogeneous solids exhibiting…
Operator learningMulti-Lattice Sampling of Quantum Field Theories via Neural Operator-based Flows
We consider the problem of sampling lattice field configurations on a lattice from the Boltzmann distribution corresponding to some action. Since such densities arise as approximationw of an underlying functional density…
Operator learningOperator learning for hyperbolic partial differential equations
We construct the first rigorously justified probabilistic algorithm for recovering the solution operator of a hyperbolic partial differential equation (PDE) in two variables from input-output training pairs. The primary …
Operator learningHyperDeepONet: learning operator with complex target function space using the limited resources via hypernetwork
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 …
Operator learningA Mathematical Guide to Operator Learning
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 proble…
Operator learningOperator-learning-inspired Modeling of Neural Ordinary Differential Equations
Neural ordinary differential equations (NODEs), one of the most influential works of the differential equation-based deep learning, are to continuously generalize residual networks and opened a new field. They are curren…
image-classificationImage ClassificationImage GenerationOperator learning+2GIT-Net: Generalized Integral Transform for Operator Learning
This article introduces GIT-Net, a deep neural network architecture for approximating Partial Differential Equation (PDE) operators, inspired by integral transform operators. GIT-NET harnesses the fact that differential …
Operator learning