Papers Operator learning
“Operator learning” 태그가 달린 논문 347편 · 필터 해제
Holistic Physics Solver: Learning PDEs in a Unified Spectral-Physical Space
Recent advances in operator learning have produced two distinct approaches for solving partial differential equations (PDEs): attention-based methods offering point-level adaptability but lacking spectral constraints, an…
Computational EfficiencyOperator learningSuper Resolution Based on Deep Operator Networks
We use Deep Operator Networks (DeepONets) to perform super-resolution reconstruction of the solutions of two types of partial differential equations and compare the model predictions with the results obtained using conve…
Operator learningSuper-ResolutionDeepOSets: Non-Autoregressive In-Context Learning of Supervised Learning Operators
We introduce DeepSets Operator Networks (DeepOSets), an efficient, non-autoregressive neural network architecture for in-context operator learning. In-context learning allows a trained machine learning model to learn fro…
In-Context LearningOperator learningQuantifying Training Difficulty and Accelerating Convergence in Neural Network-Based PDE Solvers
Neural network-based methods have emerged as powerful tools for solving partial differential equations (PDEs) in scientific and engineering applications, particularly when handling complex domains or incorporating empiri…
Operator learningUnityDimOL: Dimensional Awareness as A New 'Dimension' in Operator Learning
In the realm of computational physics, an enduring topic is the numerical solutions to partial differential equations (PDEs). Recently, the attention of researchers has shifted towards Neural Operator methods, renowned f…
Operator learningDeepONet for Solving Nonlinear Partial Differential Equations with Physics-Informed Training
In this paper, we investigate the use of operator learning, specifically DeepONet, for solving nonlinear partial differential equations (PDEs). Unlike conventional function learning methods that require training separate…
Operator learningPhysics-informed machine learningLeray-Schauder Mappings for Operator Learning
We present an algorithm for learning operators between Banach spaces, based on the use of Leray-Schauder mappings to learn a finite-dimensional approximation of compact subspaces. We show that the resulting method is a u…
Operator learningStructure-Preserving Operator Learning
Learning complex dynamics driven by partial differential equations directly from data holds great promise for fast and accurate simulations of complex physical systems. In most cases, this problem can be formulated as an…
Operator learningNeural Scaling Laws of Deep ReLU and Deep Operator Network: A Theoretical Study
Neural scaling laws play a pivotal role in the performance of deep neural networks and have been observed in a wide range of tasks. However, a complete theoretical framework for understanding these scaling laws remains u…
Operator learningBasis-to-Basis Operator Learning Using Function Encoders
We present Basis-to-Basis (B2B) operator learning, a novel approach for learning operators on Hilbert spaces of functions based on the foundational ideas of function encoders. We decompose the task of learning operators …
Operator learningScientific Machine Learning Seismology
Scientific machine learning (SciML) is an interdisciplinary research field that integrates machine learning, particularly deep learning, with physics theory to understand and predict complex natural phenomena. By incorpo…
Deep LearningOperator learningGenerative AI for fast and accurate statistical computation of fluids
We present a generative AI algorithm for addressing the pressing task of fast, accurate, and robust statistical computation of three-dimensional turbulent fluid flows. Our algorithm, termed as GenCFD, is based on an end-…
Operator learningIn-Context Learning of Linear Systems: Generalization Theory and Applications to Operator Learning
We study theoretical guarantees for solving linear systems in-context using a linear transformer architecture. For in-domain generalization, we provide neural scaling laws that bound the generalization error in terms of …
DiversityDomain GeneralizationIn-Context LearningOperator learningTowards Gaussian Process for operator learning: an uncertainty aware resolution independent operator learning algorithm for computational mechanics
The growing demand for accurate, efficient, and scalable solutions in computational mechanics highlights the need for advanced operator learning algorithms that can efficiently handle large datasets while providing relia…
Computational EfficiencyOperator learningUncertainty QuantificationTime-Series Forecasting, Knowledge Distillation, and Refinement within a Multimodal PDE Foundation Model
Symbolic encoding has been used in multi-operator learning as a way to embed additional information for distinct time-series data. For spatiotemporal systems described by time-dependent partial differential equations, th…
Knowledge DistillationOperator learningTime SeriesTime Series ForecastingPROSE-FD: A Multimodal PDE Foundation Model for Learning Multiple Operators for Forecasting Fluid Dynamics
We propose PROSE-FD, a zero-shot multimodal PDE foundational model for simultaneous prediction of heterogeneous two-dimensional physical systems related to distinct fluid dynamics settings. These systems include shallow …
Operator learningPredictionFB-HyDON: Parameter-Efficient Physics-Informed Operator Learning of Complex PDEs via Hypernetwork and Finite Basis Domain Decomposition
Deep operator networks (DeepONet) and neural operators have gained significant attention for their ability to map infinite-dimensional function spaces and perform zero-shot super-resolution. However, these models often r…
Operator learningSuper-ResolutionStratospheric aerosol source inversion: Noise, variability, and uncertainty quantification
Stratospheric aerosols play an important role in the earth system and can affect the climate on timescales of months to years. However, estimating the characteristics of partially observed aerosol injections, such as tho…
Dimensionality ReductionOperator learningUncertainty QuantificationComponent Fourier Neural Operator for Singularly Perturbed Differential Equations
Solving Singularly Perturbed Differential Equations (SPDEs) poses computational challenges arising from the rapid transitions in their solutions within thin regions. The effectiveness of deep learning in addressing diffe…
Operator learningOperator Learning with Gaussian Processes
Operator learning focuses on approximating mappings $\mathcal{G}^\dagger:\mathcal{U} \rightarrow\mathcal{V}$ between infinite-dimensional spaces of functions, such as $u: \Omega_u\rightarrow\mathbb{R}$ and $v: \Omega_v\r…
Gaussian ProcessesOperator learning