Related papers: MNO : A Multi-modal Neural Operator for Parametric…
Fourier Neural Operators (FNOs) have demonstrated exceptional accuracy in mapping functional spaces by leveraging Fourier transforms to establish a connection with underlying physical principles. However, their opaque inner workings often…
Supervised learning in function spaces is an emerging area of machine learning research with applications to the prediction of complex physical systems such as fluid flows, solid mechanics, and climate modeling. By directly learning maps…
Neural operators (NOs) are designed to learn maps between infinite-dimensional function spaces. We propose a novel reframing of their use. By introducing an auxiliary base-space, any finite-dimensional function can be viewed as an operator…
Memory complexity and data scarcity have so far prohibited learning solution operators of partial differential equations (PDEs) at high resolutions. We address these limitations by introducing a new data efficient and highly parallelizable…
In the era of smart manufacturing, predictive maintenance (PdM) plays a pivotal role in improving equipment reliability and reducing operating costs. In this paper, we propose a novel Markov Decision Process (MDP) framework that integrates…
Classical neural networks are known for their ability to approximate mappings between finite-dimensional spaces, but they fall short in capturing complex operator dynamics across infinite-dimensional function spaces. Neural operators, in…
This paper presents a method for modeling transient fluid flow in subsurface reservoir systems based on the developed neural operator architecture (TFNO-opt). Reservoir systems are complex dynamic objects with distributed parameters…
As an alternative to classical numerical solvers for partial differential equations (PDEs) subject to boundary value constraints, there has been a surge of interest in investigating neural networks that can solve such problems efficiently.…
This paper introduces the Kernel Neural Operator (KNO), a provably convergent operator-learning architecture that utilizes compositions of deep kernel-based integral operators for function-space approximation of operators (maps from…
We introduce MENO (''Matrix Exponential-based Neural Operator''), a hybrid surrogate modeling framework for efficiently solving stiff systems of ordinary differential equations (ODEs) that exhibit a sparse nonlinear structure. In such…
Solving cell problems in homogenization is hard, and available deep-learning frameworks fail to match the speed and generality of traditional computational frameworks. More to the point, it is generally unclear what to expect of…
A large class of inverse problems for PDEs are only well-defined as mappings from operators to functions. Existing operator learning frameworks map functions to functions and need to be modified to learn inverse maps from data. We propose a…
Multiple operator learning concerns learning operator families $\{G[\alpha]:U\to V\}_{\alpha\in W}$ indexed by an operator descriptor $\alpha$. Training data are collected hierarchically by sampling operator instances $\alpha$, then input…
This research investigates the application of Multigrid Neural Operator (MgNO), a neural operator architecture inspired by multigrid methods, in the simulation for multiphase flow within porous media. The architecture is adjusted to manage…
High-frequency features are critical in multiscale phenomena such as turbulent flows and phase transitions, since they encode essential physical information. The recently proposed Wavelet Neural Operator (WNO) utilizes wavelets'…
In this paper, we present a novel Fredholm Integral Equation Neural Operator (FIE-NO) method, an integration of Random Fourier Features and Fredholm Integral Equations (FIE) into the deep learning framework, tailored for solving data-driven…
Deep neural operators are recognized as an effective tool for learning solution operators of complex partial differential equations (PDEs). As compared to laborious analytical and computational tools, a single neural operator can predict…
Neural operators such as the Fourier Neural Operator (FNO) have been shown to provide resolution-independent deep learning models that can learn mappings between function spaces. For example, an initial condition can be mapped to the…
Partial differential equations (PDEs) govern diverse physical phenomena, yet high-fidelity numerical solutions are computationally expensive and Machine Learning approaches lack generalization. While Scientific Foundation Models (SFMs) aim…
Fourier neural operators (FNOs) can learn highly nonlinear mappings between function spaces, and have recently become a popular tool for learning responses of complex physical systems. However, to achieve good accuracy and efficiency, FNOs…