Universal approximation to nonlinear operators by neural networks with arbitrary activation functions and its application to dynamical systems

1995/07/01 by Tianping Chen, Hong Chen · 87 citations

paper · doi:10.1109/72.392253

Cited by

• Can Data-Driven Dynamics Reveal Hidden Physics? There Is A Need for Interpretable Neural Operators
• A Physics-informed Multi-resolution Neural Operator
• Common Task Framework For a Critical Evaluation of Scientific Machine Learning Algorithms
• Sensing Without Colocation: Operator-Based Virtual Instrumentation for Domains Beyond Physical Reach
• Deep Neural ODE Operator Networks for PDEs
• AMORE: Adaptive Multi-Output Operator Network for Stiff Chemical Kinetics
• PO-CKAN:Physics Informed Deep Operator Kolmogorov Arnold Networks with Chunk Rational Structure
• Bridging the Physics-Data Gap with FNO-Guided Conditional Flow Matching: Designing Inductive Bias through Hierarchical Physical Constraints
• RheOFormer: A generative transformer model for simulation of complex fluids and flows
• Stabilization of nonlinear systems with unknown delays via delay-adaptive neural operator approximate predictors
• A Greedy PDE Router for Blending Neural Operators and Classical Methods
• Equation-Free Coarse Control of Distributed Parameter Systems via Local Neural Operators
• Shape-Informed Clustering of Multi-Dimensional Functional Data via Deep Functional Autoencoders
• Global Forecasting of Tropical Cyclone Intensity Using Neural Weather Models
• A Variational Framework for Residual-Based Adaptivity in Neural PDE Solvers and Operator Learning
• Learning Nonlinear Responses in PET Bottle Buckling with a Hybrid DeepONet-Transolver Framework
• FEDONet : Fourier-Embedded DeepONet for Spectrally Accurate Operator Learning
• Deep operator network for surrogate modeling of poroelasticity with random permeability fields
• Reduced Order Modeling of Energetic Materials Using Physics-Aware Recurrent Convolutional Neural Networks in a Latent Space (LatentPARC)
• ReBaNO: Reduced Basis Neural Operator Mitigating Generalization Gaps and Achieving Discretization Invariance
• Physics-informed waveform inversion using pretrained wavefield neural operators
• Learning Turbulent Flows with Generative Models: Super-resolution, Forecasting, and Sparse Flow Reconstruction
• Fourier Neural Operators for Time-Periodic Quantum Systems: Learning Floquet Hamiltonians, Observable Dynamics, and Operator Growth
• Nano Machine Intelligence: From a Communication Perspective
• Neural Network Solution of Non-Markovian Quantum State Diffusion and Operator Construction of Quantum Stochastic Process
• An Evolutionary Multi-objective Optimization for Replica-Exchange-based Physics-informed Operator Learning Network
• Delay-adaptive Control of Nonlinear Systems with Approximate Neural Operator Predictors
• Physics-Informed DeepONet Coupled with FEM for Convective Transport in Porous Media with Sharp Gaussian Sources
• Neural operators for solving nonlinear inverse problems
• Hybrid Least Squares/Gradient Descent Methods for DeepONets
• Physics-informed deep operator network for traffic state estimation
• Are Fourier Neural Operators Really Faster for Time-Domain Wave Propagation?
• Fast and Generalizable parameter-embedded Neural Operators for Lithium-Ion Battery Simulation
• From Product Hilbert Spaces to the Generalized Koopman Operator and the Nonlinear Fundamental Lemma
• Unsupervised operator learning approach for dissipative equations via Onsager principle
• Machine Learning-Based Nonlinear Nudging for Chaotic Dynamical Systems
• Bridging ocean wave physics and deep learning: Physics-informed neural operators for nonlinear wavefield reconstruction in real-time
• DD-DeepONet: Domain decomposition and DeepONet for solving partial differential equations in three application scenarios
• Modeling turbulent and self-gravitating fluids with Fourier neural operators
• Merging Memory and Space: A State Space Neural Operator
• AI paradigm for solving differential equations: first-principles data generation and scale-dilation operator AI solver
• LVM-GP: Uncertainty-Aware PDE Solver via coupling latent variable model and Gaussian process
• Quantum optical shallow networks
• Locally Adaptive Conformal Inference for Operator Models
• Low-rank adaptive physics-informed HyperDeepONets for solving differential equations
• Deep Micro Solvers for Rough-Wall Stokes Flow in a Heterogeneous Multiscale Method
• Distribution-Free Uncertainty-Aware Virtual Sensing via Conformalized Neural Operators
• Operator Learning for Consolidation: An Architectural Comparison for DeepONet Variants
• Modeling Partially Observed Nonlinear Dynamical Systems and Efficient Data Assimilation via Discrete-Time Conditional Gaussian Koopman Network
• Neural Parameter-varying Data-enabled Predictive Control of Cold Atmospheric Pressure Plasma Jets
• Stochastic Operator Network: A Stochastic Maximum Principle Based Approach to Operator Learning
• An AI Approach for Learning the Spectrum of the Laplace-Beltrami Operator
• Learning Structural Eigenmodes with Modal Operator Network (ModalONet)
• Discretization-independent multifidelity operator learning for partial differential equations
• Operator-based machine learning framework for generalizable prediction of unsteady treatment dynamics in stormwater infrastructure
• Single vs. Multiple Branches in DeepONet and S-DeepONet: Network Architecture Follows Coupling in Multiphysics Systems
• The concept of null in general spaces and contexts
• Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators
• A Neural Operator based Hybrid Microscale Model for Multiscale Simulation of Rate-Dependent Materials
• Using Deep Operators to Create Spatio-temporal Surrogates for Dynamical Systems under Uncertainty
• LaDEEP: A Deep Learning-based Surrogate Model for Large Deformation of Elastic-Plastic Solids
• Employing Deep Neural Operators for PDE control by decoupling training and optimization
• SetONet: A Set-Based Operator Network for Solving PDEs with Variable-Input Sampling
• Hybrid deep learning and iterative methods for accelerated solutions of viscous incompressible flow
• PMNO: A novel physics guided multi-step neural operator predictor for partial differential equations
• A novel implementation of Yau-Yau filter for time-variant nonlinear problems
• Autoregressive regularized score-based diffusion models for multi-scenarios fluid flow prediction
• Nonparametric Estimation of Conditional Survival Function with Time-Varying Covariates Using DeepONet
• Deep Operator Neural Network Model Predictive Control
• TI-DeepONet: Learnable Time Integration for Stable Long-Term Extrapolation
• A Learning-Based Ansatz Satisfying Boundary Conditions in Variational Problems
• Reformulating Neural Operators in d+1 Dimensions for Embedding Evolution
• Block-Biased Mamba for Long-Range Sequence Processing
• Automatically Differentiable Model Updating (ADiMU): conventional, hybrid, and neural network material model discovery including history-dependency
• Physics-informed Multiple-Input Operators for efficient dynamic response prediction of structures
• Universal Approximation Theorem for Deep Q-Learning via FBSDE System
• Learning dynamically inspired invariant subspaces for Koopman and transfer operator approximation
• A Physics-preserved Transfer Learning Method for Differential Equations
• Universality of shallow and deep neural networks on non-Euclidean spaces
• Neural Networks with Local Converging Inputs for Efficient Options Pricing Models
• Extending Neural Operators: Robust Handling of Functions Beyond the Training Set
• Universal Approximation of Nonlinear Operators and Their Derivatives
• PaRO-DeepONet: a particle-informed reduced-order deep operator network for Poisson solver in PIC simulations
• Multi-scale DeepOnet (Mscale-DeepOnet) for Mitigating Spectral Bias in Learning High Frequency Operators of Oscillatory Functions
• A Structure-Preserving Framework for Solving Parabolic Partial Differential Equations with Neural Networks
• Leveraging Deep Operator Networks (DeepONet) for Acoustic Full Waveform Inversion (FWI)
• Dynamic hysteresis model of grain-oriented ferromagnetic material using neural operators