Research graph
References from Stabilizing PDE–ML coupled systems. Local targets link to admitted publications; unresolved targets remain external evidence.
Approximation by superpositions of a sigmoidal function
10.1007/bf02551274 · 1989 · External reference
Approximation capabilities of multilayer feedforward networks
10.1016/0893-6080(91)90009-t · 1991 · External reference
Universal approximation to nonlinear operators by neural networks with arbitrary activation functions and its application to dynamical systems
10.1109/72.392253 · 1995 · External reference
Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators
10.1038/s42256-021-00302-5 · 2021 · External reference
Unresolved reference
2014 · External reference
Unresolved reference
2017 · External reference
Learning partial differential equations via data discovery and sparse optimization
10.1098/rspa.2016.0446 · 2017 · External reference
Generalizable physics-constrained modeling using learning and inference assisted by feature-space engineering
10.1103/physrevfluids.6.124602 · 2021 · External reference
Unresolved reference
2022 · External reference
Unresolved reference
2025 · External reference
Data-driven equation discovery of ocean mesoscale closures
10.1029/2020gl088376 · 2020 · External reference
Unresolved reference
2024 · External reference
On closures for reduced order models—A spectrum of first-principle to machine-learned avenues
10.1063/5.0061577 · 2021 · External reference
A multifidelity deep operator network approach to closure for multiscale systems
10.1016/j.cma.2023.116161 · 2023 · External reference
Deep learning to represent subgrid processes in climate models
10.1073/pnas.1810286115 · 2018 · External reference
Deep neural networks for data-driven LES closure models
10.1016/j.jcp.2019.108910 · 2019 · External reference
Stable machine-learning parameterization of subgrid processes for climate modeling at a range of resolutions
10.1038/s41467-020-17142-3 · 2020 · External reference
Data assimilation empowered neural network parametrizations for subgrid processes in geophysical flows
10.1103/physrevfluids.6.050501 · 2021 · External reference
Stable climate simulations using a realistic gcm with neural network parameterizations for atmospheric moist physics and radiation processes
2021 · External reference
An ensemble of neural networks for moist physics processes, its generalizability and stable integration
10.1029/2022ms003508 · 2023 · External reference
Unresolved reference
2023 · External reference
Unresolved reference
2024 · External reference
Stable a posteriori LES of 2D turbulence using convolutional neural networks: Backscattering analysis and generalization to higher re via transfer learning
10.1016/j.jcp.2022.111090 · 2022 · External reference
Unresolved reference
2025 · External reference
On the spectral bias of neural networks
2019 · External reference
Optimal prediction with memory
10.1016/s0167-2789(02)00446-3 · 2002 · External reference
Problem reduction, renormalization, and memory
10.2140/camcos.2006.1.1 · 2007 · External reference
Computing nearly singular solutions using pseudo-spectral methods
10.1016/j.jcp.2007.04.014 · 2007 · External reference
Multi-stage neural networks: Function approximator of machine precision
10.1016/j.jcp.2024.112865 · 2024 · External reference
The immersed boundary method
10.1017/s0962492902000077 · 2002 · External reference
Unresolved reference
2024 · External reference
Computing the non-Markovian coarse-grained interactions derived from the Mori–Zwanzig formalism in molecular systems: Application to polymer melts
10.1063/1.4973347 · 2017 · External reference
Unresolved reference
2021 · External reference
Unresolved reference
External reference
Unresolved reference
2026 · External reference
Approximation by superpositions of a sigmoidal function
10.1007/bf02551274 · ExternalCitation · doi-reference
Approximation capabilities of multilayer feedforward networks
10.1016/0893-6080(91)90009-t · ExternalCitation · doi-reference
A multifidelity deep operator network approach to closure for multiscale systems
10.1016/j.cma.2023.116161 · ExternalCitation · doi-reference
Computing nearly singular solutions using pseudo-spectral methods
10.1016/j.jcp.2007.04.014 · ExternalCitation · doi-reference
Deep neural networks for data-driven LES closure models
10.1016/j.jcp.2019.108910 · ExternalCitation · doi-reference
Stable a posteriori LES of 2D turbulence using convolutional neural networks: Backscattering analysis and generalization to higher re via transfer learning
10.1016/j.jcp.2022.111090 · ExternalCitation · doi-reference
Multi-stage neural networks: Function approximator of machine precision
10.1016/j.jcp.2024.112865 · ExternalCitation · doi-reference
Optimal prediction with memory
10.1016/s0167-2789(02)00446-3 · ExternalCitation · doi-reference
The immersed boundary method
10.1017/s0962492902000077 · ExternalCitation · doi-reference
Data-driven equation discovery of ocean mesoscale closures
10.1029/2020gl088376 · ExternalCitation · doi-reference
An ensemble of neural networks for moist physics processes, its generalizability and stable integration
10.1029/2022ms003508 · ExternalCitation · doi-reference
Stable machine-learning parameterization of subgrid processes for climate modeling at a range of resolutions
10.1038/s41467-020-17142-3 · ExternalCitation · doi-reference
Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators
10.1038/s42256-021-00302-5 · ExternalCitation · doi-reference
Computing the non-Markovian coarse-grained interactions derived from the Mori–Zwanzig formalism in molecular systems: Application to polymer melts
10.1063/1.4973347 · ExternalCitation · doi-reference
On closures for reduced order models—A spectrum of first-principle to machine-learned avenues
10.1063/5.0061577 · ExternalCitation · doi-reference
Deep learning to represent subgrid processes in climate models
10.1073/pnas.1810286115 · ExternalCitation · doi-reference
Learning partial differential equations via data discovery and sparse optimization
10.1098/rspa.2016.0446 · ExternalCitation · doi-reference
Data assimilation empowered neural network parametrizations for subgrid processes in geophysical flows
10.1103/physrevfluids.6.050501 · ExternalCitation · doi-reference
Generalizable physics-constrained modeling using learning and inference assisted by feature-space engineering
10.1103/physrevfluids.6.124602 · ExternalCitation · doi-reference
Universal approximation to nonlinear operators by neural networks with arbitrary activation functions and its application to dynamical systems
10.1109/72.392253 · ExternalCitation · doi-reference
Problem reduction, renormalization, and memory
10.2140/camcos.2006.1.1 · ExternalCitation · doi-reference
