The ADMM-PINNs algorithmic framework for nonsmooth PDE-constrained optimization: a deep learning approach
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Publication:6649881
DOI10.1137/23M1566935MaRDI QIDQ6649881
Hangrui Yue, Xiaoming Yuan, Yongcun Song
Publication date: 6 December 2024
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
Artificial neural networks and deep learning (68T07) Numerical optimization and variational techniques (65K10) Nonsmooth analysis (49J52) PDEs in connection with control and optimization (35Q93) PDE constrained optimization (numerical aspects) (49M41)
Cites Work
- Nonlinear total variation based noise removal algorithms
- Elliptic optimal control problems with \(L^1\)-control cost and applications for the placement of control devices
- An algorithm for total variation minimization and applications
- Multilayer feedforward networks are universal approximators
- The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems
- DGM: a deep learning algorithm for solving partial differential equations
- Iterative surrogate model optimization (ISMO): an active learning algorithm for PDE constrained optimization with deep neural networks
- Optimal control of PDEs using physics-informed neural networks
- B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data
- Solving inverse-PDE problems with physics-aware neural networks
- Solving and learning nonlinear PDEs with Gaussian processes
- Hybrid FEM-NN models: combining artificial neural networks with the finite element method
- Physics constrained learning for data-driven inverse modeling from sparse observations
- Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems
- CAN-PINN: a fast physics-informed neural network based on coupled-automatic-numerical differentiation method
- Scientific machine learning through physics-informed neural networks: where we are and what's next
- Neural-net-induced Gaussian process regression for function approximation and PDE solution
- Physics-constrained deep learning for high-dimensional surrogate modeling and uncertainty quantification without labeled data
- Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems
- Numerical solution and bifurcation analysis of nonlinear partial differential equations with extreme learning machines
- Local extreme learning machines and domain decomposition for solving linear and nonlinear partial differential equations
- Extreme learning machine collocation for the numerical solution of elliptic PDEs with sharp gradients
- An ADMM numerical approach to linear parabolic state constrained optimal control problems
- Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
- Machine learning approximation algorithms for high-dimensional fully nonlinear partial differential equations and second-order backward stochastic differential equations
- A LONE code for the sparse control of quantum systems
- A comparison of algorithms for control constrained optimal control of the Burgers equation
- Multiplier and gradient methods
- Physics and equality constrained artificial neural networks: application to forward and inverse problems with multi-fidelity data fusion
- Uncertainty quantification in scientific machine learning: methods, metrics, and comparisons
- Distributed optimal control of the Cahn-Hilliard system including the case of a double-obstacle homogeneous free energy density
- Numerical Gaussian Processes for Time-Dependent and Nonlinear Partial Differential Equations
- Proximal schemes for parabolic optimal control problems with sparsity promoting cost functionals
- Convergence and regularization results for optimal control problems with sparsity functional
- Optimization with PDE Constraints
- Split Bregman Methods and Frame Based Image Restoration
- Updating Quasi-Newton Matrices with Limited Storage
- Weakly Differentiable Functions
- An Augmented Lagrangian Method for Identifying Discontinuous Parameters in Elliptic Systems
- A Nonlinear Primal-Dual Method for Total Variation-Based Image Restoration
- Regularization of linear least squares problems by total bounded variation
- Identification of Discontinuous Coefficients in Elliptic Problems Using Total Variation Regularization
- Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising
- Inverse Problem Theory and Methods for Model Parameter Estimation
- Solving high-dimensional partial differential equations using deep learning
- An ADMM-Newton-CNN numerical approach to a TV model for identifying discontinuous diffusion coefficients in elliptic equations: convex case with gradient observations
- Solving parametric PDE problems with artificial neural networks
- 12 Numerical issues and turnpike phenomenon in optimal shape design
- Control and numerical approximation of fractional diffusion equations
- DeepXDE: A Deep Learning Library for Solving Differential Equations
- Physics-Informed Neural Networks with Hard Constraints for Inverse Design
- An Inexact Uzawa Algorithmic Framework for Nonlinear Saddle Point Problems with Applications to Elliptic Optimal Control Problem
- Exact and Approximate Controllability for Distributed Parameter Systems
- A SQP-Semismooth Newton-type Algorithm applied to Control of the instationary Navier--Stokes System Subject to Control Constraints
- Alternating Direction Method of Multipliers for Linear Inverse Problems
- Application of the Alternating Direction Method of Multipliers to Control Constrained Parabolic Optimal Control Problems and Beyond
- An introduction to the mathematical theory of inverse problems
- Approximation by superpositions of a sigmoidal function
- Distributed control problems for the Burgers equation
- A numerical approach to the optimal control of thermally convective flows
- The Random Feature Method for Time-Dependent Problems
- Physics-informed deep learning for simultaneous surrogate modeling and PDE-constrained optimization of an airfoil geometry
- NeuralUQ: A Comprehensive Library for Uncertainty Quantification in Neural Differential Equations and Operators
- A two-stage numerical approach for the sparse initial source identification of a diffusion–advection equation *
- Sparse Gaussian processes for solving nonlinear PDEs
- Error analysis of kernel/GP methods for nonlinear and parametric PDEs
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