PDE-constrained models with neural network terms: optimization and global convergence
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Publication:2699336
DOI10.1016/j.jcp.2023.112016OpenAlexW3162692524MaRDI QIDQ2699336
Jonathan F. MacArt, Konstantinos V. Spiliopoulos, Justin A. Sirignano
Publication date: 26 April 2023
Published in: Journal of Computational Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2105.08633
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- Machine learning strategies for systems with invariance properties
- Simultaneous single-step one-shot optimization with unsteady PDEs
- Adjoint-based optimization of PDE systems with alternative gradients
- High order conservative finite difference scheme for variable density low Mach number turbulent flows
- Application of a fractional-step method to incompressible Navier-Stokes equations
- Optimum aerodynamic design using the Navier-Stokes equations
- The numerical computation of turbulent flows
- Elliptic partial differential equations of second order
- Simultaneous pseudo-timestepping for PDE-model based optimization problems
- \textit{hp}-VPINNs: variational physics-informed neural networks with domain decomposition
- DPM: a deep learning PDE augmentation method with application to large-eddy simulation
- B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data
- NSFnets (Navier-Stokes flow nets): physics-informed neural networks for the incompressible Navier-Stokes equations
- Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
- Adjoint methods for obstacle problems and weakly coupled systems of PDE
- Physics and Computation of Aero-Optics
- One-Shot Approaches to Design Optimzation
- Automated Extension of Fixed Point PDE Solvers for Optimal Design with Bounded Retardation
- Recent Advances in Understanding of Thermal Expansion Effects in Premixed Turbulent Flames
- Machine Learning for Fluid Mechanics
- Flow over an espresso cup: inferring 3-D velocity and pressure fields from tomographic background oriented Schlieren via physics-informed neural networks
- Numerical Calculation of Time-Dependent Viscous Incompressible Flow of Fluid with Free Surface
- Optimization with PDE Constraints
- Global existence for semilinear parabolic systems.
- Adjoint Recovery of Superconvergent Functionals from PDE Approximations
- Turbulent Flows
- Deep learning of vortex-induced vibrations
- Turbulence statistics in fully developed channel flow at low Reynolds number
- The harmonic adjoint approach to unsteady turbomachinery design
- An Introduction to Partial Differential Equations
- Quantitative Propagation of Chaos in a Bimolecular Chemical Reaction-Diffusion Model
- Reynolds averaged turbulence modelling using deep neural networks with embedded invariance
- Convergence of Linearized and Adjoint Approximations for Discontinuous Solutions of Conservation Laws. Part 1: Linearized Approximations and Linearized Output Functionals
- Convergence of Linearized and Adjoint Approximations for Discontinuous Solutions of Conservation Laws. Part 2: Adjoint Approximations and Extensions
- Numerical Solution of the Navier-Stokes Equations
- One-shot methods in function space for PDE-constrained optimal control problems
- Approximation by superpositions of a sigmoidal function
- An introduction to the adjoint approach to design
