• Corpus ID: 239885970

An extended physics informed neural network for preliminary analysis of parametric optimal control problems

  title={An extended physics informed neural network for preliminary analysis of parametric optimal control problems},
  author={Nicola Demo and Maria Strazzullo and Gianluigi Rozza},
In this work we propose an extension of physics informed supervised learning strategies to parametric partial differential equations. Indeed, even if the latter are indisputably useful in many applications, they can be computationally expensive most of all in a real-time and many-query setting. Thus, our main goal is to provide a physics informed learning paradigm to simulate parametrized phenomena in a small amount of time. The physics information will be exploited in many ways, in the loss… 
Optimal control of PDEs using physics-informed neural networks
Physics-informed neural networks (PINNs) have recently become a popular method for solving forward and inverse problems governed by partial differential equations (PDEs). By incorporating the
Fast and accurate numerical simulations for the study of coronary artery bypass grafts by artificial neural network
An artificial neural network, an empirical interpolation method, and a non-uniform rational basis spline model for orthogonal decomposition are described.
Finite element based model order reduction for parametrized one-way coupled steady state linear thermomechanical problems
This contribution focuses on the development of Model Order Reduction (MOR) for one-way coupled steady state linear thermo-mechanical problems in a finite element setting. We apply Proper Orthogonal


Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
Abstract We introduce physics-informed neural networks – neural networks that are trained to solve supervised learning tasks while respecting any given laws of physics described by general nonlinear
Adaptive activation functions accelerate convergence in deep and physics-informed neural networks
It is theoretically proved that in the proposed method, gradient descent algorithms are not attracted to suboptimal critical points or local minima, and the proposed adaptive activation functions are shown to accelerate the minimization process of the loss values in standard deep learning benchmarks with and without data augmentation.
Physics-Informed Neural Networks for Heat Transfer Problems
Physics-informed neural networks (PINNs) have gained popularity across different engineering fields due to their effectiveness in solving realistic problems with noisy data and often partially
nPINNs: nonlocal Physics-Informed Neural Networks for a parametrized nonlocal universal Laplacian operator. Algorithms and Applications
The results show that nPINNs can jointly infer this function as well as $\delta$ and exhibit a universal behavior with respect to the Reynolds number, a finding that contributes to the understanding of nonlocal interactions in wall-bounded turbulence.
Conservative physics-informed neural networks on discrete domains for conservation laws: Applications to forward and inverse problems
Abstract We propose a conservative physics-informed neural network (cPINN) on discrete domains for nonlinear conservation laws. Here, the term discrete domain represents the discrete sub-domains
Data-driven physics-informed constitutive metamodeling of complex fluids: A multifidelity neural network (MFNN) framework
In this work, we introduce a comprehensive machine-learning algorithm, namely, a multifidelity neural network (MFNN) architecture for data-driven constitutive metamodeling of complex fluids. The
Multi-fidelity regression using artificial neural networks: efficient approximation of parameter-dependent output quantities
The results show that cross-validation in combination with Bayesian optimization consistently leads to neural network models that outperform the co-kriging scheme and an application of multi-fidelity regression to an engineering problem.
Model Reduction for Parametrized Optimal Control Problems in Environmental Marine Sciences and Engineering
This work proposes reduced order methods as a suitable approach to face parametrized optimal control problems governed by partial differential equations, with applications in en- vironmental marine sciences and engineering and proposes a POD-Galerkin reduction of the optimality system.
Adam: A Method for Stochastic Optimization
This work introduces Adam, an algorithm for first-order gradient-based optimization of stochastic objective functions, based on adaptive estimates of lower-order moments, and provides a regret bound on the convergence rate that is comparable to the best known results under the online convex optimization framework.
Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators
A new deep neural network called DeepONet can lean various mathematical operators with small generalization error and can learn various explicit operators, such as integrals and fractional Laplacians, as well as implicit operators that represent deterministic and stochastic differential equations.