Improving hp-Variational Physics-Informed Neural Networks for Steady-State Convection-Dominated Problems

• URL: http://arxiv.org/abs/2411.09329v1
• Date: Thu, 14 Nov 2024 10:21:41 GMT
• Title: Improving hp-Variational Physics-Informed Neural Networks for Steady-State Convection-Dominated Problems
• Authors: Thivin Anandh, Divij Ghose, Himanshu Jain, Pratham Sunkad, Sashikumaar Ganesan, Volker John,
• Abstract summary: This paper studies two extensions of applying hp-variational physics-informed neural networks, more precisely the FastVPINNs framework, to convection-dominated convection-diffusion-reaction problems. First, a term in the spirit of a SUPG stabilization is included in the loss functional and a network architecture is proposed that predicts spatially varying stabilization parameters. The second novelty is the proposal of a network architecture that learns good parameters for a class of indicator functions.
• Score: 4.0974219394860505
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: This paper proposes and studies two extensions of applying hp-variational physics-informed neural networks, more precisely the FastVPINNs framework, to convection-dominated convection-diffusion-reaction problems. First, a term in the spirit of a SUPG stabilization is included in the loss functional and a network architecture is proposed that predicts spatially varying stabilization parameters. Having observed that the selection of the indicator function in hard-constrained Dirichlet boundary conditions has a big impact on the accuracy of the computed solutions, the second novelty is the proposal of a network architecture that learns good parameters for a class of indicator functions. Numerical studies show that both proposals lead to noticeably more accurate results than approaches that can be found in the literature.

Related papers

• Backscatter Device-aided Integrated Sensing and Communication: A Pareto Optimization Framework [59.30060797118097]
  Integrated sensing and communication (ISAC) systems potentially encounter significant performance degradation in densely obstructed urban non-line-of-sight scenarios.<n>This paper proposes a backscatter approximation (BD)-assisted ISAC system, which leverages passive BDs naturally distributed in environments of enhancement.
  arXiv  Detail & Related papers  (2025-07-12T17:11:06Z)
• Fast State-Augmented Learning for Wireless Resource Allocation with Dual Variable Regression [83.27791109672927]
  We show how a state-augmented graph neural network (GNN) parametrization for the resource allocation policy circumvents the drawbacks of the ubiquitous dual subgradient methods.<n>Lagrangian maximizing state-augmented policies are learned during the offline training phase.<n>We prove a convergence result and an exponential probability bound on the excursions of the dual function (iterate) optimality gaps.
  arXiv  Detail & Related papers  (2025-06-23T15:20:58Z)
• Multiresolution Analysis and Statistical Thresholding on Dynamic Networks [49.09073800467438]
  ANIE (Adaptive Network Intensity Estimation) is a multi-resolution framework designed to automatically identify the time scales at which network structure evolves.<n>We show that ANIE adapts to the appropriate time resolution and is able to capture sharp structural changes while remaining robust to noise.
  arXiv  Detail & Related papers  (2025-06-01T22:55:55Z)
• Learning Fluid-Structure Interaction Dynamics with Physics-Informed Neural Networks and Immersed Boundary Methods [0.5991851254194096]
  We introduce neural network architectures that combine physics-informed neural networks (PINNs) with the immersed boundary method (IBM) to solve fluid-structure interaction (FSI) problems.<n>Our approach features two distinct architectures: a Single-FSI network with a unified parameter space, and an innovative Eulerian-Lagrangian network that maintains separate parameter spaces for fluid and structure domains.
  arXiv  Detail & Related papers  (2025-05-24T07:07:53Z)
• Unifying Perplexing Behaviors in Modified BP Attributions through Alignment Perspective [61.5509267439999]
  We present a unified theoretical framework for methods like GBP, RectGrad, LRP, and DTD. We demonstrate that they achieve input alignment by combining the weights of activated neurons. This alignment improves the visualization quality and reduces sensitivity to weight randomization.
  arXiv  Detail & Related papers  (2025-03-14T07:58:26Z)
• Finite Element Neural Network Interpolation. Part I: Interpretable and Adaptive Discretization for Solving PDEs [44.99833362998488]
  We present a sparse neural network architecture extending previous work on Embedded Finite Element Neural Networks (EFENN) Due to their mesh-based structure, EFENN requires significantly fewer trainable parameters than fully connected neural networks. Our FENNI framework, within the EFENN framework, brings improvements to the HiDeNN approach.
  arXiv  Detail & Related papers  (2024-12-07T18:31:17Z)
• PACMANN: Point Adaptive Collocation Method for Artificial Neural Networks [44.99833362998488]
  PINNs minimize a loss function which includes the PDE residual determined for a set of collocation points. Previous work has shown that the number and distribution of these collocation points have a significant influence on the accuracy of the PINN solution. We present the Point Adaptive Collocation Method for Artificial Neural Networks (PACMANN)
  arXiv  Detail & Related papers  (2024-11-29T11:31:11Z)
• Adaptive Training of Grid-Dependent Physics-Informed Kolmogorov-Arnold Networks [4.216184112447278]
  Physics-Informed Neural Networks (PINNs) have emerged as a robust framework for solving Partial Differential Equations (PDEs) We present a fast JAX-based implementation of grid-dependent Physics-Informed Kolmogorov-Arnold Networks (PIKANs) for solving PDEs. We demonstrate that the adaptive features significantly enhance solution accuracy, decreasing the L2 error relative to the reference solution by up to 43.02%.
  arXiv  Detail & Related papers  (2024-07-24T19:55:08Z)
• Residual resampling-based physics-informed neural network for neutron diffusion equations [7.105073499157097]
  The neutron diffusion equation plays a pivotal role in the analysis of nuclear reactors. Traditional PINN approaches often utilize fully connected network (FCN) architecture. R2-PINN effectively overcomes the limitations inherent in current methods, providing more accurate and robust solutions for neutron diffusion equations.
  arXiv  Detail & Related papers  (2024-06-23T13:49:31Z)
• An Optimization-based Deep Equilibrium Model for Hyperspectral Image Deconvolution with Convergence Guarantees [71.57324258813675]
  We propose a novel methodology for addressing the hyperspectral image deconvolution problem. A new optimization problem is formulated, leveraging a learnable regularizer in the form of a neural network. The derived iterative solver is then expressed as a fixed-point calculation problem within the Deep Equilibrium framework.
  arXiv  Detail & Related papers  (2023-06-10T08:25:16Z)
• Implicit Stochastic Gradient Descent for Training Physics-informed Neural Networks [51.92362217307946]
  Physics-informed neural networks (PINNs) have effectively been demonstrated in solving forward and inverse differential equation problems. PINNs are trapped in training failures when the target functions to be approximated exhibit high-frequency or multi-scale features. In this paper, we propose to employ implicit gradient descent (ISGD) method to train PINNs for improving the stability of training process.
  arXiv  Detail & Related papers  (2023-03-03T08:17:47Z)
• Super Resolution for Turbulent Flows in 2D: Stabilized Physics Informed Neural Networks [0.05735035463793007]
  We propose a new design of a neural network for solving a zero shot super resolution problem for turbulent flows. We embed Luenberger-type observer into the network's architecture to inform the network of the physics of the process.
  arXiv  Detail & Related papers  (2022-04-15T10:22:56Z)
• Learning Physics-Informed Neural Networks without Stacked Back-propagation [82.26566759276105]
  We develop a novel approach that can significantly accelerate the training of Physics-Informed Neural Networks. In particular, we parameterize the PDE solution by the Gaussian smoothed model and show that, derived from Stein's Identity, the second-order derivatives can be efficiently calculated without back-propagation. Experimental results show that our proposed method can achieve competitive error compared to standard PINN training but is two orders of magnitude faster.
  arXiv  Detail & Related papers  (2022-02-18T18:07:54Z)
• Adversarially Robust Learning for Security-Constrained Optimal Power Flow [55.816266355623085]
  We tackle the problem of N-k security-constrained optimal power flow (SCOPF) N-k SCOPF is a core problem for the operation of electrical grids. Inspired by methods in adversarially robust training, we frame N-k SCOPF as a minimax optimization problem.
  arXiv  Detail & Related papers  (2021-11-12T22:08:10Z)
• Effects of boundary conditions in fully convolutional networks for learning spatio-temporal dynamics [0.0]
  Several strategies to impose boundary conditions are investigated in this paper. The choice of the optimal padding strategy is directly linked to the data semantics. The inclusion of additional input spatial context or explicit physics-based rules allows a better handling of boundaries in particular for large number of recurrences.
  arXiv  Detail & Related papers  (2021-06-21T14:58:41Z)
• Learning the ground state of a non-stoquastic quantum Hamiltonian in a rugged neural network landscape [0.0]
  We investigate a class of universal variational wave-functions based on artificial neural networks. In particular, we show that in the present setup the neural network expressivity and Monte Carlo sampling are not primary limiting factors.
  arXiv  Detail & Related papers  (2020-11-23T05:25:47Z)
• Supporting Optimal Phase Space Reconstructions Using Neural Network Architecture for Time Series Modeling [68.8204255655161]
  We propose an artificial neural network with a mechanism to implicitly learn the phase spaces properties. Our approach is either as competitive as or better than most state-of-the-art strategies.
  arXiv  Detail & Related papers  (2020-06-19T21:04:47Z)
• Network Diffusions via Neural Mean-Field Dynamics [52.091487866968286]
  We propose a novel learning framework for inference and estimation problems of diffusion on networks. Our framework is derived from the Mori-Zwanzig formalism to obtain an exact evolution of the node infection probabilities. Our approach is versatile and robust to variations of the underlying diffusion network models.
  arXiv  Detail & Related papers  (2020-06-16T18:45:20Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.