A Physics-Informed Neural Network Framework For Partial Differential Equations on 3D Surfaces: Time-Dependent Problems

• URL: http://arxiv.org/abs/2103.13878v1
• Date: Fri, 19 Mar 2021 13:47:46 GMT
• Title: A Physics-Informed Neural Network Framework For Partial Differential Equations on 3D Surfaces: Time-Dependent Problems
• Authors: Zhiwei Fang, Justin Zhang, Xiu Yang
• Abstract summary: We show a physics-informed neural network solver for the time-dependent surface PDEs. We show a simplified prior estimate of the surface differential operators so that PINN's loss value will be an indicator of the residue of the surface PDEs.
• Score: 3.3406650564566225
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, we show a physics-informed neural network solver for the time-dependent surface PDEs. Unlike the traditional numerical solver, no extension of PDE and mesh on the surface is needed. We show a simplified prior estimate of the surface differential operators so that PINN's loss value will be an indicator of the residue of the surface PDEs. Numerical experiments verify efficacy of our algorithm.

Related papers

• Randomized Neural Networks for Partial Differential Equation on Static and Evolving Surfaces [5.950635488980616]
  We present formulations for parametrized surfaces, implicit level-set surfaces, and provide an analysis for the parametrization-based formulation with compatibility.
  arXiv  Detail & Related papers  (2026-03-02T10:17:09Z)
• Learning to Solve PDEs on Neural Shape Representations [6.867079032925542]
  Solving partial differential equations on shapes underpins many shape analysis and engineering tasks.<n>Yet, prevailing PDE solvers operate on polygonal/triangle meshes while modern 3D assets increasingly live as neural representations.<n>We present a novel, mesh-free formulation that learns a local update operator conditioned on neural (local) shape attributes.
  arXiv  Detail & Related papers  (2025-12-24T18:14:02Z)
• Mechanistic PDE Networks for Discovery of Governing Equations [52.492158106791365]
  We present Mechanistic PDE Networks, a model for discovery of partial differential equations from data. The represented PDEs are then solved and decoded for specific tasks. We develop a native, GPU-capable, parallel, sparse, and differentiable multigrid solver specialized for linear partial differential equations.
  arXiv  Detail & Related papers  (2025-02-25T17:21:44Z)
• Advancing Generalization in PINNs through Latent-Space Representations [71.86401914779019]
  Physics-informed neural networks (PINNs) have made significant strides in modeling dynamical systems governed by partial differential equations (PDEs) We propose PIDO, a novel physics-informed neural PDE solver designed to generalize effectively across diverse PDE configurations. We validate PIDO on a range of benchmarks, including 1D combined equations and 2D Navier-Stokes equations.
  arXiv  Detail & Related papers  (2024-11-28T13:16:20Z)
• Deep Equilibrium Based Neural Operators for Steady-State PDEs [100.88355782126098]
  We study the benefits of weight-tied neural network architectures for steady-state PDEs. We propose FNO-DEQ, a deep equilibrium variant of the FNO architecture that directly solves for the solution of a steady-state PDE.
  arXiv  Detail & Related papers  (2023-11-30T22:34:57Z)
• Solving PDEs on Spheres with Physics-Informed Convolutional Neural Networks [17.69666422395703]
  Physics-informed neural networks (PINNs) have been demonstrated to be efficient in solving partial differential equations (PDEs) In this paper, we establish rigorous analysis of the physics-informed convolutional neural network (PICNN) for solving PDEs on the sphere.
  arXiv  Detail & Related papers  (2023-08-18T14:58:23Z)
• MAgNet: Mesh Agnostic Neural PDE Solver [68.8204255655161]
  Climate predictions require fine-temporal resolutions to resolve all turbulent scales in the fluid simulations. Current numerical model solveers PDEs on grids that are too coarse (3km to 200km on each side) We design a novel architecture that predicts the spatially continuous solution of a PDE given a spatial position query.
  arXiv  Detail & Related papers  (2022-10-11T14:52:20Z)
• High Precision Differentiation Techniques for Data-Driven Solution of Nonlinear PDEs by Physics-Informed Neural Networks [0.0]
  Time-dependent Partial Differential Equations with given initial conditions are considered in this paper. New differentiation techniques of the unknown solution with respect to time variable are proposed.
  arXiv  Detail & Related papers  (2022-10-02T13:36:01Z)
• Physics-Aware Neural Networks for Boundary Layer Linear Problems [0.0]
  Physics-Informed Neural Networks (PINNs) approximate the solution of general partial differential equations (PDEs) by adding them in some form as terms of the loss/cost of a Neural Network. This paper explores PINNs for linear PDEs whose solutions may present one or more boundary layers.
  arXiv  Detail & Related papers  (2022-07-15T21:15:06Z)
• LordNet: An Efficient Neural Network for Learning to Solve Parametric Partial Differential Equations without Simulated Data [47.49194807524502]
  We propose LordNet, a tunable and efficient neural network for modeling entanglements. The experiments on solving Poisson's equation and (2D and 3D) Navier-Stokes equation demonstrate that the long-range entanglements can be well modeled by the LordNet.
  arXiv  Detail & Related papers  (2022-06-19T14:41:08Z)
• Learning to Solve PDE-constrained Inverse Problems with Graph Networks [51.89325993156204]
  In many application domains across science and engineering, we are interested in solving inverse problems with constraints defined by a partial differential equation (PDE) Here we explore GNNs to solve such PDE-constrained inverse problems. We demonstrate computational speedups of up to 90x using GNNs compared to principled solvers.
  arXiv  Detail & Related papers  (2022-06-01T18:48:01Z)
• 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)
• Lie Point Symmetry Data Augmentation for Neural PDE Solvers [69.72427135610106]
  We present a method, which can partially alleviate this problem, by improving neural PDE solver sample complexity. In the context of PDEs, it turns out that we are able to quantitatively derive an exhaustive list of data transformations. We show how it can easily be deployed to improve neural PDE solver sample complexity by an order of magnitude.
  arXiv  Detail & Related papers  (2022-02-15T18:43:17Z)
• Solving Partial Differential Equations with Point Source Based on Physics-Informed Neural Networks [33.18757454787517]
  In recent years, deep learning technology has been used to solve partial differential equations (PDEs) We propose a universal solution to tackle this problem with three novel techniques. We evaluate the proposed method with three representative PDEs, and the experimental results show that our method outperforms existing deep learning-based methods with respect to the accuracy, the efficiency and the versatility.
  arXiv  Detail & Related papers  (2021-11-02T06:39:54Z)

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.