Filtered Partial Differential Equations: a robust surrogate constraint in physics-informed deep learning framework

• URL: http://arxiv.org/abs/2311.03776v2
• Date: Tue, 14 May 2024 15:56:14 GMT
• Title: Filtered Partial Differential Equations: a robust surrogate constraint in physics-informed deep learning framework
• Authors: Dashan Zhang, Yuntian Chen, Shiyi Chen,
• Abstract summary: We propose a surrogate constraint (filtered PDE, FPDE in short) of the original physical equations to reduce the influence of noisy and sparse observation data. In the noise and sparsity experiment, the proposed FPDE models have better robustness than the conventional PDE models. For combining real-world experiment data into physics-informed training, the proposed FPDE constraint is useful.
• Score: 1.220743263007369
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Embedding physical knowledge into neural network (NN) training has been a hot topic. However, when facing the complex real-world, most of the existing methods still strongly rely on the quantity and quality of observation data. Furthermore, the neural networks often struggle to converge when the solution to the real equation is very complex. Inspired by large eddy simulation in computational fluid dynamics, we propose an improved method based on filtering. We analyzed the causes of the difficulties in physics informed machine learning, and proposed a surrogate constraint (filtered PDE, FPDE in short) of the original physical equations to reduce the influence of noisy and sparse observation data. In the noise and sparsity experiment, the proposed FPDE models (which are optimized by FPDE constraints) have better robustness than the conventional PDE models. Experiments demonstrate that the FPDE model can obtain the same quality solution with 100% higher noise and 12% quantity of observation data of the baseline. Besides, two groups of real measurement data are used to show the FPDE improvements in real cases. The final results show that FPDE still gives more physically reasonable solutions when facing the incomplete equation problem and the extremely sparse and high-noise conditions. For combining real-world experiment data into physics-informed training, the proposed FPDE constraint is useful and performs well in two real-world experiments: modeling the blood velocity in vessels and cell migration in scratches.

Related papers

• Text2PDE: Latent Diffusion Models for Accessible Physics Simulation [7.16525545814044]
  We introduce several methods to apply latent diffusion models to physics simulation. We show that the proposed approach is competitive with current neural PDE solvers in both accuracy and efficiency. By introducing a scalable, accurate, and usable physics simulator, we hope to bring neural PDE solvers closer to practical use.
  arXiv  Detail & Related papers  (2024-10-02T01:09:47Z)
• PDE-Refiner: Achieving Accurate Long Rollouts with Neural PDE Solvers [40.097474800631]
  Time-dependent partial differential equations (PDEs) are ubiquitous in science and engineering. Deep neural network based surrogates have gained increased interest.
  arXiv  Detail & Related papers  (2023-08-10T17:53:05Z)
• Training Deep Surrogate Models with Large Scale Online Learning [48.7576911714538]
  Deep learning algorithms have emerged as a viable alternative for obtaining fast solutions for PDEs. Models are usually trained on synthetic data generated by solvers, stored on disk and read back for training. It proposes an open source online training framework for deep surrogate models.
  arXiv  Detail & Related papers  (2023-06-28T12:02:27Z)
• NeuralStagger: Accelerating Physics-constrained Neural PDE Solver with Spatial-temporal Decomposition [67.46012350241969]
  This paper proposes a general acceleration methodology called NeuralStagger. It decomposing the original learning tasks into several coarser-resolution subtasks. We demonstrate the successful application of NeuralStagger on 2D and 3D fluid dynamics simulations.
  arXiv  Detail & Related papers  (2023-02-20T19:36:52Z)
• Deep Physics Corrector: A physics enhanced deep learning architecture for solving stochastic differential equations [0.0]
  We propose a novel gray-box modeling algorithm for physical systems governed by differential equations (SDE) The proposed approach, referred to as the Deep Physics Corrector (DPC), blends approximate physics represented in terms of SDE with deep neural network (DNN) We illustrate the performance of the proposed DPC on four benchmark examples from the literature.
  arXiv  Detail & Related papers  (2022-09-20T14:30:07Z)
• Physics-informed machine learning with differentiable programming for heterogeneous underground reservoir pressure management [64.17887333976593]
  Avoiding over-pressurization in subsurface reservoirs is critical for applications like CO2 sequestration and wastewater injection. Managing the pressures by controlling injection/extraction are challenging because of complex heterogeneity in the subsurface. We use differentiable programming with a full-physics model and machine learning to determine the fluid extraction rates that prevent over-pressurization.
  arXiv  Detail & Related papers  (2022-06-21T20:38:13Z)
• Multi-fidelity Hierarchical Neural Processes [79.0284780825048]
  Multi-fidelity surrogate modeling reduces the computational cost by fusing different simulation outputs. We propose Multi-fidelity Hierarchical Neural Processes (MF-HNP), a unified neural latent variable model for multi-fidelity surrogate modeling. We evaluate MF-HNP on epidemiology and climate modeling tasks, achieving competitive performance in terms of accuracy and uncertainty estimation.
  arXiv  Detail & Related papers  (2022-06-10T04:54:13Z)
• Bayesian Physics-Informed Extreme Learning Machine for Forward and Inverse PDE Problems with Noisy Data [5.805560469343597]
  Physics-informed extreme learning machine (PIELM) has recently received significant attention as a rapid version of physics-informed neural network (PINN) We develop the Bayesian physics-informed extreme learning machine (BPIELM) to solve both forward and inverse linear PDE problems with noisy data. Results show that, compared with PIELM, BPIELM quantifies uncertainty arising from noisy data and provides more accurate predictions.
  arXiv  Detail & Related papers  (2022-05-14T02:32:48Z)
• Physics-Informed Neural Operator for Learning Partial Differential Equations [55.406540167010014]
  PINO is the first hybrid approach incorporating data and PDE constraints at different resolutions to learn the operator. The resulting PINO model can accurately approximate the ground-truth solution operator for many popular PDE families.
  arXiv  Detail & Related papers  (2021-11-06T03:41:34Z)
• Physics-Guided Discovery of Highly Nonlinear Parametric Partial Differential Equations [29.181177365252925]
  Partial differential equations (PDEs) that fit scientific data can represent physical laws with explainable mechanisms. We propose a novel physics-guided learning method, which encodes observation knowledge and incorporates basic physical principles and laws. Experiments show that our proposed method is more robust against data noise, and can reduce the estimation error by a large margin.
  arXiv  Detail & Related papers  (2021-06-02T11:24:49Z)
• Large-scale Neural Solvers for Partial Differential Equations [48.7576911714538]
  Solving partial differential equations (PDE) is an indispensable part of many branches of science as many processes can be modelled in terms of PDEs. Recent numerical solvers require manual discretization of the underlying equation as well as sophisticated, tailored code for distributed computing. We examine the applicability of continuous, mesh-free neural solvers for partial differential equations, physics-informed neural networks (PINNs) We discuss the accuracy of GatedPINN with respect to analytical solutions -- as well as state-of-the-art numerical solvers, such as spectral solvers.
  arXiv  Detail & Related papers  (2020-09-08T13:26:51Z)

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.