DeepPhysics: a physics aware deep learning framework for real-time
simulation
- URL: http://arxiv.org/abs/2109.09491v1
- Date: Fri, 17 Sep 2021 12:15:47 GMT
- Title: DeepPhysics: a physics aware deep learning framework for real-time
simulation
- Authors: Alban Odot (MIMESIS), Ryadh Haferssas (MIMESIS), St\'ephane Cotin
(MIMESIS)
- Abstract summary: We propose a solution to simulate hyper-elastic materials using a data-driven approach.
A neural network is trained to learn the non-linear relationship between boundary conditions and the resulting displacement field.
The results show that our network architecture trained with a limited amount of data can predict the displacement field in less than a millisecond.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Real-time simulation of elastic structures is essential in many applications,
from computer-guided surgical interventions to interactive design in mechanical
engineering. The Finite Element Method is often used as the numerical method of
reference for solving the partial differential equations associated with these
problems. Yet, deep learning methods have recently shown that they could
represent an alternative strategy to solve physics-based problems 1,2,3. In
this paper, we propose a solution to simulate hyper-elastic materials using a
data-driven approach, where a neural network is trained to learn the non-linear
relationship between boundary conditions and the resulting displacement field.
We also introduce a method to guarantee the validity of the solution. In total,
we present three contributions: an optimized data set generation algorithm
based on modal analysis, a physics-informed loss function, and a Hybrid
Newton-Raphson algorithm. The method is applied to two benchmarks: a cantilever
beam and a propeller. The results show that our network architecture trained
with a limited amount of data can predict the displacement field in less than a
millisecond. The predictions on various geometries, topologies, mesh
resolutions, and boundary conditions are accurate to a few micrometers for
non-linear deformations of several centimeters of amplitude.
Related papers
- Learning the solution operator of two-dimensional incompressible
Navier-Stokes equations using physics-aware convolutional neural networks [68.8204255655161]
We introduce a technique with which it is possible to learn approximate solutions to the steady-state Navier--Stokes equations in varying geometries without the need of parametrization.
The results of our physics-aware CNN are compared to a state-of-the-art data-based approach.
arXiv Detail & Related papers (2023-08-04T05:09:06Z) - 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) - Physics-aware deep learning framework for linear elasticity [0.0]
The paper presents an efficient and robust data-driven deep learning (DL) computational framework for linear continuum elasticity problems.
For an accurate representation of the field variables, a multi-objective loss function is proposed.
Several benchmark problems including the Airimaty solution to elasticity and the Kirchhoff-Love plate problem are solved.
arXiv Detail & Related papers (2023-02-19T20:33:32Z) - Neural Operator: Is data all you need to model the world? An insight
into the impact of Physics Informed Machine Learning [13.050410285352605]
We provide an insight into how data-driven approaches can complement conventional techniques to solve engineering and physics problems.
We highlight a novel and fast machine learning-based approach to learning the solution operator of a PDE operator learning.
arXiv Detail & Related papers (2023-01-30T23:29:33Z) - Message Passing Neural PDE Solvers [60.77761603258397]
We build a neural message passing solver, replacing allally designed components in the graph with backprop-optimized neural function approximators.
We show that neural message passing solvers representationally contain some classical methods, such as finite differences, finite volumes, and WENO schemes.
We validate our method on various fluid-like flow problems, demonstrating fast, stable, and accurate performance across different domain topologies, equation parameters, discretizations, etc., in 1D and 2D.
arXiv Detail & Related papers (2022-02-07T17:47:46Z) - FEM-based Real-Time Simulations of Large Deformations with Probabilistic
Deep Learning [1.2617078020344616]
We propose a highly efficient deep-learning surrogate framework that is able to predict the response of hyper-elastic bodies under load.
The framework takes the form of special convolutional neural network architecture, so-called U-Net, which is trained with force-displacement data.
arXiv Detail & Related papers (2021-11-02T20:05:22Z) - Physics informed neural networks for continuum micromechanics [68.8204255655161]
Recently, physics informed neural networks have successfully been applied to a broad variety of problems in applied mathematics and engineering.
Due to the global approximation, physics informed neural networks have difficulties in displaying localized effects and strong non-linear solutions by optimization.
It is shown, that the domain decomposition approach is able to accurately resolve nonlinear stress, displacement and energy fields in heterogeneous microstructures obtained from real-world $mu$CT-scans.
arXiv Detail & Related papers (2021-10-14T14:05:19Z) - Meshless physics-informed deep learning method for three-dimensional
solid mechanics [0.0]
Deep learning and the collocation method are merged and used to solve partial differential equations describing structures' deformation.
We consider different types of materials: linear elasticity, hyperelasticity (neo-Hookean) with large deformation, and von Mises plasticity with isotropic and kinematic hardening.
arXiv Detail & Related papers (2020-12-02T21:40:37Z) - Scalable Differentiable Physics for Learning and Control [99.4302215142673]
Differentiable physics is a powerful approach to learning and control problems that involve physical objects and environments.
We develop a scalable framework for differentiable physics that can support a large number of objects and their interactions.
arXiv Detail & Related papers (2020-07-04T19:07:51Z) - Learning to Simulate Complex Physics with Graph Networks [68.43901833812448]
We present a machine learning framework and model implementation that can learn to simulate a wide variety of challenging physical domains.
Our framework---which we term "Graph Network-based Simulators" (GNS)--represents the state of a physical system with particles, expressed as nodes in a graph, and computes dynamics via learned message-passing.
Our results show that our model can generalize from single-timestep predictions with thousands of particles during training, to different initial conditions, thousands of timesteps, and at least an order of magnitude more particles at test time.
arXiv Detail & Related papers (2020-02-21T16:44:28Z) - Physics Informed Deep Learning for Transport in Porous Media. Buckley
Leverett Problem [0.0]
We present a new hybrid physics-based machine-learning approach to reservoir modeling.
The methodology relies on a series of deep adversarial neural network architecture with physics-based regularization.
The proposed methodology is a simple and elegant way to instill physical knowledge to machine-learning algorithms.
arXiv Detail & Related papers (2020-01-15T08:20:11Z)
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.