Physics-enhanced deep surrogates for partial differential equations

• URL: http://arxiv.org/abs/2111.05841v4
• Date: Thu, 14 Dec 2023 21:56:38 GMT
• Title: Physics-enhanced deep surrogates for partial differential equations
• Authors: Rapha\"el Pestourie, Youssef Mroueh, Chris Rackauckas, Payel Das, Steven G. Johnson
• Abstract summary: We present a "physics-enhanced deep-surrogate" ("PEDS") approach towards developing fast surrogate models for complex physical systems. Specifically, a combination of a low-fidelity, explainable physics simulator and a neural network generator is proposed, which is trained end-to-end to globally match the output of an expensive high-fidelity numerical solver.
• Score: 30.731686639510517
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Many physics and engineering applications demand Partial Differential Equations (PDE) property evaluations that are traditionally computed with resource-intensive high-fidelity numerical solvers. Data-driven surrogate models provide an efficient alternative but come with a significant cost of training. Emerging applications would benefit from surrogates with an improved accuracy-cost tradeoff, while studied at scale. Here we present a "physics-enhanced deep-surrogate" ("PEDS") approach towards developing fast surrogate models for complex physical systems, which is described by PDEs. Specifically, a combination of a low-fidelity, explainable physics simulator and a neural network generator is proposed, which is trained end-to-end to globally match the output of an expensive high-fidelity numerical solver. Experiments on three exemplar testcases, diffusion, reaction-diffusion, and electromagnetic scattering models, show that a PEDS surrogate can be up to 3$\times$ more accurate than an ensemble of feedforward neural networks with limited data ($\approx 10^3$ training points), and reduces the training data need by at least a factor of 100 to achieve a target error of 5%. Experiments reveal that PEDS provides a general, data-driven strategy to bridge the gap between a vast array of simplified physical models with corresponding brute-force numerical solvers modeling complex systems, offering accuracy, speed, data efficiency, as well as physical insights into the process.

Related papers

• DPOT: Auto-Regressive Denoising Operator Transformer for Large-Scale PDE Pre-Training [87.90342423839876]
  We present a new auto-regressive denoising pre-training strategy, which allows for more stable and efficient pre-training on PDE data. We train our PDE foundation model with up to 0.5B parameters on 10+ PDE datasets with more than 100k trajectories.
  arXiv  Detail & Related papers  (2024-03-06T08:38:34Z)
• 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)
• 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)
• Interfacing Finite Elements with Deep Neural Operators for Fast Multiscale Modeling of Mechanics Problems [4.280301926296439]
  In this work, we explore the idea of multiscale modeling with machine learning and employ DeepONet, a neural operator, as an efficient surrogate of the expensive solver. DeepONet is trained offline using data acquired from the fine solver for learning the underlying and possibly unknown fine-scale dynamics. We present various benchmarks to assess accuracy and speedup, and in particular we develop a coupling algorithm for a time-dependent problem.
  arXiv  Detail & Related papers  (2022-02-25T20:46:08Z)
• Adaptive Anomaly Detection for Internet of Things in Hierarchical Edge Computing: A Contextual-Bandit Approach [81.5261621619557]
  We propose an adaptive anomaly detection scheme with hierarchical edge computing (HEC) We first construct multiple anomaly detection DNN models with increasing complexity, and associate each of them to a corresponding HEC layer. Then, we design an adaptive model selection scheme that is formulated as a contextual-bandit problem and solved by using a reinforcement learning policy network.
  arXiv  Detail & Related papers  (2021-08-09T08:45:47Z)
• Transfer Learning on Multi-Fidelity Data [0.0]
  Neural networks (NNs) are often used as surrogates or emulators of partial differential equations (PDEs) that describe the dynamics of complex systems. We rely on multi-fidelity simulations to reduce the cost of data generation for subsequent training of a deep convolutional NN (CNN) using transfer learning. Our numerical experiments demonstrate that a mixture of a comparatively large number of low-fidelity data and smaller numbers of high- and low-fidelity data provides an optimal balance of computational speed-up and prediction accuracy.
  arXiv  Detail & Related papers  (2021-04-29T00:06:19Z)
• Efficient training of physics-informed neural networks via importance sampling [2.9005223064604078]
  Physics-In Neural Networks (PINNs) are a class of deep neural networks that are trained to compute systems governed by partial differential equations (PDEs) We show that an importance sampling approach will improve the convergence behavior of PINNs training.
  arXiv  Detail & Related papers  (2021-04-26T02:45:10Z)
• 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.