Surrogate modeling for fluid flows based on physics-constrained deep learning without simulation data

2019/06/30 by Luning Sun, Han Gao, Shaowu Pan +2 · 1,015 citations
Decision Sciences · Engineering · Mathematics · Physics and Astronomy · #Applied mathematics #Artificial intelligence #Artificial neural network #Computational fluid dynamics #Computer science #Curse of dimensionality #Discretization #Flow (mathematics) #Fluid Dynamics and Vibration Analysis #Fluid dynamics #Geometry #Machine learning #Mathematical analysis #Mathematical optimization #Mathematics #Mechanics #Model Reduction and Neural Networks #Nonlinear system #Parametric statistics #Partial differential equation #Physics #Probabilistic and Robust Engineering Design #Surrogate model #Uncertainty quantification #physics.comp-ph

paper · pdf · doi:10.1016/j.cma.2019.112732

published in Computer Methods in Applied Mechanics and Engineering 361, 112732 (Elsevier BV) · 43 pages, 12 figures

arxiv created 2019/07/18 · openalex publication_date 2019/11/21 · arxiv updated 2021/07/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

Numerical simulations on fluid dynamics problems primarily rely on spatially or/and temporally discretization of the governing equation into the finite-dimensional algebraic system solved by computers. Due to complicated nature of the physics and geometry, such process can be computational prohibitive for most real-time applications and many-query analyses. Therefore, developing a cost-effective surrogate model is of great practical significance. Deep learning (DL) has shown new promises for surrogate modeling due to its capability of handling strong nonlinearity and high dimensionality. However, the off-the-shelf DL architectures fail to operate when the data becomes sparse. Unfortunately, data is often insufficient in most parametric fluid dynamics problems since each data point in the parameter space requires an expensive numerical simulation based on the first principle, e.g., Naiver--Stokes equations. In this paper, we provide a physics-constrained DL approach for surrogate modeling of fluid flows without relying on any simulation data. Specifically, a structured deep neural network (DNN) architecture is devised to enforce the initial and boundary conditions, and the governing partial differential equations are incorporated into the loss of the DNN to drive the training. Numerical experiments are conducted on a number of internal flows relevant to hemodynamics applications, and the forward propagation of uncertainties in fluid properties and domain geometry is studied as well. The results show excellent agreement on the flow field and forward-propagated uncertainties between the DL surrogate approximations and the first-principle numerical simulations.

Citations

• Predicting the output from a complex computer code when fast approximations are available
• A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems
• Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• A composite neural network that learns from multi-fidelity data: Application to function approximation and inverse PDE problems

Cited by

• An adaptive adjoint-oriented neural network for solving parametric optimal control problems with singularities
• Discontinuity-aware physics-informed neural network for phase-field method in three-phase flow with phase change
• A Physics-Informed U-net-LSTM Network for Data-Driven Seismic Response Modeling of Structures
• Periodicity-Enforced Neural Network for Designing Deterministic Lateral Displacement Devices
• Multi-Objective Loss Balancing for Physics-Informed Deep Learning
• When and why PINNs fail to train: A neural tangent kernel perspective
• An Adjoint Formulation of Energetic Particle Confinement
• Physics-Informed Neural Networks for Real-Time Gas Crossover Prediction in PEM Electrolyzers: First Application with Multi-Membrane Validation
• Scalable Autoregressive Deep Surrogates for Dendritic Microstructure Dynamics
• Physics-constrained neural networks for half-space seismic wave modeling
• Understanding and Mitigating Gradient Flow Pathologies in Physics-Informed Neural Networks
• Conditional neural field for spatial dimension reduction of turbulence data: a comparison study
• Physics-Informed Neural Networks for Solving Multiscale Mode-Resolved Phonon Boltzmann Transport Equation
• PO-CKAN:Physics Informed Deep Operator Kolmogorov Arnold Networks with Chunk Rational Structure
• Aligning Perception, Reasoning, Modeling and Interaction: A Survey on Physical AI
• Physics-Informed Neural Operator for Learning Partial Differential Equations
• SoC-DT: Standard-of-Care Aligned Digital Twins for Patient-Specific Tumor Dynamics
• Understanding and mitigating gradient pathologies in physics-informed neural networks
• Optimal Transport Based Refinement of Physics-Informed Neural Networks
• Can AI Follow In Einstein's Footsteps?
• Learning the solution operator of parametric partial differential equations with physics-informed DeepONets
• A Combined Data-driven and Physics-driven Method for Steady Heat Conduction Prediction using Deep Convolutional Neural Networks
• Semi-Discrete in Time Method for Time-Dependent Equations by Random Neural Basis
• Multi-Objective Loss Balancing in Physics-Informed Neural Networks for Fluid Flow Applications
• Augmenting a pure and hybrid vertical equilibrium scheme via data-driven surrogate modelling
• M4GN: Mesh-based Multi-segment Hierarchical Graph Network for Dynamic Simulations
• Scientific Machine Learning Through Physics–Informed Neural Networks: Where we are and What’s Next
• Solving Approximation Tasks with Greedy Deep Kernel Methods
• Improved Training Strategies for Physics-Informed Neural Networks using Real Experimental Data in Aluminum Spot Welding
• Hybrid Boundary Physics-Informed Neural Networks for Solving Navier-Stokes Equations with Complex Boundary
• Variational inference formulation for a model-free simulation of a dynamical system with unknown parameters by a recurrent neural network
• Recurrent convolutional neural network for the surrogate modeling of subsurface flow simulation
• Controllable Patching for Compute-Adaptive Surrogate Modeling of Partial Differential Equations
• Resolving Extreme Data Scarcity by Explicit Physics Integration: An Application to Groundwater Heat Transport
• Variable separated physics-informed neural networks based on adaptive weighted loss functions for blood flow model
• Physical Informed Neural Networks for modeling ocean pollutant
• Single vs. Multiple Branches in DeepONet and S-DeepONet: Network Architecture Follows Coupling in Multiphysics Systems
• Three-dimensional crustal deformation analysis using physics-informed deep learning
• Machine learning for metal additive manufacturing: Predicting temperature and melt pool fluid dynamics using physics-informed neural networks
• Stochastic and Non-local Closure Modeling for Nonlinear Dynamical Systems via Latent Score-based Generative Models
• PhysiX: A Foundation Model for Physics Simulations
• Improved Surrogate Modeling of Fluid Dynamics with Physics-Informed Neural Networks
• Diffusion-Based Hierarchical Graph Neural Networks for Simulating Nonlinear Solid Mechanics
• Learning Only on Boundaries: A Physics-Informed Neural Operator for Solving Parametric Partial Differential Equations in Complex Geometries
• Deformable registration and generative modelling of aortic anatomies by auto-decoders and neural ODEs
• PDE-Transformer: Efficient and Versatile Transformers for Physics Simulations
• Physics-Constrained Bayesian Neural Network for Fluid Flow Reconstruction with Sparse and Noisy Data
• A decomposition-based robust training of physics-informed neural networks for nearly incompressible linear elasticity
• Full Domain Analysis in Fluid Dynamics
• Machine Learning for Naval Architecture, Ocean and Marine Engineering
• Modeling Unknown Nonlocal PDE Systems via Flow Map Learning
• Convergence Properties of PINNs for the Navier-Stokes-Cahn-Hilliard System
• Learning and Transferring Physical Models through Derivatives
• LawMind: A Law-Driven Paradigm for Discovering Analytical Solutions to Partial Differential Equations
• Physics-informed, Generative Adversarial Design of Funicular Shells
• Reliable and efficient inverse analysis using physics-informed neural networks with normalized distance functions and adaptive weight tuning
• FlexPINN: Modeling Fluid Dynamics and Mass Transfer in 3D Micromixer Geometries Using a Flexible Physics-Informed Neural Network
• Physics-informed multi-LSTM networks for metamodeling of nonlinear structures
• A Novel Deep Learning Approach for Emulating Computationally Expensive Postfire Debris Flows