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

Abstract

Numerical simulations on fluid dynamics problems primarily rely on spatially or/and temporally discretization of the governing equation using polynomials into a finite-dimensional algebraic system. Due to the multi-scale nature of the physics and sensitivity from meshing a complicated geometry, such process can be computational prohibitive for most realtime applications (e.g., clinical diagnosis and surgery planning) and many-query analyses (e.g., optimization design and uncertainty quantification). Therefore, developing a costeffective 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, success of which heav-* Corresponding author. 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.

A deep-learning-based surrogate model for data assimilation in dynamic subsurface flow problems

“…The approaches cited above all require numerical simulation data to train the neural network. In physics informed surrogate models [9,10,11,12,13], by contrast, simulation data are not needed for training. With these procedures the governing partial differential equations (PDEs) are approximated by formulating PDE residuals, along with the initial and boundary conditions, as the objective function to be minimized by the neural network [14].…”

Microstructure-informed probability-driven point-particle model for hydrodynamic forces and torques in particle-laden flows

“…This process, also known as the 'learning' or 'training' phase, is an iterative optimisation procedure aimed at minimising errors between the real data and those predicted by the algorithm. This approach works successfully for computer vision tasks, for example, due to an abundance of labelled data and the interpolatory nature of the problem (Sun et al 2019). However, the application of off-the-shelf ML techniques to flow dynamics problems (or any other physical phenomena for that matter) inevitably suffers from non-interpretability in terms of governing physics due to ML's 'black-box' nature.…”

Driven by Data or Derived Through Physics? A Review of Hybrid Physics Guided Machine Learning Techniques With Cyber-Physical System (CPS) Focus

“…The loss function of the pix2pix architecture in a conditional GAN [217], [218] was penalized by using a constraint enforcing module for spatial sensitivity analysis for predicting urban land use [219]. The loss of a fully connected NN was made to include boundary conditions and residuals of the governing equations for surrogate modeling in hemodynamics [220]. Reinforcement learning was also used for learning non-parametric models under constrained state spaces in continuous environments [221].…”