Learning the solution operator of parametric partial differential equations with physics-informed DeepONets.
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ABSTRACT:
SUBMITTER: Wang S
PROVIDER: S-EPMC8480920 | biostudies-literature |
REPOSITORIES: biostudies-literature
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Project description:This work proposes a new machine learning (ML)-based paradigm aiming to enhance the computational efficiency of non-equilibrium reacting flow simulations while ensuring compliance with the underlying physics. The framework combines dimensionality reduction and neural operators through a hierarchical and adaptive deep learning strategy to learn the solution of multi-scale coarse-grained governing equations for chemical kinetics. The proposed surrogate's architecture is structured as a tree, with leaf nodes representing separate neural operator blocks where physics is embedded in the form of multiple soft and hard constraints. The hierarchical attribute has two advantages: (i) It allows the simplification of the training phase via transfer learning, starting from the slowest temporal scales; (ii) It accelerates the prediction step by enabling adaptivity as the surrogate's evaluation is limited to the necessary leaf nodes based on the local degree of non-equilibrium of the gas. The model is applied to the study of chemical kinetics relevant for application to hypersonic flight, and it is tested here on pure oxygen gas mixtures. In 0-[Formula: see text] scenarios, the proposed ML framework can adaptively predict the dynamics of almost thirty species with a maximum relative error of 4.5% for a wide range of initial conditions. Furthermore, when employed in 1-[Formula: see text] shock simulations, the approach shows accuracy ranging from 1% to 4.5% and a speedup of one order of magnitude compared to conventional implicit schemes employed in an operator-splitting integration framework. Given the results presented in the paper, this work lays the foundation for constructing an efficient ML-based surrogate coupled with reactive Navier-Stokes solvers for accurately characterizing non-equilibrium phenomena in multi-dimensional computational fluid dynamics simulations.
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Project description:PurposeTo develop a physics-guided deep learning (PG-DL) reconstruction strategy based on a signal intensity informed multi-coil (SIIM) encoding operator for highly-accelerated simultaneous multislice (SMS) myocardial perfusion cardiac MRI (CMR).MethodsFirst-pass perfusion CMR acquires highly-accelerated images with dynamically varying signal intensity/SNR following the administration of a gadolinium-based contrast agent. Thus, using PG-DL reconstruction with a conventional multi-coil encoding operator leads to analogous signal intensity variations across different time-frames at the network output, creating difficulties in generalization for varying SNR levels. We propose to use a SIIM encoding operator to capture the signal intensity/SNR variations across time-frames in a reformulated encoding operator. This leads to a more uniform/flat contrast at the output of the PG-DL network, facilitating generalizability across time-frames. PG-DL reconstruction with the proposed SIIM encoding operator is compared to PG-DL with conventional encoding operator, split slice-GRAPPA, locally low-rank (LLR) regularized reconstruction, low-rank plus sparse (L + S) reconstruction, and regularized ROCK-SPIRiT.ResultsResults on highly accelerated free-breathing first pass myocardial perfusion CMR at three-fold SMS and four-fold in-plane acceleration show that the proposed method improves upon the reconstruction methods use for comparison. Substantial noise reduction is achieved compared to split slice-GRAPPA, and aliasing artifacts reduction compared to LLR regularized reconstruction, L + S reconstruction and PG-DL with conventional encoding. Furthermore, a qualitative reader study indicated that proposed method outperformed all methods.ConclusionPG-DL reconstruction with the proposed SIIM encoding operator improves generalization across different time-frames /SNRs in highly accelerated perfusion CMR.
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