Data-driven and physical-based identification of partial differential equations for multivariable system

Zhang, Weiwei

doi:10.1016/j.taml.2022.100334

Cited by 7 publications

(3 citation statements)

References 30 publications

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“…A great number of reviews meant that an even greater number of original research articles had been published. If we limited the results of the Scopus search to reviews related to fluids, three major fields of application emerge that attracted research interest in applying ML methods to (a) theoretical and industrial oil and gas [33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52], (b) CFD simulations [53][54][55][56][57][58][59][60][61][62][63][64][65][66][67][68], and (c) health and medical applications [69][70][71][72][73][74][75][76][77][78][79][80]…”

Section: A Brief Overview and Methods Classificationmentioning

confidence: 99%

Can Artificial Intelligence Accelerate Fluid Mechanics Research?

Drikakis

Sofos

2023

Fluids

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The significant growth of artificial intelligence (AI) methods in machine learning (ML) and deep learning (DL) has opened opportunities for fluid dynamics and its applications in science, engineering and medicine. Developing AI methods for fluid dynamics encompass different challenges than applications with massive data, such as the Internet of Things. For many scientific, engineering and biomedical problems, the data are not massive, which poses limitations and algorithmic challenges. This paper reviews ML and DL research for fluid dynamics, presents algorithmic challenges and discusses potential future directions.

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Section: A Brief Overview and Methods Classificationmentioning

confidence: 99%

Can Artificial Intelligence Accelerate Fluid Mechanics Research?

Drikakis

Sofos

2023

Fluids

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“…Normally, regression frameworks (e.g., Gaussian processes and neural networks) combined with model selection [29], [30] are well suited for data-driven discovery tasks. The true PDE terms can emerge through various spaces (e.g., a frequency space [31] or a manifold's embedding space [29], [30], [32]) and candidate representations (e.g., a polynomial interaction [2] or a weak form representation [33], [34]).…”

Section: Related Workmentioning

confidence: 99%

Adaptive Uncertainty-Penalized Model Selection for Data-Driven PDE Discovery

Thanasutives,

Morita,

Numao

et al. 2024

IEEE Access

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We propose a new parameter-adaptive uncertainty-penalized Bayesian information criterion (UBIC) to discover the stable governing partial differential equation (PDE) composed of a few important terms. Since the naive use of the BIC for model selection yields an overfitted PDE, the UBIC penalizes the found PDE not only by its complexity but also by its quantified uncertainty. Representing the PDE as the best subset of a few candidate terms, we use Bayesian regression to compute the coefficient of variation (CV) of the posterior PDE coefficients. The PDE uncertainty is then derived from the obtained CV. The UBIC follows the premise that the true PDE shows relatively lower uncertainty when compared with overfitted PDEs. Thus, the quantified uncertainty is an effective indicator for identifying the true PDE. We also introduce physicsinformed neural network learning as a simulation-based approach to further validate the UBIC-selected PDE against the other potential PDE. Numerical results confirm the successful application of the UBIC for data-driven PDE discovery from noisy spatio-temporal data. Additionally, we reveal an interesting effect of denoising the observed data on improving the trade-off between the BIC score and model complexity.

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“…The investigation of complex and nonlinear dynamic systems demands deep understanding of the physical behavior in order to provide a reliable model [ 125 ]. Identifying differential equations via data-driven models, is a way to provide governing equations directly from data instead of physical laws, as equations in complex physical systems are scarce [ 126 ]. Nevertheless, issues may arise due to data scarcity or low fidelity, as oftentimes noise is present [ 80 ].…”

Section: Symbolic Regressionmentioning

confidence: 99%

Artificial Intelligence in Physical Sciences: Symbolic Regression Trends and Perspectives

Angelis

Sofos

Karakasidis

2023

Arch Computat Methods Eng

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Symbolic regression (SR) is a machine learning-based regression method based on genetic programming principles that integrates techniques and processes from heterogeneous scientific fields and is capable of providing analytical equations purely from data. This remarkable characteristic diminishes the need to incorporate prior knowledge about the investigated system. SR can spot profound and elucidate ambiguous relations that can be generalizable, applicable, explainable and span over most scientific, technological, economical, and social principles. In this review, current state of the art is documented, technical and physical characteristics of SR are presented, the available programming techniques are investigated, fields of application are explored, and future perspectives are discussed.

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Data-driven and physical-based identification of partial differential equations for multivariable system

Cited by 7 publications

References 30 publications

Can Artificial Intelligence Accelerate Fluid Mechanics Research?

Can Artificial Intelligence Accelerate Fluid Mechanics Research?

Adaptive Uncertainty-Penalized Model Selection for Data-Driven PDE Discovery

Artificial Intelligence in Physical Sciences: Symbolic Regression Trends and Perspectives

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