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Uncertainty Quantification in Scientific Machine Learning: Theory, Methods, and Software /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Uncertainty Quantification in Scientific Machine Learning: Theory, Methods, and Software // Zongren Zou.
作者:	Zou, Zongren,
面頁冊數:	1 electronic resource (299 pages)
附註:	Source: Dissertations Abstracts International, Volume: 86-12, Section: B.
Contained By:	Dissertations Abstracts International86-12B.
標題:	Applied mathematics. -
電子資源:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=32007340
ISBN:	9798283492490

Uncertainty Quantification in Scientific Machine Learning: Theory, Methods, and Software /
Zou, Zongren,

Uncertainty Quantification in Scientific Machine Learning: Theory, Methods, and Software /Zongren Zou. - 1 electronic resource (299 pages)

Source: Dissertations Abstracts International, Volume: 86-12, Section: B.

Accurate modeling and prediction of the dynamic response of physical systems remain an open scientific problem, despite decades of successful research. Persistent challenges include solving ill-posed problems, such as those with unknown parameters or boundary conditions, assimilating imprecise and/or incomplete data, and reducing computational costs, particularly for high-dimensional systems. In this regard, physics-informed machine learning and, more broadly, scientific machine learning (SciML) have emerged as promising interdisciplinary research areas. These approaches offer innovative tools for addressing many of the aforementioned challenges. For comprehensive reviews of recent advances in this field, see [142, 60, 7, 305, 281].Machine learning, particularly deep learning which uses neural networks (NNs), excels at processing large volumes of data and making rapid and accurate predictions; see, e.g., [104, 122]. SciML builds on these capabilities by integrating observational data with available physical models. Broadly, SciML techniques can be classified into three main categories:1. Data-driven emulation of physical systems:These approaches utilize large datasets to emulate physical systems. Examples include the deep operator network (DeepONet) developed by [178], with variations discussed in [107, 298] and theoretical insights provided by [165]. An alternative approach, the Fourier neural operator (FNO), is presented in [171].2. Physics-encoded architectures:These methods incorporate physics directly into the NN architecture design, as exemplified by the work of [64, 65].3. Physics-informed optimization:In these approaches, physical constraints are included as soft penalties in the NN optimization process. Notable examples include the physics-informed neural networks (PINNs) proposed by [244], with extensions detailed in [162, 269, 219, 134, 200, 151], and theoretical analyses found in [266, 203].These techniques are particularly advantageous in scenarios where conventional solvers face limitations. For instance, they are effective in addressing mixed problems with partial observational data and incomplete knowledge of the underlying physical system (e.g., [244]). They can seamlessly incorporate noisy or multi-fidelity data (e.g., [199, 198, 49, 50]) and generate physically consistent predictions, even for extrapolation tasks (e.g., [315]). Additionally, they eliminate the need for computationally expensive mesh generation (e.g., [244]) and benefit from open-source software that is continuously developed and extended (e.g., [180, 121]).Quantifying prediction uncertainty, particularly in scenarios involving noisy or limited data and NN overparameterization, is crucial for the reliable application of deep learning in critical domains such as physical and biological systems. Among the various uncertainty quantification (UQ) methods in deep learning, the Bayesian framework has been the most prominent and widely studied [209, 184, 210, 19, 164, 95, 109, 211, 124, 182, 88, 308, 24, 133, 175, 325, 287]. Alternative approaches include methods based on ensembles of NN optimization iterates or independently trained NNs [163, 129, 189, 93, 149, 226, 185, 84, 119, 240, 216, 57], evidential frameworks [188, 264, 8, 44, 158, 43], combining NNs with Gaussian processes [61, 241, 167, 191, 4, 6], and the conformal prediction framework [10, 72]. While Bayesian methods and ensemble-based techniques are discussed extensively in this chapter, readers seeking additional insights are encouraged to consult recent review articles on UQ in deep learning [233, 141, 37, 102, 177, 272, 293, 94, 2, 131, 207, 336, 139].

English

ISBN: 9798283492490Subjects--Topical Terms:

2122814
Applied mathematics.

Uncertainty Quantification in Scientific Machine Learning: Theory, Methods, and Software /
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520 $a Accurate modeling and prediction of the dynamic response of physical systems remain an open scientific problem, despite decades of successful research. Persistent challenges include solving ill-posed problems, such as those with unknown parameters or boundary conditions, assimilating imprecise and/or incomplete data, and reducing computational costs, particularly for high-dimensional systems. In this regard, physics-informed machine learning and, more broadly, scientific machine learning (SciML) have emerged as promising interdisciplinary research areas. These approaches offer innovative tools for addressing many of the aforementioned challenges. For comprehensive reviews of recent advances in this field, see [142, 60, 7, 305, 281].Machine learning, particularly deep learning which uses neural networks (NNs), excels at processing large volumes of data and making rapid and accurate predictions; see, e.g., [104, 122]. SciML builds on these capabilities by integrating observational data with available physical models. Broadly, SciML techniques can be classified into three main categories:1. Data-driven emulation of physical systems:These approaches utilize large datasets to emulate physical systems. Examples include the deep operator network (DeepONet) developed by [178], with variations discussed in [107, 298] and theoretical insights provided by [165]. An alternative approach, the Fourier neural operator (FNO), is presented in [171].2. Physics-encoded architectures:These methods incorporate physics directly into the NN architecture design, as exemplified by the work of [64, 65].3. Physics-informed optimization:In these approaches, physical constraints are included as soft penalties in the NN optimization process. Notable examples include the physics-informed neural networks (PINNs) proposed by [244], with extensions detailed in [162, 269, 219, 134, 200, 151], and theoretical analyses found in [266, 203].These techniques are particularly advantageous in scenarios where conventional solvers face limitations. For instance, they are effective in addressing mixed problems with partial observational data and incomplete knowledge of the underlying physical system (e.g., [244]). They can seamlessly incorporate noisy or multi-fidelity data (e.g., [199, 198, 49, 50]) and generate physically consistent predictions, even for extrapolation tasks (e.g., [315]). Additionally, they eliminate the need for computationally expensive mesh generation (e.g., [244]) and benefit from open-source software that is continuously developed and extended (e.g., [180, 121]).Quantifying prediction uncertainty, particularly in scenarios involving noisy or limited data and NN overparameterization, is crucial for the reliable application of deep learning in critical domains such as physical and biological systems. Among the various uncertainty quantification (UQ) methods in deep learning, the Bayesian framework has been the most prominent and widely studied [209, 184, 210, 19, 164, 95, 109, 211, 124, 182, 88, 308, 24, 133, 175, 325, 287]. Alternative approaches include methods based on ensembles of NN optimization iterates or independently trained NNs [163, 129, 189, 93, 149, 226, 185, 84, 119, 240, 216, 57], evidential frameworks [188, 264, 8, 44, 158, 43], combining NNs with Gaussian processes [61, 241, 167, 191, 4, 6], and the conformal prediction framework [10, 72]. While Bayesian methods and ensemble-based techniques are discussed extensively in this chapter, readers seeking additional insights are encouraged to consult recent review articles on UQ in deep learning [233, 141, 37, 102, 177, 272, 293, 94, 2, 131, 207, 336, 139].
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