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    Gaussian Processes for Design Using Nondifferentiable Functions With Jump Discontinuities

    Source: Journal of Mechanical Design:;2025:;volume( 147 ):;issue: 006::page 61705-1
    Author:
    van Beek, Anton
    DOI: 10.1115/1.4068267
    Publisher: The American Society of Mechanical Engineers (ASME)
    Abstract: Available Gaussian processes (GPs) are inappropriate when used to globally emulate and optimize nondifferentiable functions with jump discontinuities. This is a substantial limitation as many contemporary engineering challenges are underpinned by functions with these characteristics and would benefit from a data-efficient emulator (e.g., contact problems in mechanics and material properties because of phase changes). Available GP models are inappropriate as jump discontinuities and nondifferentiabilities are local phenomena that cannot be modeled through covariance structures that describe a function’s global behavior. To overcome this limitation, we introduce the discontinuous Gaussian process (DCGP) model that involves learning a parametric, yet flexible function on the inputs to ensure that the residuals of the random process are continuous and differentiable. Through validation on a set of six test problems and one engineering problem, we show that the DCGP model outperforms available models that use multiple local emulators. The performance of the DCGP model is measured in terms of predictive fidelity and optimization efficiency. In addition, we show that there exist physical systems for which the correlation between its outputs can be modeled across discontinuities and nondifferentiabilities (i.e., globally). We believe this to be a profound insight as it suggests that statistical models, such as DCGP, could be used to expedite the discovery of emerging properties even for discontinuous and nondifferentiable functions.
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      Gaussian Processes for Design Using Nondifferentiable Functions With Jump Discontinuities

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    contributor authorvan Beek, Anton
    date accessioned2025-08-20T09:36:55Z
    date available2025-08-20T09:36:55Z
    date copyright4/8/2025 12:00:00 AM
    date issued2025
    identifier issn1050-0472
    identifier othermd-24-1473.pdf
    identifier urihttp://yetl.yabesh.ir/yetl1/handle/yetl/4308565
    description abstractAvailable Gaussian processes (GPs) are inappropriate when used to globally emulate and optimize nondifferentiable functions with jump discontinuities. This is a substantial limitation as many contemporary engineering challenges are underpinned by functions with these characteristics and would benefit from a data-efficient emulator (e.g., contact problems in mechanics and material properties because of phase changes). Available GP models are inappropriate as jump discontinuities and nondifferentiabilities are local phenomena that cannot be modeled through covariance structures that describe a function’s global behavior. To overcome this limitation, we introduce the discontinuous Gaussian process (DCGP) model that involves learning a parametric, yet flexible function on the inputs to ensure that the residuals of the random process are continuous and differentiable. Through validation on a set of six test problems and one engineering problem, we show that the DCGP model outperforms available models that use multiple local emulators. The performance of the DCGP model is measured in terms of predictive fidelity and optimization efficiency. In addition, we show that there exist physical systems for which the correlation between its outputs can be modeled across discontinuities and nondifferentiabilities (i.e., globally). We believe this to be a profound insight as it suggests that statistical models, such as DCGP, could be used to expedite the discovery of emerging properties even for discontinuous and nondifferentiable functions.
    publisherThe American Society of Mechanical Engineers (ASME)
    titleGaussian Processes for Design Using Nondifferentiable Functions With Jump Discontinuities
    typeJournal Paper
    journal volume147
    journal issue6
    journal titleJournal of Mechanical Design
    identifier doi10.1115/1.4068267
    journal fristpage61705-1
    journal lastpage61705-13
    page13
    treeJournal of Mechanical Design:;2025:;volume( 147 ):;issue: 006
    contenttypeFulltext
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