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Model-Free and Prior-Free Data-Driven Inference in Mechanics

Conti, Sergio and Hoffmann, Franca and Ortiz, Michael (2023) Model-Free and Prior-Free Data-Driven Inference in Mechanics. Archive for Rational Mechanics and Analysis, 247 (1). Art. No. 7. ISSN 0003-9527. doi:10.1007/s00205-022-01836-7.

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We present a model-free data-driven inference method that enables inferences on system outcomes to be derived directly from empirical data without the need for intervening modeling of any type, be it modeling of a material law or modeling of a prior distribution of material states. We specifically consider physical systems with states characterized by points in a phase space determined by the governing field equations. We assume that the system is characterized by two likelihood measures: one μ_D measuring the likelihood of observing a material state in phase space; and another μ_E measuring the likelihood of states satisfying the field equations, possibly under random actuation. We introduce a notion of intersection between measures which can be interpreted to quantify the likelihood of system outcomes. We provide conditions under which the intersection can be characterized as the athermal limit μ_∞ of entropic regularizations μ_B, or thermalizations, of the product measure μ = μ_D x μ_E as β → +∞. We also supply conditions under which μ_∞ can be obtained as the athermal limit of carefully thermalized (μ_[h,β_(h)]) sequences of empirical data sets (μ_h) approximating weakly an unknown likelihood function μ. In particular, we find that the cooling sequence β_h → +∞ must be slow enough, corresponding to annealing, in order for the proper limit μ_∞ to be delivered. Finally, we derive explicit analytic expressions for expectations E[⨍] of outcomes ⨍ that are explicit in the data, thus demonstrating the feasibility of the model-free data-driven paradigm as regards making convergent inferences directly from the data without recourse to intermediate modeling steps.

Item Type:Article
Related URLs:
URLURL TypeDescription
Conti, Sergio0000-0001-7987-9174
Hoffmann, Franca0000-0002-1182-5521
Ortiz, Michael0000-0001-5877-4824
Additional Information:This work was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) via Project 211504053 - SFB 1060; Project 441211072 - SPP 2256; and Project 390685813 - GZ 2047/1 - HCM.
Funding AgencyGrant Number
Deutsche Forschungsgemeinschaft (DFG)211504053 - SFB 1060
Deutsche Forschungsgemeinschaft (DFG)441211072 - SPP 2256
Deutsche Forschungsgemeinschaft (DFG)390685813 - GZ 2047/1 - HCM
Issue or Number:1
Record Number:CaltechAUTHORS:20230203-893210800.26
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:119020
Deposited By: Research Services Depository
Deposited On:24 Feb 2023 21:21
Last Modified:24 Feb 2023 21:21

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