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. https://resolver.caltech.edu/CaltechAUTHORS:20230203-893210800.26
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Abstract
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.
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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. | ||||||||
Group: | GALCIT | ||||||||
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Issue or Number: | 1 | ||||||||
DOI: | 10.1007/s00205-022-01836-7 | ||||||||
Record Number: | CaltechAUTHORS:20230203-893210800.26 | ||||||||
Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20230203-893210800.26 | ||||||||
Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||
ID Code: | 119020 | ||||||||
Collection: | CaltechAUTHORS | ||||||||
Deposited By: | Research Services Depository | ||||||||
Deposited On: | 24 Feb 2023 21:21 | ||||||||
Last Modified: | 24 Feb 2023 21:21 |
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