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Model-free Data-Driven Inference

Conti, S. and Hoffmann, F. and Ortiz, M. (2021) Model-free Data-Driven Inference. . (Unpublished)

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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_β, 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 quenching, in order for the proper limit µ∞ to be delivered. Finally, we derive explicit analytic expressions for expectations E[f] of outcomes f 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:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription Paper
Conti, S.0000-0001-7987-9174
Hoffmann, F.0000-0002-1182-5521
Ortiz, M.0000-0001-5877-4824
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
Record Number:CaltechAUTHORS:20210719-210156414
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:109924
Deposited By: George Porter
Deposited On:19 Jul 2021 22:52
Last Modified:19 Jul 2021 22:52

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