Distilling Free-Form Natural Laws from Experimental Data (Images)

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Images

Credit: Lindsay France, Photographer, University Photography, Cornell UniversityCredit: Lindsay France, Photographer, University Photography, Cornell University

Credit: Lindsay France, Photographer, University Photography, Cornell UniversityCredit: Lindsay France, Photographer, University Photography, Cornell University

Credit: Lindsay France, Photographer, University Photography, Cornell UniversityCredit: Lindsay France, Photographer, University Photography, Cornell University

Credit: Lindsay France, Photographer, University Photography, Cornell UniversityCredit: Lindsay France, Photographer, University Photography, Cornell University

Credit: Michael Schmidt, Cornell UniversityCredit: Michael Schmidt, Cornell University

Credit: Michael Schmidt, Cornell UniversityCredit: Michael Schmidt, Cornell University

Credit: Jonathan Hiller, Cornell UniversityCredit: Jonathan Hiller, Cornell University

Figure 1. Mining physical systems: We captured the angles and angular velocities of a chaotic double-pendulum (A) over time, using motion tracking (B), then automatically searched for equations that describe a single natural law relating these variables.Figure 1. Mining physical systems: We captured the angles and angular velocities of a chaotic double-pendulum (A) over time, using motion tracking (B), then automatically searched for equations that describe a single natural law relating these variables.

Figure 2. The computational approach for detecting conservation laws from experimentally collected data.Figure 2. The computational approach for detecting conservation laws from experimentally collected data.

Figure 3. Summary of laws inferred from experimental data collected from physical systems. Depending on the types of variables provided to the algorithm, it detects different types of laws.Figure 3. Summary of laws inferred from experimental data collected from physical systems. Depending on the types of variables provided to the algorithm, it detects different types of laws.

Figure 4. Parsimony vs. accuracy, and performance. (A) The Pareto front (solid black curve) for physical laws of the double-pendulum and the frequency of sampling during the law equation search (grayscale).Figure 4. Parsimony vs. accuracy, and performance. (A) The Pareto front (solid black curve) for physical laws of the double-pendulum and the frequency of sampling during the law equation search (grayscale).

 

Double PendulumDouble Pendulum

Air TrackAir Track

 

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