Global minimization via classical tunneling assisted by collective force field formation

Journal Article · 22 December 2021 · Science Advances

DOI: https://doi.org/10.1126/sciadv.abh1542 · OSTI ID:1853927

Caravelli, Francesco  ^[1]; Sheldon, Forrest Crawford  ^[2]; Traversa, Fabio Lorenzo  ^[3]

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1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States); London Inst. for Mathematical Sciences, London (United Kingdom)
3. MemComputing Inc., San Diego, CA (United States)

Simple elements interacting in networks can give rise to intricate emergent behaviors. Examples such as synchronization and phase transitions often apply in many contexts, as many different systems may reduce to the same effective model. Here, we demonstrate such a behavior in a model inspired by memristors. When weakly driven, the system is described by movement in an effective potential, but when strongly driven, instabilities cause escapes from local minima, which can be interpreted as an unstable tunneling mechanism. We dub this collective and nonperturbative effect a “Lyapunov force,” which steers the system toward the global minimum of the potential function, even if the full system has a constellation of equilibrium points growing exponentially with the system size. This mechanism is appealing for its physical relevance in nanoscale physics and for its possible applications in optimization, Monte Carlo schemes, and machine learning.

• Research Organization: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: LDRD; USDOE
• Grant/Contract Number: 89233218CNA000001; AC52-06NA25396
• OSTI ID: 1853927
• Report Number(s): LA-UR-21-20810
• Journal Information: Science Advances, Journal Name: Science Advances Journal Issue: 52 Vol. 7; ISSN 2375-2548
• Publisher: AAASCopyright Statement
• Country of Publication: United States
• Language: English