Physics successfully implements Lagrange multiplier optimization.
Physics successfully implements Lagrange multiplier optimization.
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DOI：
10.1073/pnas.2015192117
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发表时间：
2020-10-27
影响因子：
11.1
通讯作者：
Yablonovitch E
中科院分区：
文献类型：
--
作者：
Vadlamani SK;Xiao TP;Yablonovitch E
在整个人类文明中，从空气动力学到航班调度、交付路线和电信解码，优化都发挥了重要作用。优化正受到越来越多的关注，因为它是当今人工智能的核心。所有这些优化问题都是人类或机器最难解决的问题之一。人们忽略了物理学本身在动力系统的正常演化中进行优化，例如寻找最小能量状态。我们表明，在这样的物理原理，最小功耗的想法，也被称为最小熵产生的原则，似乎是最有用的，因为它可以很容易地实现在电气或光学电路。优化是人类努力的重要组成部分。虽然是数学的，但优化也内置于物理中。例如，物理学有最小作用原理;最小功率耗散原理，也称为最小熵产生;和变分原理。物理学也有物理退火，当然，在计算模拟退火之前。物理学有绝热原理，在量子形式中，称为量子退火。因此，物理机器可以解决优化的数学问题，包括约束。二元约束可以被构建到物理优化中。在这种情况下，机器是数字的，就像触发器是数字的一样。最近，各种各样的机器在优化伊辛磁能方面取得了成功。在本文中，我们证明了几乎所有的机器进行优化，根据最小功耗的原则提出的Onsager。此外，我们表明，这种优化实际上是等价的拉格朗日乘子优化的约束问题。我们发现驱动这些系统的物理增益系数实际上起着相应的拉格朗日乘子的作用。
All through human civilization, optimization has played a major role, from aerodynamics to airline scheduling, delivery routing, and telecommunications decoding. Optimization is receiving increasing attention, since it is central to today’s artificial intelligence. All of these optimization problems are among the hardest for human or machine to solve. It has been overlooked that physics itself does optimization in the normal evolution of dynamical systems, such as seeking out the minimum energy state. We show that among such physics principles, the idea of minimum power dissipation, also called the Principle of Minimum Entropy Generation, appears to be the most useful, since it can be readily implemented in electrical or optical circuits. Optimization is a major part of human effort. While being mathematical, optimization is also built into physics. For example, physics has the Principle of Least Action; the Principle of Minimum Power Dissipation, also called Minimum Entropy Generation; and the Variational Principle. Physics also has Physical Annealing, which, of course, preceded computational Simulated Annealing. Physics has the Adiabatic Principle, which, in its quantum form, is called Quantum Annealing. Thus, physical machines can solve the mathematical problem of optimization, including constraints. Binary constraints can be built into the physical optimization. In that case, the machines are digital in the same sense that a flip–flop is digital. A wide variety of machines have had recent success at optimizing the Ising magnetic energy. We demonstrate in this paper that almost all those machines perform optimization according to the Principle of Minimum Power Dissipation as put forth by Onsager. Further, we show that this optimization is in fact equivalent to Lagrange multiplier optimization for constrained problems. We find that the physical gain coefficients that drive those systems actually play the role of the corresponding Lagrange multipliers.
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影响因子：
8.6
作者：
RECK, M;ZEILINGER, A;BERTANI, P
通讯作者：
BERTANI, P
影响因子：
--
作者：
Onsager, L
通讯作者：
Onsager, L
影响因子：
13.6
作者：
Goto, Hayato;Tatsumura, Kosuke;Dixon, Alexander R.
通讯作者：
Dixon, Alexander R.
影响因子：
35
作者：
Inagaki, Takahiro;Inaba, Kensuke;Takesue, Hiroki
通讯作者：
Takesue, Hiroki
影响因子：
8.6
作者：
Leleu, Timothee;Yamamoto, Yoshihisa;Aihara, Kazuyuki
通讯作者：
Aihara, Kazuyuki