Machine learning for discovering laws of nature. (arXiv:2303.17607v1 [cs.LG])

A microscopic particle obeys the principles of quantum mechanics — so where
is the sharp boundary between the macroscopic and microscopic worlds? It was
this “interpretation problem” that prompted Schr”odinger to propose his famous
thought experiment (a cat that is simultaneously both dead and alive) and
sparked a great debate about the quantum measurement problem, and there is
still no satisfactory answer yet. This is precisely the inadequacy of rigorous
mathematical models in describing the laws of nature. We propose a
computational model to describe and understand the laws of nature based on
Darwin’s natural selection. In fact, whether it’s a macro particle, a micro
electron or a security, they can all be considered as an entity, the change of
this entity over time can be described by a data series composed of states and
values. An observer can learn from this data series to construct theories
(usually consisting of functions and differential equations). We don’t model
with the usual functions or differential equations, but with a state Decision
Tree (determines the state of an entity) and a value Function Tree (determines
the distance between two points of an entity). A state Decision Tree and a
value Function Tree together can reconstruct an entity’s trajectory and make
predictions about its future trajectory. Our proposed algorithmic model
discovers laws of nature by only learning observed historical data (sequential
measurement of observables) based on maximizing the observer’s expected value.
There is no differential equation in our model; our model has an emphasis on
machine learning, where the observer builds up his/her experience by being
rewarded or punished for each decision he/she makes, and eventually leads to
rediscovering Newton’s law, the Born rule (quantum mechanics) and the efficient
market hypothesis (financial market).



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