Determining arguments of invariant functional descriptions

Abstract

Abstract. In this paper we examine the problem of determining argumcnts of invariant functional descriptions from incomplete observational data. Physical laws arc one example of invariant functional descriptions. For such functions, we show that onc can test the relcvance of the function's arguments even though their values remain constant throughout the observational data. We present a method, called COPER, for discovering invariant functional descriptions. COPER eliminates irrelevant arguments, generates additkmal relevant arguments, and gencratcs a functional formula. We focus on the first two of these features, giving two examples of how the methodology can be applied to determining arguments of physical laws.

Toward the Discovery of First Principle Based Scientific Law Equations

“…( R 3 h fe 2 R 3 h f e 2 + h ie2 R 2 h f e 1 R 2 h f e 1 + h ie1 rL 2 rL 2 + R 1 )(V 1 0 V 2 ) 0 Q C 0 Kh ie 3 X Bh fe 3 = 0 : (4) Here, L and r are photo intensity and sensitivity of the Csd device. X;K and B are position of indicator, spring constant a n d i n tensity of magnetic eld of the representations of electric circuit.…”

“…(4) is easily checked by substituting the intermediate terms to this ensemble equation. 4 Extended SDS…”

“…However, the mathematical admissibility is not introduced su ciently in the discovery process, and many redundant representations of simultaneous equations can be derived at an expense of high computational complexity. COPER, which also discovers simultaneous equations, uses very strong mathematical constraints based on the unit dimensions to prune the meaningless terms [4]. However, it inevitably requires the unit information which is not frequently obtained in non-physical domains.…”

“…However, a drawback of the BACON family, that is their low likelihood of the discovered equations being the rst principle underlying the objective process, is reported. To alleviate the drawback, some systems, e.g., ABACUS and COPER [4], utilize the information of the unit dimensions of quantities to prune the meaningless terms. However, many of these conventional scienti c equation discovery systems have some critical limitations for the real world applications.…”

Discovering Admissible Simultaneous Equation Models from Observed Data

“…However, a drawback of the BACON family, that is their low likelihood to discover the equations representing the rst principle underlying the objective process, is reported. To alleviate the drawback, some systems, e.g., ABACUS and COPER [5], utilize the information of the unit dimensions of quantities to prune the meaningless terms. However, many of these conventional scientic equation discovery systems have the following limitations.…”