Deduction from clearly defined axioms (postulates) is the only reasonable method in fundamental physics:

"By a theory I shall mean the deductive closure of a set of theoretical postulates together with an appropriate set of auxiliary hypotheses; that is, everything that can be deduced from this set." W. H. Newton-Smith, THE RATIONALITY OF SCIENCE, p. 199 http://cdn.preterhuman.net/texts/tho...%20science.pdf

Einstein also seems to suggest that deduction is the correct method:

Albert Einstein: "From a systematic theoretical point of view, we may imagine the process of evolution of an empirical science to be a continuous process of induction. Theories are evolved and are expressed in short compass as statements of a large number of individual observations in the form of empirical laws, from which the general laws can be ascertained by comparison. Regarded in this way, the development of a science bears some resemblance to the compilation of a classified catalogue. It is, as it were, a purely empirical enterprise. But this point of view by no means embraces the whole of the actual process ; for it slurs over the important part played by intuition and deductive thought in the development of an exact science. As soon as a science has emerged from its initial stages, theoretical advances are no longer achieved merely by a process of arrangement. Guided by empirical data, the investigator rather develops a system of thought which, in general, is built up logically from a small number of fundamental assumptions, the so-called axioms." https://www.marxists.org/reference/a...ative/ap03.htm

The crucial question is:

What if the theory is not deductive (no clearly defined axioms; no explicit deductive path leading from the axioms to any conclusion; unlimited permission to introduce fudge factors not deducible from axioms)?

Answer: Then the theory, e.g. Einstein's general relativity, is a not-even-wrong inductive concoction, essentially equivalent to curve fitting models:

"Curve fitting is the process of adjusting a mathematical function so that it fits as closely as possible to a given set of data points The function can then be used as a mathematical model of the underlying data."

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