Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The discovery of physical laws consistent with empirical observations lies at the heart of (applied) science and engineering. These laws typically take the form of nonlinear differential equations depending on parameters, dynamical systems theory provides, through the appropriate normal forms, an "intrinsic", prototypical characterization of the types of dynamical regimes accessible to a given model. Using an implementation of data-informed geometry learning  directly reconstruct the relevant "normal forms": a quantitative mapping from empirical observations to prototypical realizations of the underlying dynamics. Interestingly, the state variables and the parameters of these realizations are inferred from the empirical observations, without prior knowledge or understanding, they parametrize the dynamics {\em intrinsically}, without explicit reference to fundamental physical quantities.
['Or Yair', 'Ronen Talmon', 'Ronald R. Coifman', 'Ioannis G. Kevrekidis']
I am writing a research paper on a idea No equations, no parameters, no variables: data, and the reconstruction of normal forms by learning informed observation geometries
[{"from": "human", "value": "I am writing a research paper on a idea No equations, no parameters, no variables: data, and the reconstruction of normal forms by learning informed observation geometries"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The discovery of physical laws consistent with empirical observations lies at the heart of (applied) science and engineering. These laws typically take the form of nonlinear differential equations depending on parameters, dynamical systems theory provides, through the appropriate normal forms, an \"intrinsic\", prototypical characterization of the types of dynamical regimes accessible to a given model. Using an implementation of data-informed geometry learning  directly reconstruct the relevant \"normal forms\": a quantitative mapping from empirical observations to prototypical realizations of the underlying dynamics. Interestingly, the state variables and the parameters of these realizations are inferred from the empirical observations, without prior knowledge or understanding, they parametrize the dynamics {\\em intrinsically}, without explicit reference to fundamental physical quantities."}]