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In information theory, the cross-entropy between two probability distributions and , over the same underlying set of events, measures the average number of bits needed to identify an event drawn from the set when the coding scheme used for the set is optimized for an estimated probability distribution , rather than the true distribution .
A higher temperature results in a more uniform output distribution (i.e. with higher entropy; it is "more random"), while a lower temperature results in a sharper output distribution, with one value dominating. In some fields, the base is fixed, corresponding to a fixed scale, [d] while in others the parameter β (or T) is varied.
Entropy (thermodynamics) Cross entropy – is a measure of the average number of bits needed to identify an event from a set of possibilities between two probability distributions; Entropy (arrow of time) Entropy encoding – a coding scheme that assigns codes to symbols so as to match code lengths with the probabilities of the symbols. Entropy ...
The torch package also simplifies object-oriented programming and serialization by providing various convenience functions which are used throughout its packages. The torch.class(classname, parentclass) function can be used to create object factories ().
For a dynamical system with evolution equation ˙ = in an n–dimensional phase space, the spectrum of Lyapunov exponents {,, …,}, in general, depends on the starting point . However, we will usually be interested in the attractor (or attractors) of a dynamical system, and there will normally be one set of exponents associated with each ...
Transfer entropy is a non-parametric statistic measuring the amount of directed (time-asymmetric) transfer of information between two random processes. [ 1 ] [ 2 ] [ 3 ] Transfer entropy from a process X to another process Y is the amount of uncertainty reduced in future values of Y by knowing the past values of X given past values of Y .
The joint information is equal to the mutual information plus the sum of all the marginal information (negative of the marginal entropies) for each particle coordinate. Boltzmann's assumption amounts to ignoring the mutual information in the calculation of entropy, which yields the thermodynamic entropy (divided by the Boltzmann constant).
Physics-informed neural networks for solving Navier–Stokes equations. Physics-informed neural networks (PINNs), [1] also referred to as Theory-Trained Neural Networks (TTNs), [2] are a type of universal function approximators that can embed the knowledge of any physical laws that govern a given data-set in the learning process, and can be described by partial differential equations (PDEs).