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although powerful in applications requiring dimensionality reduction, autoencoders lack physical interpretability and introduce spurious correlations, not necessarily guaranteeing a discrete separation of temporal scales. To overcome these limitations, our approach relies on a class of physics-based reduced-ord...
Working in synergy with traditional numerical methods or other machine learning methods, the state-of-the-art PINN-based methods can be extended to address the problems of fractional differential equations, stochastic differential equations, and integro-differential equations (IDEs). In [44], a new ...
Figure3ashows the percentage of CMs versus cluster size. Each colored line represents a class of geometry depicted in Fig.3b–g. The CM percentages increase withNand become dominant for a large value ofN. The red (blue) lines correspond to an incident non-standing (standing) wave, which does...
This approach is not based on numerical wave functions. Instead, the dipole radial matrix elements take on the form (2)RnLSJ,n′L′S′J′=32n∗c21−ℓcn∗c21∕2∑p=0∞γpgpΔn∗,with S=S′=0 or 1. In this equation n∗ is the reduced principal quantum number (n∗≡n...
One class of such phenomena relate to the fact that in our models the dimension of space is dynamic, and does not just have a fixed integer value. Our expectation is that in the very early universe, the dimension of space was effectively infinite, gradually “cooling” to approximately 3. ...
Properties of Fluids on Vedantu, will help you to get a clear idea of all the important concepts and theories covered in this chapter. Our subject matter experts have listed below the main topics of Chapter - 9 Mechanical Properties of Fluids as per the syllabus of the upcoming CBSE Cl...
In this section, we focus on non-interferometric tests of quantum mechanics. Differently from the interferometric ones, this class of tests does not rely on the availability of quantum superpositions but is based on side-effects of modifications of quantum mechanics. Consequently, they can be perfor...
fluctuation maps lead to the idea ofequivalence classes, where materials with very different sets of hopping parameters nevertheless display topologically equivalent fluctuation maps. In particular, we find that LSCO lies in a different equivalence class from other cuprates. From each equivalence class,...