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Teamplay
Published in Volker Knecht, AI for Physics, 2023
Gravity is described by general relativity. The other three fundamental forces (the electromagnetic plus the strong and weak nuclear ones) are explained by the SM of particle physics. The SM and general relativity are fundamental as in principle the whole of established physics can be derived from them. However, these two pillars of physical science are not compatible with each other. This is because the SM is based on quantum mechanics which is incompatible with general relativity. What is missing is a quantum description of gravity. Quantum gravity is the Holy Grail of modern theoretical physics and (next to consciousness31) one of the two hardest problems in science today.32 A promising candidate for an elegant theory of everything is string theory. Here the point-like particles of the SM (considered as coarse-grained descriptions) are replaced by one-dimensional objects called strings as the most fundamental objects (see Figure 2.2A).33 Their vibration modes determine the properties of the elementary particles of the SM. Space is predicted to exhibit six extra dimensions compactified and thus not visible on a macroscopic scale. The detailed form of compactification determines the vibration modes of the strings. However, the set of possible choices of parameters governing the compactifications (denoted as string landscape, see Figure 2.2B) is incredibly large. Hence, string theory involves data considered the most comprehensive in science,34 just crying out for the use of ML methods. How ML is used to study the string landscape is described in Chapter 8.
Tetrahedral Dual Coordinate System: The Static and Dynamic Algebraic Model
Published in Mihai V. Putz, New Frontiers in Nanochemistry, 2020
String Theory represents the existence of extra dimensions, such as six and ten dimensions, without a primary coordinate system to mathematically describe the quantum properties of physics. The DCS includes the dimensions of atomic space with three and six dimensions. There are also four axes of rotational symmetry which explain the unique properties of the quasicrystals which have fifteen extra dimensions in the icosahedron and pentagonal dodecahedron. Examples of 6D engineering and architecture are observed in the tetrahedron and octahedron truss system in the Paris Louvre and the Leonardo Da Vinci Airport Rome.
Data-level transfer learning for degradation modeling and prognosis
Published in Journal of Quality Technology, 2023
Amirhossein Fallahdizcheh, Chao Wang
First, the nontransfer reports similar results as those in the consistent scenario, that is, Figure 3. This is a straightforward result because the nontransfer framework only uses information from the target process and the dimension change in the source process will not affect its performance. The same observation applies to our proposed method, which also performs similarly as those in Figure 3. The reason is also similar because our method marginalizes the extra dimension in the source process, which neglects the effects of extra dimensions in source processes. Second, the MGP performs significantly worse than that in Figure 3, even when 60% of data is available. This is a direct result of the different dimensions in source and target processes. The higher dimension source process has a different length-scale from that in the target process, and the prognosis performance of the MGP-based transfer learning is negatively affected. This situation is visualized in Figure 1, where the quadratic process 2 is ‘forced’ to help the linear process 1 in terms of the learning of the length-scale. This would only make the prediction of process 1 shift upward and report earlier failure time than it should be.
Effect of progress variable definition on the mass burning rate of premixed laminar flames predicted by the Flamelet Generated Manifold method
Published in Combustion Theory and Modelling, 2021
Harshit Gupta, Omkejan J. Teerling, Jeroen A. van Oijen
The dimension of the manifold can be increased to improve the accuracy of the reduced model. By increasing the dimension of the manifold, the component of the vector pointing out of it is reduced, as well as the associated modelling error. Extending the manifold to higher dimensions is, however, not always straightforward. While it is common to add dimensions to account for variations in chemically conserved quantities such as enthalpy and element mass fractions [10,17,23], this is certainly not the case for extra dimensions to include additional reaction time scales. Additional dimensions to account for changes in the conserved variables as discussed in detail by van Oijen et al. [10] are not needed in the present work, because these quantities do not vary in the flames that are studied here. In general, adding more dimensions will enhance the accuracy, but one cannot guarantee that the state remains inside the manifold. Therefore, the projection should not be regarded as a replacement for adding more dimensions. The projection makes FGM more consistent and makes the results independent of the choice of progress variable.
Multi-sensor prognostics modeling for applications with highly incomplete signals
Published in IISE Transactions, 2021
Xiaolei Fang, Hao Yan, Nagi Gebraeel, Kamran Paynabar
Many incremental SVD algorithms have been developed in the literature (Bunch and Nielsen, 1978; Brand, 2002; Balzano and Wright, 2013). However, these algorithms are designed for either full-rank or low-rank matrices. A matrix is full-rank if its rank equals the number of its rows or columns, whichever is smaller. That is, a matrix with m rows and n columns is full-rank if its rank or equivalently, where σk is the singular value of the matrix and represents the number of nonzero singular values. For a full rank matrix, Bunch and Nielsen(1978) developed an incremental SVD algorithm, which computes the SVD of the matrix by adding one column at a time. The singular vector matrices and singular value matrix are updated and their size grows as columns are added. Balzano and Wright (2013) pointed out that the algorithm in Bunch and Nielsen (1978) can be modified such that it works for low-rank matrices (i.e., matrices whose rank or equivalently, ). This can be achieved by avoiding adding extra dimensions to the singular vector matrices and singular value matrix if the newly added column already lies in the space spanned by the singular vectors.