Computation, Optimization, and Machine Learning in Seismology provides students with a detailed understanding of seismic wave theory, optimization theory, and how to use machine learning to interpret seismic dat
Final swarm positions and objective function values, returned as a structure with these fields: X— Positions of the final swarm, returned as a matrix. Each row of the matrix represents one point. Fval— Objective function values of the final swarm. For each i, an index of a member of th...
The force field proportionally studies the estimation of potential energy and computation of forces acting on the atom, of the system under assessment. In this work, the polymeric dendritic molecules were parameterized employing the UFF i.e. Universal Forcefield. This forcefield is a broad spectra...
where T is a matrix of variables, f(T) is the nonlinear scalar function of T (given by Equation (10)), geq(T) is the vector of equality constraints, and gineq(T) is the vector of inequality constraints. In the general framework, both geq(T) and gineq(T) will be considered nonlin...
It consists in diagonalizing the autocorrelation matrix of the characters to keep only the desired number of eigen vectors corresponding to the larger eigen values. Note that the process is a mere rotation of the decision space followed by truncature and that separation has to be further completed...
Each diagonal component of the diagonal matrix Jv equals 0, –1, or 1. If all the components of l and u are finite, Jv = diag(sign(g)). At a point where gi = 0, vi might not be differentiable. Jvii=0 is defined at such a point. Nondifferentiability of this type is not a ...
Here, the computational complexity of this optimization is validated and examined by computing the cost of operations. The position update is estimated based on sorting the global matrix, as shown in Fig. 2, where the sorting of computational cost determines the best and worst states. The key ...
This method is in parts similar to SMA-ES, but instead of keeping track of per-parameter sigmas, covariance matrix, and using Gaussian sampling, SpherOpt simply selects random points on a hyper-spheroid (with a bit of added jitter at lower dimensions), which eventually converges to a point...
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Moreover, as another application of the derived formulas, we establish necessary and sufficient conditions for the solvability to the system of matrix equations (0.2)A1X=C1,A2XB2=C2,B3X+(B3X)∗=A3and provide an expression of the general solution to (0.2) when it is solvable. The findings...