We propose a unified data-driven reduced order model (ROM) that bridges the performance gap between linear and nonlinear manifold approaches. Deep learning ROM (DL-ROM) using deep-convolutional autoencoders (DC–AE) has been shown to capture nonlinear solution manifolds but fails to perform adequa...
When comparing differential expression we used a chi-squared test to assess relationships between differentially expressed genes between studies. In silico analysis of TFBS. TFBS were detected using the Regulatory Genomics Toolbox (regen.googlecode.com). A region 1 kilobases (kb) upstream of the ...
where the reduced velocity and reduced pressure modes are denoted by\({\phi }_i({\varvec{x}})\)and\({\chi _i}({\varvec{x}})\), respectively. The reduced modes of both variables depend only on the spatial variables. The coefficients\(a_i(t;{\varvec{\mu }})\)and\(b_i (t...
Performance for each σ was evaluated using the mean squared error (MSE) of predictions from 1000 cross-validation repetitions. σ was chosen so as to minimize the MSE obtained by the linear model, yielding σ = 0.8 (Supplementary Fig. 1). To test whether a linear model with repulsive...
To close the system and solve for the unknown generalized coordinates, u ^ st 𝒖̂st, the LSPG method takes the squared norm of the residual vector function and minimize it: u ^ st = argmin v ^ ∈ R n s n t 1 2 r ˜ st ( v ^ ; μ ) 2 2 . 𝒖̂st=argmin𝒗...
[16,17,18]. This test combines skew and kurtosis to produce a test of normality. The function returns two values: the first is a statistic value based on the skew test squared plus the kurtosis test squared and the second is a 2-sided chi-squared probability for the hypothesis test, ...