lasdi.latent_dynamics.wsindy

Classes

wSINDy

Module Contents

class lasdi.latent_dynamics.wsindy.wSINDy(dim, nt, dt, config)

Bases: lasdi.latent_dynamics.LatentDynamics

fd_type = ''

fd = None

fd_oper = None

ncoefs

dt

coef_norm_order = 1

MSE

test_func = 'PC-poly'

test_func_width

overlap = 0.8

pq = 5

LS_loss_type = 'weak'

T

calibrate(Z, dt, compute_loss=True, numpy=False)

loop over all train cases, if Z dimension is 3

compute_time_derivative(Z, Dt)

Builds the SINDy dataset, assuming only linear terms in the SINDy dataset. The time derivatives are computed through finite difference.

Z is the encoder output (2D tensor), with shape [time_dim, space_dim] Dt is the size of timestep (assumed to be a uniform scalar)

The output dZdt is a 2D tensor with the same shape of Z.

simulate(coefs, z0, t_grid)

Integrates each system of ODEs corresponding to each training points, given the initial condition Z0 = encoder(U0)

export()

getUniformGrid(T, L, s, p)

generates uniform grid for test functions s is overlap L is test function width

get_test_functions(T, n_t, test_func_width, overlap, pq, test_func='PC-poly', H=30)

H: number of test functions compactly supported on time interval [0,T], assumes equally spaces n_t: number of time points, assumes equally spaced

returns: Phis: dim (H, n_t), each of H test functions evaluated at n_t time points

dPhis: dim (H, n_t), each of H test function time derivatives evaluated at n_t time points

compute_Gk_bk(n_s, Phi, dPhi, Theta, U)

n_s: reduced dim Phi: dimension (H,n_T) dPhi: dimension (H,n_T) Theta: dimension (n_T, J)

Gk = I_{n_s} otimes Phi Theta : dimension (H*n_s,J*n_s) bk = -vec(dPhi*U): dimension (H*n_s)