Calculated Hessian for the elastic example. It gives zero values

[ADharaUTEXAS123007]

I calculated the full hessian (using the method : https://ausargeo.com/deepwave/example_hessian) for the model in elastic FWI example (https://ausargeo.com/deepwave/example_elastic). got zero values between vp and vs. Attaching plot of the hessian.

Here is the code snippet
def wrap(vp,vs,rho):
out = deepwave.elastic(
*deepwave.common.vpvsrho_to_lambmubuoyancy(vp, vs, rho),
dx, dt,
source_amplitudes_y=source_amplitudes,
source_locations_y=source_locations,
receiver_locations_y=receiver_locations,
pml_freq=freq,
)[-2]
return loss_fn(out, observed_data)

hess = torch.autograd.functional.hessian(wrap, (vp, vs, rho))

[ADharaUTEXAS123007]

Here is the complete code

ny = 100
nx = 100
dx = 4.0

vp_background = torch.ones(ny, nx, device=device) * 1500
vs_background = torch.ones(ny, nx, device=device) * 1000
rho_background = torch.ones(ny, nx, device=device) * 2200

vp_true = vp_background.clone()
vp_true[10:20, 30:40] = 1600
vs_true = vs_background.clone()
vs_true[10:20, 45:55] = 1100
rho_true = rho_background.clone()
rho_true[10:20, 60:70] = 2300

n_shots = 8

n_sources_per_shot = 1
d_source = 12
first_source = 8
source_depth = 2

n_receivers_per_shot = nx-1
d_receiver = 1
first_receiver = 0
receiver_depth = 2

freq = 15
nt = 200
dt = 0.004
peak_time = 1.5 / freq

source_locations

source_locations = torch.zeros(n_shots, n_sources_per_shot, 2,
dtype=torch.long, device=device)
source_locations[..., 0] = source_depth
source_locations[:, 0, 1] = (torch.arange(n_shots) * d_source +
first_source)

receiver_locations

receiver_locations = torch.zeros(n_shots, n_receivers_per_shot, 2,
dtype=torch.long, device=device)
receiver_locations[..., 0] = receiver_depth
receiver_locations[:, :, 1] = (
(torch.arange(n_receivers_per_shot) * d_receiver +
first_receiver)
.repeat(n_shots, 1)
)

source_amplitudes

source_amplitudes = (
(deepwave.wavelets.ricker(freq, nt, dt, peak_time))
.repeat(n_shots, n_sources_per_shot, 1).to(device)
)

def wrap(vp,vs,rho):
out = deepwave.elastic(
*deepwave.common.vpvsrho_to_lambmubuoyancy(vp, vs, rho),
dx, dt,
source_amplitudes_y=source_amplitudes,
source_locations_y=source_locations,
receiver_locations_y=receiver_locations,
pml_freq=freq,
)[-2]
return loss_fn(out, observed_data)

hess = torch.autograd.functional.hessian(wrap, (vp, vs, rho))

[ar4]

Hello, and thank you for your question and full code. I am glad to hear that you are interested in the new Hessian feature. Unfortunately, however, double backpropagation (which is needed to calculate the Hessian) is currently only supported for the scalar propagator. I will try to clarify this in the documentation. I am sorry that it was not previously sufficiently clear, causing you to waste time on this.