Merge pull request #79 from kc-ml2/DEV/main

Dev/main

Author: yonghakim

QA/1D_grating_in_2D_pattern.py

@@ -0,0 +1,87 @@
+# This demo shows a case with 1D grating and TM polarization.
+# If phi is set to 'None', this will use 1D TETM formulation (without azimuthal rotation, phi == 0)
+# But if phi is set to '0', then the simulation will be taken for 1D conical or 2D case which is general but slower.
+
+import numpy as np
+from time import time
+
+from meent import call_mee
+
+
+def compare():
+    backend = 0
+    pol = 1  # 0: TE, 1: TM
+
+    n_top = 1  # n_incidence
+    n_bot = 1  # n_transmission
+
+    theta = 1E-10  # angle of incidence in radian
+
+    wavelength = 300  # wavelength
+    thickness = [460, 22]
+    period = [700, 700]
+    fto = [100, 0]
+
+    ucell_1d = np.array([
+        [
+            [1, 1, 1, 3.48, 3.48, 3.48, 1, 1, 1, 1],
+        ],
+        [
+            [1, 1, 1, 3.48, 3.48, 3.48, 1, 1, 1, 1],
+        ],
+    ])
+    ucell_2d = np.array([
+        [
+            [1, 1, 1, 3.48, 3.48, 3.48, 1, 1, 1, 1],
+            [1, 1, 1, 3.48, 3.48, 3.48, 1, 1, 1, 1],
+        ],
+        [
+            [1, 1, 1, 3.48, 3.48, 3.48, 1, 1, 1, 1],
+            [1, 1, 1, 3.48, 3.48, 3.48, 1, 1, 1, 1],
+        ],
+    ])
+
+    mee = call_mee(backend=backend, pol=pol, n_top=n_top, n_bot=n_bot, theta=theta, fto=fto,
+                   wavelength=wavelength, period=period, thickness=thickness)
+
+    # 1D
+    mee.phi = None  # which is default
+    mee.ucell = ucell_1d
+
+    t0_1d = time()
+    res = mee.conv_solve().res
+    t1_1d = time()
+    de_ri1, de_ti1 = res.de_ri, res.de_ti
+    print('1D (de_ri, de_ti): ', de_ri1, de_ti1)
+
+    # 1D conical
+    mee.phi = 0
+    t0_1dc = time()
+    res = mee.conv_solve().res
+    t1_1dc = time()
+    de_ri1c, de_ti1c = res.de_ri, res.de_ti
+    print('1Dc (de_ri, de_ti): ', de_ri1c, de_ti1c)
+
+    # 2D
+    mee.phi = 0
+    t0_2d = time()
+    mee.ucell = ucell_2d
+    res = mee.conv_solve().res
+    t1_2d = time()
+    de_ri2, de_ti2 = res.de_ri, res.de_ti
+    print('2D (de_ri, de_ti): ', de_ri2, de_ti2)
+
+    print('time for 1D  formulation: ', t1_1d-t0_1d, 's')
+    print('time for 1Dc formulation: ', t1_1dc-t0_1dc, 's')
+    print('time for 2D  formulation: ', t1_2d-t0_2d, 's')
+    print('Simulation Difference between 1D and 1Dc formulation: ',
+          np.linalg.norm(de_ri1 - de_ri1c), np.linalg.norm(de_ti1 - de_ti1c))
+    print('Simulation Difference between 1D and 2D formulation: ',
+          np.linalg.norm(de_ri1 - de_ri2), np.linalg.norm(de_ti1 - de_ti2))
+
+    print('Simulation Difference between 1Dc and 2D formulation: ',
+          np.linalg.norm(de_ri1c - de_ri2), np.linalg.norm(de_ti1c - de_ti2))
+
+
+if __name__ == '__main__':
+    compare()

QA/1d_pattern_in_1dc_and_2d.py

@@ -8,7 +8,7 @@
 import torch
 
 import meent
-from meent.on_torch.optimizer.loss import LossDeflector
+
 
 type_complex = 0
 device = 0
@@ -48,7 +48,19 @@
 
 pois = ['ucell', 'thickness']  # Parameter Of Interests
 forward = jmee.conv_solve
-loss_fn = LossDeflector(x_order=0, y_order=0)
+
+
+class Loss:
+    def __call__(self, meent_result, *args, **kwargs):
+        res_psi, res_te, res_ti = meent_result.res, meent_result.res_te_inc, meent_result.res_tm_inc
+        de_ti = res_psi.de_ti
+        center = [a // 2 for a in de_ti.shape]
+        res = de_ti[center[0], center[1]+1]
+
+        return res
+
+
+loss_fn = Loss()
 
 # case 1: Gradient
 grad_j = jmee.grad(pois, forward, loss_fn)
@@ -58,7 +70,7 @@
 print('thickness gradient:')
 print(grad_j['thickness'])
 
-optimizer = optax.sgd(learning_rate=1e-2)
+optimizer = optax.sgd(learning_rate=1E2)
 t0 = time.time()
 res_j = jmee.fit(pois, forward, loss_fn, optimizer, iteration=iteration)
 print('Time JAX', time.time() - t0)
@@ -74,7 +86,6 @@
                       thickness=thickness, type_complex=type_complex, device=device)
 
 forward = tmee.conv_solve
-loss_fn = LossDeflector(x_order=0)  # predefined in meent
 
 grad_t = tmee.grad(pois, forward, loss_fn)
 print('ucell gradient:')
@@ -83,7 +94,7 @@
 print(grad_t['thickness'])
 
 opt_torch = torch.optim.SGD
-opt_options = {'lr': 1E-2}
+opt_options = {'lr': 1E2}
 
 t0 = time.time()
 res_t = tmee.fit(pois, forward, loss_fn, opt_torch, opt_options, iteration=iteration)
@@ -102,6 +113,6 @@
 
 print('End')
 
-# Note that the gradient in JAX is conjugated.
+# Note that the gradient in JAX is conjugation of PyTorch's.
 # https://github.com/google/jax/issues/4891
 # https://pytorch.org/docs/stable/notes/autograd.html#autograd-for-complex-numbers

QA/autograd_complex_ucell.py renamed to QA/autodiff_raster1.py

@@ -0,0 +1,172 @@
+import jax
+import torch
+
+import jax.numpy as jnp
+import numpy as np
+
+from time import time
+
+from meent import call_mee
+
+
+def load_setting():
+    pol = 1  # 0: TE, 1: TM
+
+    n_top = 1  # n_incidence
+    n_bot = 1  # n_transmission
+
+    theta = 0 * np.pi / 180
+    phi = 0 * np.pi / 180
+
+    wavelength = 900
+
+    fto = [5, 5]
+
+    period = [1000, 1000]
+    thickness = [1120]
+
+    ucell = np.array([[[2.58941352 + 0.47745679j, 4.17771602 + 0.88991205j,
+                        2.04255624 + 2.23670125j, 2.50478974 + 2.05242759j,
+                        3.32747593 + 2.3854387j],
+                       [2.80118605 + 0.53053715j, 4.46498861 + 0.10812571j,
+                        3.99377545 + 1.0441131j, 3.10728537 + 0.6637353j,
+                        4.74697849 + 0.62841253j],
+                       [3.80944424 + 2.25899274j, 3.70371553 + 1.32586402j,
+                        3.8011133 + 1.49939415j, 3.14797238 + 2.91158289j,
+                        4.3085404 + 2.44344691j],
+                       [2.22510179 + 2.86017146j, 2.36613053 + 2.82270351j,
+                        4.5087168 + 0.2035904j, 3.15559949 + 2.55311298j,
+                        4.29394604 + 0.98362617j],
+                       [3.31324163 + 2.77590131j, 2.11744834 + 1.65894674j,
+                        3.59347907 + 1.28895345j, 3.85713467 + 1.90714056j,
+                        2.93805426 + 2.63385392j]]])
+    ucell = ucell.real
+
+    type_complex = 0
+    device = 0
+
+    setting = {'pol': pol, 'n_top': n_top, 'n_bot': n_bot, 'theta': theta, 'phi': phi, 'fto': fto,
+               'wavelength': wavelength, 'period': period, 'ucell': ucell, 'thickness': thickness, 'device': device,
+               'type_complex': type_complex}
+
+    return setting
+
+
+def optimize_jax(setting):
+    ucell = setting['ucell']
+
+    mee = call_mee(backend=1, **setting)
+
+    @jax.jit
+    def grad_loss(ucell):
+        mee.ucell = ucell
+        res = mee.conv_solve().res
+        de_ri, de_ti = res.de_ri, res.de_ti
+
+        loss = de_ti[de_ti.shape[0] // 2, de_ti.shape[1] // 2]
+
+        return loss
+
+    def grad_numerical(ucell, delta):
+        grad_arr = jnp.zeros(ucell.shape, dtype=ucell.dtype)
+
+        @jax.jit
+        def compute(ucell):
+            mee.ucell = ucell
+            result = mee.conv_solve()
+            de_ti = result.res.de_ti
+            loss = de_ti[de_ti.shape[0] // 2, de_ti.shape[1] // 2]
+
+            return loss
+
+        for layer in range(ucell.shape[0]):
+            for r in range(ucell.shape[1]):
+                for c in range(ucell.shape[2]):
+                    ucell_delta_m = ucell.copy()
+                    ucell_delta_m[layer, r, c] -= delta
+                    mee.ucell = ucell_delta_m
+                    de_ti_delta_m = compute(ucell_delta_m, )
+
+                    ucell_delta_p = ucell.copy()
+                    ucell_delta_p[layer, r, c] += delta
+                    mee.ucell = ucell_delta_p
+                    de_ti_delta_p = compute(ucell_delta_p, )
+
+                    grad_numeric = (de_ti_delta_p - de_ti_delta_m) / (2 * delta)
+                    grad_arr = grad_arr.at[layer, r, c].set(grad_numeric)
+
+        return grad_arr
+
+    jax.grad(grad_loss)(ucell)  # Dry run for jit compilation. This is to make time comparison fair.
+    t0 = time()
+    grad_ad = jax.grad(grad_loss)(ucell)
+    t_ad = time() - t0
+    print('JAX grad_ad:\n', grad_ad)
+    t0 = time()
+    grad_nume = grad_numerical(ucell, 1E-6)
+    t_nume = time() - t0
+    print('JAX grad_numeric:\n', grad_nume)
+    print('JAX norm of difference: ', jnp.linalg.norm(grad_nume - grad_ad) / grad_nume.size)
+    return t_ad, t_nume
+
+
+def optimize_torch(setting):
+    mee = call_mee(backend=2, **setting)
+
+    mee.ucell.requires_grad = True
+
+    t0 = time()
+    res = mee.conv_solve().res
+    de_ri, de_ti = res.de_ri, res.de_ti
+
+    loss = de_ti[de_ti.shape[0] // 2, de_ti.shape[1] // 2]
+
+    loss.backward()
+    grad_ad = mee.ucell.grad
+    t_ad = time() - t0
+
+    def grad_numerical(ucell, delta):
+        ucell.requires_grad = False
+        grad_arr = torch.zeros(ucell.shape, dtype=ucell.dtype)
+
+        for layer in range(ucell.shape[0]):
+            for r in range(ucell.shape[1]):
+                for c in range(ucell.shape[2]):
+                    ucell_delta_m = ucell.clone().detach()
+                    ucell_delta_m[layer, r, c] -= delta
+                    mee.ucell = ucell_delta_m
+                    res = mee.conv_solve().res
+                    de_ri_delta_m, de_ti_delta_m = res.de_ri, res.de_ti
+
+                    ucell_delta_p = ucell.clone().detach()
+                    ucell_delta_p[layer, r, c] += delta
+                    mee.ucell = ucell_delta_p
+                    res = mee.conv_solve().res
+                    de_ri_delta_p, de_ti_delta_p = res.de_ri, res.de_ti
+
+                    cy, cx = np.array(de_ti_delta_p.shape) // 2
+                    grad_numeric = (de_ti_delta_p[cy, cx] - de_ti_delta_m[cy, cx]) / (2 * delta)
+                    grad_arr[layer, r, c] = grad_numeric
+
+        return grad_arr
+
+    t0 = time()
+    grad_nume = grad_numerical(mee.ucell, 1E-6)
+    t_nume = time() - t0
+
+    print('Torch grad_ad:\n', grad_ad)
+    print('Torch grad_numeric:\n', grad_nume)
+    print('torch.norm: ', torch.linalg.norm(grad_nume - grad_ad) / grad_nume.numel())
+    return t_ad, t_nume
+
+
+if __name__ == '__main__':
+    setting = load_setting()
+
+    print('JaxMeent')
+    j_t_ad, j_t_nume = optimize_jax(setting)
+    print('TorchMeent')
+    t_t_ad, t_t_nume = optimize_torch(setting)
+
+    print(f'Time for Backprop, JAX, AD: {j_t_ad} s, Numerical: {j_t_nume} s')
+    print(f'Time for Backprop, Torch, AD: {t_t_ad} s, Numerical: {t_t_nume} s')