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mpm_solver_bridge.py
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mpm_solver_bridge.py
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import taichi as ti
import numpy as np
import engine.utils as utils
import matplotlib.pyplot as plt
ti.reset()
real = ti.f32
ti.init(arch=ti.cuda, default_fp=real, device_memory_GB=12)
# init parameters
size = 1
dim = 2
N = 60 # reduce to 30 if run out of GPU memory
n_particles = N * N
n_grid = 20
dx = 1 / n_grid
inv_dx = 1 / dx
dt_scale = 1e0
# dt = 2e-2 * dx / size * dt_scale
dt = 3e-4
p_mass = 1
p_vol = 1
E = ti.field(dtype=real, shape=(), needs_grad=True)
nu = 0.2
mu = ti.field(dtype=real, shape=(), needs_grad=True)
la = ti.field(dtype=real, shape=(), needs_grad=True)
E[None] = 1000
# E = 100
# mu = E
# la = E
max_steps = 1024
steps = max_steps
gravity = 1
target = [0.3, 0.6]
scalar = lambda: ti.field(dtype=real)
vec = lambda: ti.Vector.field(dim, dtype=real)
mat = lambda: ti.Matrix.field(dim, dim, dtype=real)
x = ti.Vector.field(dim,
dtype=real,
shape=(max_steps, n_particles),
needs_grad=True)
x_avg = ti.Vector.field(dim, dtype=real, shape=(), needs_grad=True)
v = ti.Vector.field(dim,
dtype=real,
shape=(max_steps, n_particles),
needs_grad=True)
grid_v_in = ti.Vector.field(dim,
dtype=real,
shape=(max_steps, n_grid, n_grid),
needs_grad=True)
grid_v_out = ti.Vector.field(dim,
dtype=real,
shape=(max_steps, n_grid, n_grid),
needs_grad=True)
f_ext = ti.Vector.field(dim,
dtype=real,
shape=(max_steps, n_grid, n_grid),
needs_grad=True)
grid_m_in = ti.field(dtype=real,
shape=(max_steps, n_grid, n_grid),
needs_grad=True)
C = ti.Matrix.field(dim,
dim,
dtype=real,
shape=(max_steps, n_particles),
needs_grad=True)
F = ti.Matrix.field(dim,
dim,
dtype=real,
shape=(max_steps, n_particles),
needs_grad=True)
strain = ti.Matrix.field(dim,
dim,
dtype=real,
shape=(max_steps, n_particles),
needs_grad=True)
strain2 = ti.Vector.field(3,
dtype=real,
shape=(max_steps + 1, n_particles),
needs_grad=True)
init_v = ti.Vector.field(dim, dtype=real, shape=(), needs_grad=True)
loss = ti.field(dtype=real, shape=(), needs_grad=True)
@ti.kernel
def set_v():
for i in range(n_particles):
v[0, i] = init_v[None]
@ti.kernel
def p2g(f: ti.i32):
for p in range(n_particles):
base = ti.cast(x[f, p] * inv_dx - 0.5, ti.i32)
fx = x[f, p] * inv_dx - ti.cast(base, ti.i32)
w = [0.5 * (1.5 - fx)**2, 0.75 - (fx - 1)**2, 0.5 * (fx - 0.5)**2]
new_F = (ti.Matrix.diag(dim=2, val=1) + dt * C[f, p]) @ F[f, p]
F[f + 1, p] = new_F
J = (new_F).determinant()
r, s = ti.polar_decompose(new_F)
cauchy = 2 * E[None] / (2 * (1 + nu)) * (new_F - r) @ new_F.transpose() + \
ti.Matrix.diag(2, E[None] * nu / ((1 + nu) * (1 - 2 * nu)) * (J - 1) * J)
# cauchy = 2 * mu * (new_F - r) @ new_F.transpose() + \
# ti.Matrix.diag(2, la * (J - 1) * J)
stress = -(dt * p_vol * 4 * inv_dx * inv_dx) * cauchy
affine = stress + p_mass * C[f, p]
strain[f, p] += 0.5 * (new_F.transpose() @ new_F - ti.math.eye(dim))
for i in ti.static(range(3)):
for j in ti.static(range(3)):
offset = ti.Vector([i, j])
dpos = (ti.cast(ti.Vector([i, j]), real) - fx) * dx
weight = w[i][0] * w[j][1]
grid_v_in[f, base + offset] += weight * (p_mass * v[f, p] +
affine @ dpos)
grid_m_in[f, base + offset] += weight * p_mass
bound = 2
@ti.kernel
def grid_op(f: ti.i32):
for i, j in ti.ndrange(n_grid, n_grid):
inv_m = 1 / (grid_m_in[f, i, j] + 1e-10)
v_out = inv_m * grid_v_in[f, i, j] + dt * f_ext[f, i, j]
v_out[1] -= dt * gravity
if i < bound and v_out[0] < 0:
v_out[0] = 0
if i > n_grid - bound and v_out[0] > 0:
v_out[0] = 0
if j < bound and v_out[1] < 0:
v_out[1] = 0
if j > n_grid - bound and v_out[1] > 0:
v_out[1] = 0
grid_v_out[f, i, j] = v_out
@ti.kernel
def g2p(f: ti.i32):
# ti.loop_config(serialize=True)
for p in range(n_particles):
base = ti.cast(x[f, p] * inv_dx - 0.5, ti.i32)
fx = x[f, p] * inv_dx - ti.cast(base, real)
w = [0.5 * (1.5 - fx)**2, 0.75 - (fx - 1.0)**2, 0.5 * (fx - 0.5)**2]
new_v = ti.Vector([0.0, 0.0])
new_C = ti.Matrix([[0.0, 0.0], [0.0, 0.0]])
for i in ti.static(range(3)):
for j in ti.static(range(3)):
dpos = ti.cast(ti.Vector([i, j]), real) - fx
g_v = grid_v_out[f, base[0] + i, base[1] + j]
weight = w[i][0] * w[j][1]
new_v += weight * g_v
new_C += 4 * weight * g_v.outer_product(dpos) * inv_dx
# grad = ti.Matrix([[0.0, 0.0], [0.0, 0.0], [0.0, 0.0], [0.0, 0.0]])
# vi = ti.Matrix([[0.0, 0.0], [0.0, 0.0], [0.0, 0.0], [0.0, 0.0]])
grad = ti.Matrix([[0.0, 0.0], [0.0, 0.0], [0.0, 0.0],
[0.0, 0.0], [0.0, 0.0], [0.0, 0.0],
[0.0, 0.0], [0.0, 0.0], [0.0, 0.0]])
vi = ti.Matrix([[0.0, 0.0], [0.0, 0.0], [0.0, 0.0],
[0.0, 0.0], [0.0, 0.0], [0.0, 0.0],
[0.0, 0.0], [0.0, 0.0], [0.0, 0.0]])
strain_rate = ti.Vector([0.0, 0.0, 0.0])
# 3----2
# | |
# 0----1
# # ident base node
# base2 = ti.cast(x[f, p] * inv_dx, ti.i32)
# # calc local coords
# local = (x[f, p] - base2 * dx) / dx
# # calc dn_dx
# grad[0, 0] = -0.25 * (1 - fx[1])
# grad[1, 0] = 0.25 * (1 - fx[1])
# grad[2, 0] = 0.25 * (1 + fx[1])
# grad[3, 0] = -0.25 * (1 + fx[1])
# grad[0, 1] = -0.25 * (1 - fx[0])
# grad[1, 1] = -0.25 * (1 + fx[0])
# grad[2, 1] = 0.25 * (1 + fx[0])
# grad[3, 1] = 0.25 * (1 - fx[0])
# # get nodal velocities
# vi[0, 0] = grid_v_out[f, base2[0], base2[1]][0]
# vi[1, 0] = grid_v_out[f, base2[0] + 1, base2[1]][0]
# vi[2, 0] = grid_v_out[f, base2[0] + 1, base2[1] + 1][0]
# vi[3, 0] = grid_v_out[f, base2[0], base2[1] + 1][0]
# vi[0, 1] = grid_v_out[f, base2[0], base2[1]][1]
# vi[1, 1] = grid_v_out[f, base2[0] + 1, base2[1]][1]
# vi[2, 1] = grid_v_out[f, base2[0] + 1, base2[1] + 1][1]
# vi[3, 1] = grid_v_out[f, base2[0], base2[1] + 1][1]
fx = fx * dx
grad[0, 0] = 0.25 * fx[1] * (fx[1] - 1.) * (2 * fx[0] - 1.)
grad[1, 0] = 0.25 * fx[1] * (fx[1] - 1.) * (2 * fx[0] + 1.)
grad[2, 0] = 0.25 * fx[1] * (fx[1] + 1.) * (2 * fx[0] + 1.)
grad[3, 0] = 0.25 * fx[1] * (fx[1] + 1.) * (2 * fx[0] - 1.)
grad[4, 0] = -fx[0] * fx[1] * (fx[1] - 1.)
grad[5, 0] = -0.5 * (2. * fx[0] + 1.) * ((fx[1] * fx[1]) - 1.)
grad[6, 0] = -fx[0] * fx[1] * (fx[1] + 1.)
grad[7, 0] = -0.5 * (2. * fx[0] - 1.) * ((fx[1] * fx[1]) - 1.)
grad[8, 0] = 2. * fx[0] * ((fx[1] * fx[1]) - 1.)
grad[0, 1] = 0.25 * fx[0] * (fx[0] - 1.) * (2. * fx[1] - 1.)
grad[1, 1] = 0.25 * fx[0] * (fx[0] + 1.) * (2. * fx[1] - 1.)
grad[2, 1] = 0.25 * fx[0] * (fx[0] + 1.) * (2. * fx[1] + 1.)
grad[3, 1] = 0.25 * fx[0] * (fx[0] - 1.) * (2. * fx[1] + 1.)
grad[4, 1] = -0.5 * (2. * fx[1] - 1.) * ((fx[0] * fx[0]) - 1.)
grad[5, 1] = -fx[0] * fx[1] * (fx[0] + 1.)
grad[6, 1] = -0.5 * (2. * fx[1] + 1.) * ((fx[0] * fx[0]) - 1.)
grad[7, 1] = -fx[0] * fx[1] * (fx[0] - 1.)
grad[8, 1] = 2. * fx[1] * ((fx[0] * fx[0]) - 1.)
vi[0, 0] = grid_v_out[f, base[0], base[1]][0]
vi[1, 0] = grid_v_out[f, base[0] + 2, base[1]][0]
vi[2, 0] = grid_v_out[f, base[0] + 2, base[1] + 2][0]
vi[3, 0] = grid_v_out[f, base[0], base[1] + 2][0]
vi[4, 0] = grid_v_out[f, base[0] + 1, base[1]][0]
vi[5, 0] = grid_v_out[f, base[0] + 2, base[1] + 1][0]
vi[6, 0] = grid_v_out[f, base[0] + 1, base[1] + 2][0]
vi[7, 0] = grid_v_out[f, base[0], base[1] + 1][0]
vi[8, 0] = grid_v_out[f, base[0] + 1, base[1] + 1][0]
vi[0, 1] = grid_v_out[f, base[0], base[1]][1]
vi[1, 1] = grid_v_out[f, base[0] + 2, base[1]][1]
vi[2, 1] = grid_v_out[f, base[0] + 2, base[1] + 2][1]
vi[3, 1] = grid_v_out[f, base[0], base[1] + 2][1]
vi[4, 1] = grid_v_out[f, base[0] + 1, base[1]][1]
vi[5, 1] = grid_v_out[f, base[0] + 2, base[1] + 1][1]
vi[6, 1] = grid_v_out[f, base[0] + 1, base[1] + 2][1]
vi[7, 1] = grid_v_out[f, base[0], base[1] + 1][1]
vi[8, 1] = grid_v_out[f, base[0] + 1, base[1] + 1][1]
# calc strain rate
for k in ti.static(range(9)):
strain_rate[0] += grad[k, 0] * vi[k, 0]
strain_rate[1] += grad[k, 1] * vi[k, 1]
strain_rate[2] += grad[k, 0] * vi[k, 1] + grad[k, 1] * vi[k, 0]
# update strain
strain2[f + 1, p] = strain2[f, p] + strain_rate * dt
v[f + 1, p] = new_v
x[f + 1, p] = x[f, p] + dt * v[f + 1, p]
C[f + 1, p] = new_C
@ti.kernel
def compute_x_avg():
for i in range(n_particles):
x_avg[None] += (1 / n_particles) * x[steps - 1, i]
@ti.kernel
def compute_loss():
for i in range(steps - 1):
for j in range(n_particles):
dist = (1 / ((steps - 1) * n_particles)) * \
(target_x[i, j] - x[i, j]) ** 2
loss[None] += 0.5 * (dist[0] + dist[1])
# dist = (1 / ((steps - 1) * n_particles)) * \
# (target_strain[i, j] - strain[i, j]) ** 2
# loss[None] += 0.5 * (dist[0, 0] + dist[1, 1])
# dist = (x_avg[None] - ti.Vector(target))**2
# loss[None] = 0.5 * (dist[0] + dist[1])
def substep(s):
p2g(s)
grid_op(s)
g2p(s)
# @ti.kernel
# def set_E():
# mu[None] = E[None] / (2 * (1 + nu))
# la[None] = E[None] * nu / ((1 + nu) * (1 - 2 * nu))
# print(mu, la)
# @ti.kernel
# def reset_sim():
# strain.fill(0)
# grid_m_in.fill(0)
# grid_v_in.fill(0)
# # for i in range(n_particles):
# # F[0, i] = [[1, 0], [0, 1]]
# for i in range(N):
# for j in range(N):
# x[0, i * N + j] = [(i)/(4*N), (j)/(4*N)]
@ti.kernel
def assign_ext_load():
pass
# for t in range(max_steps):
# for node in node_ids_fext_x:
# f_ext[t, node, node] = [0, f_ext_scale * e[t, node]]
# for t in range(max_steps):
# for i in range(n_grid):
# for j in range(n_grid):
# f_ext[t, 9, j] = [0, -1e2]
# f_ext[t, 17, j] = [0, 1e2]
f_ext_scale = 1
velocity = 4
frequency = 5
node_x_locs = np.arange(0, 1, 1 / n_grid)
time_to_center = node_x_locs / velocity
t_steps = np.arange(max_steps) * dt
t_steps_n = np.array([t_steps - time for time in time_to_center])
t_steps_n = np.stack(t_steps_n, axis=1)
node_ids_fext_x = range(n_grid)
_, _, e, = utils.gausspulse(t_steps_n)
print('assigning external loads')
assign_ext_load()
init_v[None] = [0, 0]
for i in range(n_particles):
F[0, i] = [[1, 0], [0, 1]]
for i in range(N):
for j in range(N):
# x[0, i * N + j] = [(i)/(4*N) + 0.2, (j)/(4*N) + 0.2]
x[0, i * N + j] = [(i)/(N), (j)/(N)]
print('running target sim')
# reset_sim()
set_v()
# set_E()
for s in range(steps):
substep(s)
# print('loading target')
# # target_x = x
# # target_strain = strain
# # target_strain_np = np.load('target_strain_simple.npy')
# target_x_np = np.load('x_simple.npy')
# target_x = ti.Vector.field(dim,
# dtype=real,
# shape=(max_steps, n_particles),
# needs_grad=True)
# # target_strain = ti.Matrix.field(dim,
# # dim,
# # dtype=real,
# # shape=(max_steps, n_particles),
# # needs_grad=True)
# @ti.kernel
# def load_target(target_np: ti.types.ndarray()):
# for i, j, k in ti.ndrange(steps, n_particles, dim):
# target_x[i, j][k] = target_np[i, j, k]
# # for i, j, k, l in ti.ndrange(steps, n_particles, dim, dim):
# # target_strain[i, j][k, l] = target_np[i, j, k, l]
# load_target(target_x_np)
node_locs = ti.Vector.field(dim,
dtype=real,
shape=(max_steps, n_grid * n_grid))
@ti.kernel
def assign_node_locs():
for s in range(max_steps):
for i in range(n_grid):
for j in range(n_grid):
node_locs[s, i * n_grid + j] = [i * dx, j * dx]
print('assigning node locs')
assign_node_locs()
gui = ti.GUI("Taichi Elements", (640, 640), background_color=0x112F41)
out_dir = 'out_test'
frame = 0
x_np = x.to_numpy()
node_locs_np = node_locs.to_numpy()
for s in range(steps):
scale = 4
gui.circles(x_np[s], color=0xFFFFFF, radius=1.5)
gui.circles(node_locs_np[s], color=0xFFA500, radius=1)
gui.show(f'{out_dir}/{frame:06d}.png')
frame += 1
# np.save('x_simple.npy', x.to_numpy())
# np.save('x_np.npy', x.to_numpy())
# np.save('strain_test.npy', strain.to_numpy())
# np.save('strain_test2.npy', strain2.to_numpy())
# np.save('target_strain_simple.npy', target_strain.to_numpy())
# target_strain = strain
# E[None] = 95
# grad_iterations = 30
# losses = []
# vs = np.zeros((grad_iterations, dim))
# init_v[None] = [0, 0]
# print('running grad iterations')
# for i in range(grad_iterations):
# grid_v_in.fill(0)
# grid_m_in.fill(0)
# loss[None] = 0
# x_avg[None] = [0, 0]
# with ti.ad.Tape(loss=loss):
# # reset_sim()
# set_v()
# for s in range(steps - 1):
# substep(s)
# compute_x_avg()
# compute_loss()
# l = loss[None]
# losses.append(l)
# v = init_v[None]
# # grad = E.grad[None]
# grad = init_v.grad[None]
# # learning_rate = 1e-5
# # E[None] -= learning_rate * grad
# learning_rate = 1e1
# init_v[None][0] -= learning_rate * grad[0]
# init_v[None][1] -= learning_rate * grad[1]
# vs[i, :] = np.array([v[0], v[1]])
# # print('loss=', l,
# # ' grad=', grad,
# # ' E=', E[None])
# print('loss=', l, ' grad=', (grad[0], grad[1]), ' v=', init_v[None])
# print('done')
# # vs = np.vstack(np.array(vs))
# print(vs)
# plt.title("Optimization of $V_0$ via $x(t)$ (Single Step)")
# plt.ylabel("Loss")
# plt.xlabel("Gradient Descent Iterations")
# plt.plot(losses)
# plt.yscale('log')
# plt.show()
# plt.title("$V_{0,x}$ Learning Curve via $x(t)$ (Single Step)")
# plt.ylabel("$V_{0,x}$")
# plt.xlabel("Iterations")
# plt.hlines(0.3, 0, 30, color='r', label='True Value')
# plt.plot(vs[:,0], color='b', label='Estimated Value')
# plt.legend()
# plt.show()
# plt.title("$V_{0,y}$ Learning Curve via $x(t)$ (Single Step)")
# plt.ylabel("$V_{0,y}$")
# plt.xlabel("Iterations")
# plt.hlines(0.6, 0, 30, color='r', label='True Value')
# plt.plot(vs[:,1], color='b', label='Estimated Value')
# plt.legend()
# plt.show()