Transient Channel Flow
Backward Facing Step Flow (BFS) DEMO code
This notebook demonstrates solving steady-state Backward Facing Step Flow (BFS) using DeepFlow. The BFS flow is a common benchmark problem in fluid dynamics, where the flow separates and reattaches after encountering a step.
import deepflow as df
print("Deepflow is runned on:", df.device) # to change to cpu use df.device = 'cpu'
df.manual_seed(69) # for reproducibility
Deepflow is runned on: cuda
1. Define Geometry Domain
Set up the computational domain: a rectangle with a circular obstacle (cylinder). This defines the area for simulation.
rectangle_pde = df.geometry.rectangle([0,5], [0,1])
rectange_ic = df.geometry.rectangle([0,5], [0,1])
2. Define Physics
Define the Navier-Stokes equations for fluid flow and apply boundary conditions (e.g., no-slip walls, inlet velocity).
domain.bound_list[0].define_bc({'u': df.parabolic('y', 1,1,0.5),'v': 0})
domain.bound_list[1].define_bc({'u': 0,'v': 0})
domain.bound_list[2].define_bc({'p': 0})
domain.bound_list[3].define_bc({'u': 0,'v': 0})
domain.area_list[0].define_pde(df.NavierStokes(U=0.001, L=1, mu=0.001, rho=1000))
domain.area_list[1].define_ic({'u': 0,'v': 0})
for geom in domain:
geom.define_time([0, 10], 'random')
domain.show_setup()
C:\Users\thamm\OneDrive\Documents\1 - Projects\0 - STEM\2 - Numerical Physics\9 - PINNs\deepflow\src\deepflow\physicsinformed.py:122: UserWarning: expo_scaling has not yet defined. False is set as default.
warnings.warn("expo_scaling has not yet defined. False is set as default.")
Sample initial points for training.
domain.sampling_lhs(bound_sampling_res=[1000, 1000, 1000, 1000], area_sampling_res=[2000, 2000])
domain.show_coordinates(display_physics=False)
3. Train the PINN model
Define how collocation points are sampled during training.
def do_in_adam(epoch, model):
return
def do_in_lbfgs(epoch, model):
if epoch % 100 == 0 and epoch > 0:
domain.sampling_R3(bound_sampling_res=[1000, 1000, 1000, 1000], area_sampling_res=[2000, 2000])
print(domain)
Train the model using Adam for initial training (faster convergence).
model0 = df.PINN(width=50, length=5, input_vars=['x','y','t'], output_vars=['u','v','p'])
# Train the model
model1, model1best = model0.train_adam(
learning_rate=0.001,
epochs=1000,
calc_loss=df.calc_loss_simple(domain),
threshold_loss=0.005,
do_between_epochs=do_in_adam)
Epoch: 1, total_loss: 0.91400, bc_loss: 0.86594, pde_loss: 0.00009, ic_loss: 0.04798
Epoch: 200, total_loss: 0.15948, bc_loss: 0.13487, pde_loss: 0.02015, ic_loss: 0.00446
Epoch: 400, total_loss: 0.03458, bc_loss: 0.01444, pde_loss: 0.01070, ic_loss: 0.00945
Epoch: 600, total_loss: 0.02541, bc_loss: 0.01232, pde_loss: 0.00730, ic_loss: 0.00580
Epoch: 800, total_loss: 0.02111, bc_loss: 0.01105, pde_loss: 0.00541, ic_loss: 0.00465
Epoch: 1000, total_loss: 0.01774, bc_loss: 0.00972, pde_loss: 0.00420, ic_loss: 0.00383
Epoch: 1000, total_loss: 0.01774, bc_loss: 0.00972, pde_loss: 0.00420, ic_loss: 0.00383
Refine the model using LBFGS for higher precision.
# Train the model
model2 = model1best.train_lbfgs(
calc_loss=df.calc_loss_simple(domain),
epochs=350,
threshold_loss=0.0001,
do_between_epochs=do_in_lbfgs)
Epoch: 970, total_loss: 0.01532, bc_loss: 0.00655, pde_loss: 0.00497, ic_loss: 0.00379
Epoch: 1020, total_loss: 0.00327, bc_loss: 0.00056, pde_loss: 0.00224, ic_loss: 0.00047
Epoch: 1070, total_loss: 0.00192, bc_loss: 0.00034, pde_loss: 0.00129, ic_loss: 0.00028
number of bound : ['0: 1296', '1: 1404', '2: 1442', '3: 1286']
number of area : ['0: 2529', '1: 2622']
Epoch: 1120, total_loss: 0.00205, bc_loss: 0.00038, pde_loss: 0.00143, ic_loss: 0.00024
Epoch: 1170, total_loss: 0.00119, bc_loss: 0.00020, pde_loss: 0.00084, ic_loss: 0.00015
number of bound : ['0: 1605', '1: 1724', '2: 1870', '3: 1579']
number of area : ['0: 3057', '1: 3367']
Epoch: 1220, total_loss: 0.00146, bc_loss: 0.00027, pde_loss: 0.00109, ic_loss: 0.00010
Epoch: 1270, total_loss: 0.00080, bc_loss: 0.00017, pde_loss: 0.00058, ic_loss: 0.00005
number of bound : ['0: 1886', '1: 2110', '2: 2258', '3: 1964']
number of area : ['0: 3618', '1: 4054']
Epoch: 1319, total_loss: 0.00086, bc_loss: 0.00020, pde_loss: 0.00059, ic_loss: 0.00006
Save or Load the model for later use
4. Visualization
4.1 Visualize area
# Create object for evaluation
area_eval = domain.area_list[0].evaluate(model2)
# Sampling uniform points
area_eval.sampling_area([400, 80])
# Show available data's key
area_eval.define_time(10)
print(area_eval)
Available data keys: ('u', 'v', 'p', 'pde_residual', 'x', 'y', 'u_x', 'u_y', 'v_x', 'v_y', 'p_x', 'p_y', 'continuity_residual', 'x_momentum_residual', 'y_momentum_residual', 't', 'total_loss', 'bc_loss', 'pde_loss', 'ic_loss')
_ = area_eval.plot_color('v_mag', s=2, cmap='jet').savefig("colorplot_v_mag.png")
_ = area_eval.plot_color('u', s=2, cmap='rainbow')
_ = area_eval.plot_color('v', s=2, cmap='rainbow')
_ = area_eval.plot_color('p', s=2, cmap='rainbow')
_ = area_eval.plot_streamline('u', 'v', cmap = 'jet')
_ = area_eval.plot_color('pde_residual', s=2, cmap='viridis')
4.2 Animate Area
anim = area_eval.plot_animate('u', range_t=[0.05, 8.1], dt = 0.1, frame_interval=100, cmap = 'rainbow', s=1, color_range=[0,1])
anim.save("animation.gif")
4.3 Visualize Neural Network data
