diff --git a/examples/LV_example_adam_lbfgs_nncg.py b/examples/LV_example_adam_lbfgs_nncg.py new file mode 100644 index 00000000..e66d3731 --- /dev/null +++ b/examples/LV_example_adam_lbfgs_nncg.py @@ -0,0 +1,374 @@ +import torch +import os +import sys +import matplotlib.pyplot as plt +import numpy as np +import pandas as pd +from torch.nn.utils import parameters_to_vector, vector_to_parameters +import time +from scipy.integrate import quad + +os.environ['KMP_DUPLICATE_LIB_OK'] = 'TRUE' +sys.path.append(os.path.abspath(os.path.join(os.path.dirname('AAAI_expetiments')))) + + +from tedeous.data import Domain, Conditions, Equation +from tedeous.model import Model +from tedeous.models import mat_model, Fourier_embedding +from tedeous.callbacks import plot, early_stopping, adaptive_lambda +from tedeous.optimizers.optimizer import Optimizer +from tedeous.device import solver_device +from tedeous.eval import integration + + + +import pandas as pd + +solver_device('cuda') + + +# Lotka-Volterra equations also known as predator-prey equations, describe the variation in populations +# of two species which interact via predation. +# For example, wolves (predators) and deer (prey). This is a classical model to represent the dynamic of two populations. + +# Let αlpha > 0, beta > 0, delta > 0 and gamma > 0 . The system is given by + +# dx/dt = x(alpha-beta*y) +# dy/dt = y(-delta+gamma*x) + +# Where 'x' represents prey population and 'y' predators population. It’s a system of first-order ordinary differential equations. +import torch +import numpy as np +import matplotlib.pyplot as plt +from scipy import integrate +import time +import os +import sys + +os.environ['KMP_DUPLICATE_LIB_OK'] = 'TRUE' +sys.path.append(os.path.abspath(os.path.join(os.path.dirname( __file__ ), '..'))) + +from tedeous.data import Domain, Conditions, Equation +from tedeous.model import Model +from tedeous.callbacks import early_stopping +from tedeous.optimizers.optimizer import Optimizer +from tedeous.device import solver_device, check_device, device_type + + + + + +alpha = 20. +beta = 20. +delta = 20. +gamma = 20. +x0 = 4. +y0 = 2. +t0 = 0. +tmax = 1. + +def exact(grid): + # scipy.integrate solution of Lotka_Volterra equations and comparison with NN results + + def deriv(X, t, alpha, beta, delta, gamma): + x, y = X + dotx = x * (alpha - beta * y) + doty = y * (-delta + gamma * x) + return np.array([dotx, doty]) + + t = grid.cpu() + + X0 = [x0, y0] + res = integrate.odeint(deriv, X0, t, args = (alpha, beta, delta, gamma)) + x, y = res.T + return np.hstack((x.reshape(-1,1),y.reshape(-1,1))) + +def u(grid): + solution=exact(grid) + return torch.tensor(solution) + + +def u_net(net, x): + net = net.to('cpu') + x = x.to('cpu') + return net(x).detach() + + +def l2_norm(net, x): + x = x.to('cpu') + net = net.to('cpu') + predict = net(x).detach().cpu().reshape(-1) + exact = u(x).detach().cpu().reshape(-1) + + + l2_norm_pressure = torch.sqrt(sum((predict[:, 0]-exact[:, 0])**2)) + l2_norm_velocity = torch.sqrt(sum((predict[:, 1]-exact[:, 1])**2)) + l2_norm_density = torch.sqrt(sum((predict[:, 2]-exact[:, 2])**2)) + + return l2_norm_pressure.detach().cpu().numpy(),l2_norm_velocity.detach().cpu().numpy(),l2_norm_density.detach().cpu().numpy() + +def l2_norm_mat(net, x): + x = x.to('cpu') + net = net.to('cpu') + predict = net.detach().cpu().reshape(-1) + exact = u(x).detach().cpu().reshape(-1) + l2_norm = torch.sqrt(sum((predict-exact)**2)) + return l2_norm.detach().cpu().numpy() + +def l2_norm_fourier(net, x): + x = x.to(torch.device('cuda:0')) + predict = net(x).detach().cpu().reshape(-1) + exact = u(x).detach().cpu().reshape(-1) + l2_norm = torch.sqrt(sum((predict-exact)**2)) + return l2_norm.detach().cpu().numpy() + + + + +def LV_problem_formulation(grid_res): + + domain = Domain() + domain.variable('t', [0, tmax], grid_res) + + boundaries = Conditions() + #initial conditions + boundaries.dirichlet({'t': 0}, value=x0, var=0) + boundaries.dirichlet({'t': 0}, value=y0, var=1) + + #equation system + # eq1: dx/dt = x(alpha-beta*y) + # eq2: dy/dt = y(-delta+gamma*x) + + # x var: 0 + # y var:1 + + equation = Equation() + + eq1 = { + 'dx/dt':{ + 'coeff': 1, + 'term': [0], + 'pow': 1, + 'var': [0] + }, + '-x*alpha':{ + 'coeff': -alpha, + 'term': [None], + 'pow': 1, + 'var': [0] + }, + '+beta*x*y':{ + 'coeff': beta, + 'term': [[None], [None]], + 'pow': [1, 1], + 'var': [0, 1] + } + } + + eq2 = { + 'dy/dt':{ + 'coeff': 1, + 'term': [0], + 'pow': 1, + 'var': [1] + }, + '+y*delta':{ + 'coeff': delta, + 'term': [None], + 'pow': 1, + 'var': [1] + }, + '-gamma*x*y':{ + 'coeff': -gamma, + 'term': [[None], [None]], + 'pow': [1, 1], + 'var': [0, 1] + } + } + + equation.add(eq1) + equation.add(eq2) + + grid = domain.build('autograd') + + return grid,domain,equation,boundaries + + + + + +def experiment_data_amount_LV_adam_lbfgs_nncg(grid_res,exp_name='LV_adam_lbfgs_nncg'): + solver_device('cuda') + exp_dict_list = [] + + grid,domain,equation,boundaries = LV_problem_formulation(grid_res) + + net = torch.nn.Sequential( + torch.nn.Linear(1, 32), + torch.nn.Tanh(), + torch.nn.Linear(32, 32), + torch.nn.Tanh(), + torch.nn.Linear(32, 2) + ) + + model = Model(net, domain, equation, boundaries) + + model.compile("autograd", lambda_operator=1, lambda_bound=100) + + + cb_es = early_stopping.EarlyStopping(eps=1e-6, + loss_window=100, + no_improvement_patience=500, + patience=3, + randomize_parameter=1e-5, + info_string_every=500) + + optim = Optimizer('Adam', {'lr': 1e-3}) + + start=time.time() + model.train(optim, 1000, callbacks=[cb_es]) + #model.train(optim, 10, callbacks=[cb_es]) + end = time.time() + + run_time_adam = end - start + + grid = domain.build('autograd') + + grid_test = torch.linspace(0, tmax, 100) + + u_exact_train = u(grid.cpu().reshape(-1)) + + u_exact_test = u(grid_test.cpu().reshape(-1)) + + error_train_adam = torch.sqrt(torch.mean((u_exact_train - net(grid))** 2, dim=0)) + + error_test_adam = torch.sqrt(torch.mean((u_exact_test - net(grid_test.reshape(-1,1))) ** 2 , dim=0)) + + loss_adam = model.solution_cls.evaluate()[0].detach().cpu().numpy() + + + print('Time taken adam {}= {}'.format(grid_res, run_time_adam)) + print('RMSE u {}= {}'.format(grid_res, error_test_adam[0])) + print('RMSE v {}= {}'.format(grid_res, error_test_adam[1])) + + + ######## + + cb_es = early_stopping.EarlyStopping(eps=1e-6, + loss_window=100, + no_improvement_patience=100, + patience=2, + randomize_parameter=1e-5, + verbose=False, + info_string_every=100) + + optim = Optimizer('LBFGS', {'history_size': 100, + "line_search_fn": 'strong_wolfe'}) + + start = time.time() + model.train(optim, 1000, save_model=False, callbacks=[cb_es]) + end = time.time() + time_LBFGS = end - start + + + error_train_LBFGS = torch.sqrt(torch.mean((u_exact_train - net(grid))** 2, dim=0)) + + error_test_LBFGS = torch.sqrt(torch.mean((u_exact_test - net(grid_test.reshape(-1,1))) ** 2 , dim=0)) + + loss_LBFGS = model.solution_cls.evaluate()[0].detach().cpu().numpy() + + print('Time taken LBFGS {}= {}'.format(grid_res, time_LBFGS)) + print('RMSE u {}= {}'.format(grid_res, error_test_LBFGS[0])) + print('RMSE v {}= {}'.format(grid_res, error_test_LBFGS[1])) + + ######## + + cb_es = early_stopping.EarlyStopping(eps=1e-6, + loss_window=100, + no_improvement_patience=100, + patience=2, + randomize_parameter=1e-5, + verbose=False, + info_string_every=1) + + optim = Optimizer('NNCG', {'mu': 1e-1, + 'lr': 1, + "rank": 10, + 'line_search_fn': "armijo", + "precond_update_frequency": 20, + "eigencdecomp_shift_attepmt_count":10, + #'cg_max_iters':1000, + 'verbose': False}) + + start = time.time() + model.train(optim, 100, save_model=False, callbacks=[cb_es],info_string_every=1) + end = time.time() + time_NNCG = end - start + + error_train_NNCG = torch.sqrt(torch.mean((u_exact_train - net(grid))** 2, dim=0)) + + error_test_NNCG = torch.sqrt(torch.mean((u_exact_test - net(grid_test.reshape(-1,1))) ** 2 , dim=0)) + + loss_NNCG = model.solution_cls.evaluate()[0].detach().cpu().numpy() + + ######### + + exp_dict={'grid_res': grid_res, + 'error_train_u_adam': error_train_adam[0].item(), + 'error_train_v_adam': error_train_adam[1].item(), + 'error_test_u_adam': error_test_adam[0].item(), + 'error_test_v_adam': error_test_adam[1].item(), + 'error_train_u_LBFGS': error_train_LBFGS[0].item(), + 'error_train_v_LBFGS': error_train_LBFGS[1].item(), + 'error_test_u_LBFGS': error_test_LBFGS[0].item(), + 'error_test_v_LBFGS': error_test_LBFGS[1].item(), + 'error_train_u_NNCG': error_train_NNCG[0].item(), + 'error_train_v_NNCG': error_train_NNCG[1].item(), + 'error_test_u_NNCG': error_test_NNCG[0].item(), + 'error_test_v_NNCG': error_test_NNCG[1].item(), + 'loss_adam': loss_adam.item(), + 'loss_LBFGS': loss_LBFGS.item(), + 'loss_NNCG': loss_NNCG.item(), + 'time_adam': run_time_adam, + 'time_LBFGS': time_LBFGS, + 'time_NNCG': time_NNCG, + 'type': exp_name} + + print('Time taken NNCG {}= {}'.format(grid_res, time_NNCG)) + print('RMSE u {}= {}'.format(grid_res, error_test_NNCG[0])) + print('RMSE v {}= {}'.format(grid_res, error_test_NNCG[1])) + + exp_dict_list.append(exp_dict) + + return exp_dict_list + + + + + + + +if __name__ == '__main__': + + results_dir=os.path.join(os.path.abspath(os.path.join(os.path.dirname( __file__ ))),'results') + + if not os.path.isdir(results_dir): + os.mkdir(results_dir) + + nruns = 1 + + + exp_dict_list=[] + + + + for grid_res in range(10, 101, 10): + for _ in range(nruns): + exp_dict_list.append(experiment_data_amount_LV_adam_lbfgs_nncg(grid_res)) + exp_dict_list_flatten = [item for sublist in exp_dict_list for item in sublist] + df = pd.DataFrame(exp_dict_list_flatten) + df_path=os.path.join(results_dir,'LV_adam_lbfgs_nncg_{}.csv'.format(grid_res)) + df.to_csv(df_path) + + + diff --git a/examples/examples_PINNacle/example_wave/darcy_2d_coef_256.dat b/examples/examples_PINNacle/example_wave/darcy_2d_coef_256.dat new file mode 100644 index 00000000..3e109835 --- /dev/null +++ b/examples/examples_PINNacle/example_wave/darcy_2d_coef_256.dat @@ -0,0 +1,65536 @@ +0.000000000000000000e+00 0.000000000000000000e+00 1.000000000000000000e+00 +3.921568627450980338e-03 0.000000000000000000e+00 1.000000000000000000e+00 +7.843137254901960675e-03 0.000000000000000000e+00 1.000000000000000000e+00 +1.176470588235294101e-02 0.000000000000000000e+00 1.000000000000000000e+00 +1.568627450980392135e-02 0.000000000000000000e+00 1.000000000000000000e+00 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100644 index 00000000..5af1a3c7 --- /dev/null +++ b/examples/examples_PINNacle/example_wave/example_wave_1d_basic.py @@ -0,0 +1,184 @@ +# -*- coding: utf-8 -*- +""" +Created on Mon May 31 12:33:44 2021 + +@author: user +""" +import torch +import numpy as np +import os +import sys +import time + +os.environ['KMP_DUPLICATE_LIB_OK'] = 'TRUE' +sys.path.append(os.path.abspath(os.path.join(os.path.dirname(__file__), '..'))) + +from tedeous.data import Domain, Conditions, Equation +from tedeous.model import Model + +from tedeous.callbacks import early_stopping, plot, cache +from tedeous.optimizers.optimizer import Optimizer +from tedeous.device import solver_device + +solver_device('gpu') + + +def func(grid, a=4): + x, t = grid[:, 0], grid[:, 1] + sln = np.sin(np.pi * x) * np.cos(2 * np.pi * t) + 0.5 * np.sin(a * np.pi * x) * np.cos(2 * a * np.pi * t) + return sln + + +def wave1d_basic_experiment(grid_res): + exp_dict_list = [] + + x_min, x_max = 0, 1 + t_max = 1 + # grid_res *= 2 + + domain = Domain() + domain.variable('x', [x_min, x_max], grid_res) + domain.variable('t', [0, t_max], grid_res) + + x = domain.variable_dict['x'] + t = domain.variable_dict['t'] + + boundaries = Conditions() + + # Initial conditions ############################################################################################### + + init_func = torch.sin(torch.pi * x) * torch.sin(4 * torch.pi * x) / 2 + + # u(x, 0) = f_init(x, 0) + boundaries.dirichlet({'x': [x_min, x_max], 't': 0}, value=init_func) + + # u_t(x, 0) = 0 + bop = { + 'du/dt': + { + 'coeff': 1, + 'du/dx': [1], + 'pow': 1, + 'var': 0 + } + } + boundaries.operator({'x': [x_min, x_max], 't': 0}, operator=bop, value=0) + + # Boundary conditions ############################################################################################## + + bnd_func = torch.sin(torch.pi * x) * torch.cos(2 * torch.pi * t) + \ + torch.sin(4 * torch.pi * x) / 2 * torch.cos(8 * torch.pi * t) + + # u(0, t) = f_bnd(x, t) + boundaries.dirichlet({'x': x_min, 't': [0, t_max]}, value=bnd_func) + + # u(1, t) = f_bnd(x, t) + boundaries.dirichlet({'x': x_max, 't': [0, t_max]}, value=bnd_func) + + equation = Equation() + + # Operator: d2u/dt2 - 4 * d2u/dx2 = 0 + + wave_eq = { + 'd2u/dt2**1': + { + 'coeff': 1, + 'd2u/dt2': [1, 1], + 'pow': 1 + }, + '-C*d2u/dx2**1': + { + 'coeff': -4, + 'd2u/dx2': [0, 0], + 'pow': 1 + } + } + + equation.add(wave_eq) + + neurons = 100 + + net = torch.nn.Sequential( + torch.nn.Linear(2, neurons), + torch.nn.Tanh(), + torch.nn.Linear(neurons, neurons), + torch.nn.Tanh(), + torch.nn.Linear(neurons, neurons), + torch.nn.Tanh(), + torch.nn.Linear(neurons, neurons), + torch.nn.Tanh(), + torch.nn.Linear(neurons, neurons), + torch.nn.Tanh(), + torch.nn.Linear(neurons, 1) + ) + + for m in net.modules(): + if isinstance(m, torch.nn.Linear): + torch.nn.init.xavier_normal_(m.weight) + torch.nn.init.zeros_(m.bias) + + start = time.time() + + model = Model(net, domain, equation, boundaries) + + model.compile('autograd', lambda_operator=1, lambda_bound=100) + + img_dir = os.path.join(os.path.dirname(__file__), 'wave_1d_basic_img') + + cb_cache = cache.Cache(cache_verbose=True, model_randomize_parameter=1e-6) + + cb_es = early_stopping.EarlyStopping(eps=1e-6, + loss_window=100, + no_improvement_patience=1000, + patience=5, + randomize_parameter=1e-6, + info_string_every=10) + + cb_plots = plot.Plots(save_every=500, + print_every=None, + img_dir=img_dir, + img_dim='2d') # 3 image dimension options: 3d, 2d, 2d_scatter + + optimizer = Optimizer('Adam', {'lr': 1e-4}) + + model.train(optimizer, 5e6, save_model=True, callbacks=[cb_es, cb_plots, cb_cache]) + + end = time.time() + + grid = domain.build('NN').to('cuda') + net = net.to('cuda') + + error_rmse = torch.sqrt(torch.mean((func(grid).reshape(-1, 1) - net(grid)) ** 2)) + + exp_dict_list.append({'grid_res': grid_res, 'time': end - start, 'RMSE': error_rmse.detach().cpu().numpy(), + 'type': 'wave_eqn_physical', 'cache': True}) + + print('Time taken {}= {}'.format(grid_res, end - start)) + print('RMSE {}= {}'.format(grid_res, error_rmse)) + + return exp_dict_list + + +nruns = 10 + +exp_dict_list = [] + +for grid_res in range(10, 101, 10): + for _ in range(nruns): + exp_dict_list.append(wave1d_basic_experiment(grid_res)) + +import pandas as pd + +exp_dict_list_flatten = [item for sublist in exp_dict_list for item in sublist] +df = pd.DataFrame(exp_dict_list_flatten) +# df.boxplot(by='grid_res',column='time',fontsize=42,figsize=(20,10)) +# df.boxplot(by='grid_res',column='RMSE',fontsize=42,figsize=(20,10),showfliers=False) +df.to_csv('examples/benchmarking_data/wave_experiment_physical_10_100_cache={}.csv'.format(str(True))) + + + + + + + + diff --git a/examples/examples_PINNacle/example_wave/example_wave_2d_heterogeneous_medium.py b/examples/examples_PINNacle/example_wave/example_wave_2d_heterogeneous_medium.py new file mode 100644 index 00000000..25e30231 --- /dev/null +++ b/examples/examples_PINNacle/example_wave/example_wave_2d_heterogeneous_medium.py @@ -0,0 +1,286 @@ +# -*- coding: utf-8 -*- +""" +Created on Mon May 31 12:33:44 2021 + +@author: user +""" +import torch +import numpy as np +import os +import sys +import time +from scipy import interpolate + +os.environ['KMP_DUPLICATE_LIB_OK'] = 'TRUE' +sys.path.append(os.path.abspath(os.path.join(os.path.dirname(__file__), '..'))) + +from tedeous.data import Domain, Conditions, Equation +from tedeous.model import Model + +from tedeous.callbacks import early_stopping, plot, cache +from tedeous.optimizers.optimizer import Optimizer +from tedeous.device import solver_device + +solver_device('gpu') + +wave_datapath = "wave_darcy.dat" +darcy_2d_coef_data = np.loadtxt("darcy_2d_coef_256.dat") + + +def func_data(datapath): + + t_transpose = True + + input_dim = 3 + output_dim = 2 + + def trans_time_data_to_dataset(datapath, ref_data): + data = ref_data + slice = (data.shape[1] - input_dim + 1) // output_dim + assert slice * output_dim == data.shape[ + 1] - input_dim + 1, "Data shape is not multiple of pde.output_dim" + + with open(datapath, "r", encoding='utf-8') as f: + def extract_time(string): + index = string.find("t=") + if index == -1: + return None + return float(string[index + 2:].split(' ')[0]) + + t = None + for line in f.readlines(): + if line.startswith('%') and line.count('@') == slice * output_dim: + t = line.split('@')[1:] + t = list(map(extract_time, t)) + if t is None or None in t: + raise ValueError("Reference Data not in Comsol format or does not contain time info") + t = np.array(t[::output_dim]) + + t, x0 = np.meshgrid(t, data[:, 0]) + list_x = [x0.reshape(-1)] + for i in range(1, input_dim - 1): + list_x.append(np.stack([data[:, i] for _ in range(slice)]).T.reshape(-1)) + list_x.append(t.reshape(-1)) + for i in range(output_dim): + list_x.append(data[:, input_dim - 1 + i::output_dim].reshape(-1)) + return np.stack(list_x).T + + scale = 1 + + def transform_fn(data): + data[:, :input_dim] *= scale + return data + + def load_ref_data(datapath, transform_fn=None, t_transpose=False): + ref_data = np.loadtxt(datapath, comments="%", encoding='utf-8').astype(np.float32) + if t_transpose: + ref_data = trans_time_data_to_dataset(datapath, ref_data) + if transform_fn is not None: + ref_data = transform_fn(ref_data) + return ref_data + + load_ref_data(datapath) + load_ref_data(datapath, transform_fn, t_transpose) + + return load_ref_data + + +def func(grid): + wave_data = func_data(wave_datapath) + sln = torch.Tensor( + interpolate.griddata(wave_data[:, 0:2], wave_data[:, 2], + (grid.detach().cpu().numpy()[:, 0:2] + 1) / 2) + ).unsqueeze(dim=-1) + return sln + + +def coef(grid): + c = torch.Tensor( + interpolate.griddata(darcy_2d_coef_data[:, 0:2], darcy_2d_coef_data[:, 2], + (grid.detach().cpu().numpy()[:, 0:2] + 1) / 2) + ).unsqueeze(dim=-1) + return c + + +def wave2d_heterogeneous_experiment(grid_res): + exp_dict_list = [] + + x_min, x_max = -1, 1 + y_min, y_max = -1, 1 + t_max = 5 + # grid_res *= 4 + + mu_1, mu_2 = -0.5, 0 + sigma = 0.3 + + domain = Domain() + domain.variable('x', [x_min, x_max], grid_res) + domain.variable('y', [y_min, y_max], grid_res) + domain.variable('t', [0, t_max], grid_res) + + boundaries = Conditions() + + # Initial conditions ############################################################################################### + + def init_func(grid): + x, y = grid[:, 0], grid[:, 1] + return np.exp(-((x - mu_1) ** 2 + (y - mu_2) ** 2) / (2 * sigma ** 2)) + + # u(x, 0) = f_init(x, 0) + boundaries.dirichlet({'x': [x_min, x_max], 'y': [y_min, y_max], 't': 0}, value=init_func) + + # u_t(x, 0) = 0 + bop = { + 'du/dt': + { + 'coeff': 1, + 'du/dx': [2], + 'pow': 1, + 'var': 0 + } + } + boundaries.operator({'x': [x_min, x_max], 'y': [y_min, y_max], 't': 0}, operator=bop, value=0) + + # Boundary conditions ############################################################################################## + + def bop_generation(coeff, grid_i): + bop = { + 'coeff * du/dx_i': + { + 'coeff': coeff, + 'term': [grid_i], + 'pow': 1 + } + } + return bop + + # u_x_min(x_min, y, t) = 0 + bop = bop_generation(-1, 0) + boundaries.operator({'x': x_min, 'y': [y_min, y_max], 't': [0, t_max]}, operator=bop, value=0) + + # u_x_max(x_max, y, t) = 0 + bop = bop_generation(1, 0) + boundaries.operator({'x': x_max, 'y': [y_min, y_max], 't': [0, t_max]}, operator=bop, value=0) + + # u_y_min(x, y_min, t) = 0 + bop = bop_generation(-1, 1) + boundaries.operator({'x': [x_min, x_max], 'y': y_min, 't': [0, t_max]}, operator=bop, value=0) + + # u_y_max(x, y_max, t) = 0 + bop = bop_generation(1, 1) + boundaries.operator({'x': [x_min, x_max], 'y': y_max, 't': [0, t_max]}, operator=bop, value=0) + + equation = Equation() + + # Operator: d2u/dx2 + d2u/dy2 - (1 / coef) * d2u/dt2 = 0 + + wave_eq = { + 'd2u/dx2**1': + { + 'coeff': 1, + 'd2u/dx2': [0, 0], + 'pow': 1 + }, + 'd2u/dy2**1': + { + 'coeff': 1, + 'd2u/dx2': [1, 1], + 'pow': 1 + }, + '-(1 / coef) * d2u/dt2**1': + { + 'coeff': lambda grid: -1 / coef(grid), + 'd2u/dt2': [2, 2], + 'pow': 1 + }, + } + + equation.add(wave_eq) + + neurons = 100 + + net = torch.nn.Sequential( + torch.nn.Linear(3, neurons), + torch.nn.Tanh(), + torch.nn.Linear(neurons, neurons), + torch.nn.Tanh(), + torch.nn.Linear(neurons, neurons), + torch.nn.Tanh(), + torch.nn.Linear(neurons, neurons), + torch.nn.Tanh(), + torch.nn.Linear(neurons, neurons), + torch.nn.Tanh(), + torch.nn.Linear(neurons, 1) + ) + + for m in net.modules(): + if isinstance(m, torch.nn.Linear): + torch.nn.init.xavier_normal_(m.weight) + torch.nn.init.zeros_(m.bias) + + start = time.time() + + model = Model(net, domain, equation, boundaries) + + model.compile('autograd', lambda_operator=1, lambda_bound=100) + + img_dir = os.path.join(os.path.dirname(__file__), 'wave_2d_heterogeneous_medium_img') + + cb_cache = cache.Cache(cache_verbose=True, model_randomize_parameter=1e-6) + + cb_es = early_stopping.EarlyStopping(eps=1e-6, + loss_window=100, + no_improvement_patience=1000, + patience=5, + randomize_parameter=1e-6, + info_string_every=10) + + cb_plots = plot.Plots(save_every=50, + print_every=None, + img_dir=img_dir, + img_dim='2d') # 3 image dimension options: 3d, 2d, 2d_scatter + + optimizer = Optimizer('Adam', {'lr': 1e-4}) + + model.train(optimizer, 5e6, save_model=True, callbacks=[cb_es, cb_plots, cb_cache]) + + end = time.time() + + grid = domain.build('NN').to('cuda') + net = net.to('cuda') + + error_rmse = torch.sqrt(torch.mean((func(grid).reshape(-1, 1) - net(grid)) ** 2)) + + exp_dict_list.append({'grid_res': grid_res, 'time': end - start, 'RMSE': error_rmse.detach().cpu().numpy(), + 'type': 'wave_eqn_physical', 'cache': True}) + + print('Time taken {}= {}'.format(grid_res, end - start)) + print('RMSE {}= {}'.format(grid_res, error_rmse)) + + return exp_dict_list + + +nruns = 10 + +exp_dict_list = [] + +for grid_res in range(10, 101, 10): + for _ in range(nruns): + exp_dict_list.append(wave2d_heterogeneous_experiment(grid_res)) + +import pandas as pd + +exp_dict_list_flatten = [item for sublist in exp_dict_list for item in sublist] +df = pd.DataFrame(exp_dict_list_flatten) +# df.boxplot(by='grid_res',column='time',fontsize=42,figsize=(20,10)) +# df.boxplot(by='grid_res',column='RMSE',fontsize=42,figsize=(20,10),showfliers=False) +df.to_csv('examples/benchmarking_data/wave_experiment_physical_10_100_cache={}.csv'.format(str(True))) + + + + + + + + + diff --git a/examples/examples_PINNacle/example_wave/wave_darcy.dat b/examples/examples_PINNacle/example_wave/wave_darcy.dat new file mode 100644 index 00000000..c631de5b --- /dev/null +++ b/examples/examples_PINNacle/example_wave/wave_darcy.dat @@ -0,0 +1,992 @@ +% Model: wave_darcy.mph +% Version: COMSOL 6.0.0.354 +% Date: Apr 10 2023, 17:39 +% Dimension: 2 +% Nodes: 983 +% Expressions: 251 +% Description: 因变量 u +% Length unit: m +% X Y u (1) @ t=0 u (1) @ t=0.02 u (1) @ t=0.04 u (1) 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0.7708789894928642 0.7783056680697304 0.7600733541958655 0.7821143969513482 0.8513544645080181 0.8974232284799315 0.8691256119972757 0.8869585719477854 1.0125311010977187 1.086760164398819 1.0210691836111918 0.9105529990679851 0.773281418905209 0.6158920466899491 0.4963389973134221 0.3433206833617617 0.18888216572701857 0.04712253518284152 -0.14501660276950837 -0.29934133699808696 -0.424713298667774 -0.5549173337290819 -0.631931486953992 -0.6771113326200888 -0.6616651876156647 -0.6045304298134957 -0.5895201665381945 -0.5820439490116984 -0.5869640523629519 -0.5646813664535552 -0.500402752742755 -0.47849358426113153 -0.5330767744153977 diff --git a/examples/kdv_example_CSO.py b/examples/kdv_example_CSO.py new file mode 100644 index 00000000..c3ea41dc --- /dev/null +++ b/examples/kdv_example_CSO.py @@ -0,0 +1,386 @@ +import torch +import os +import sys +import matplotlib.pyplot as plt +import numpy as np +import pandas as pd +from torch.nn.utils import parameters_to_vector, vector_to_parameters +import time +from scipy.integrate import quad + +os.environ['KMP_DUPLICATE_LIB_OK'] = 'TRUE' +sys.path.append(os.path.abspath(os.path.join(os.path.dirname('AAAI_expetiments')))) + + +from tedeous.data import Domain, Conditions, Equation +from tedeous.model import Model +from tedeous.models import mat_model, Fourier_embedding +from tedeous.callbacks import plot, early_stopping, adaptive_lambda +from tedeous.optimizers.optimizer import Optimizer +from tedeous.device import solver_device +from tedeous.eval import integration + + +import pandas as pd + +solver_device('cuda') + +mu = 0.01 / np.pi + +def soliton(x,t): + E=np.exp(1) + s=((18*torch.exp((1/125)*(t + 25*x))*(16*torch.exp(2*t) + + 1000*torch.exp((126*t)/125 + (4*x)/5) + 9*torch.exp(2*x) + 576*torch.exp(t + x) + + 90*torch.exp((124*t)/125 + (6*x)/5)))/(5*(40*torch.exp((126*t)/125) + + 18*torch.exp(t + x/5) + 9*torch.exp((6*x)/5) + 45*torch.exp(t/125 + x))**2)) + return s + +def u(grid): + solution = [] + for point in grid: + x=point[0] + t=point[1] + s=soliton(x,t) + solution.append(s) + return torch.tensor(solution) + + +def u_net(net, x): + net = net.to('cpu') + x = x.to('cpu') + return net(x).detach() + + +def l2_norm(net, x): + x = x.to('cpu') + net = net.to('cpu') + predict = net(x).detach().cpu().reshape(-1) + exact = u(x).detach().cpu().reshape(-1) + l2_norm = torch.sqrt(sum((predict-exact)**2)) + return l2_norm.detach().cpu().numpy() + +def l2_norm_mat(net, x): + x = x.to('cpu') + net = net.to('cpu') + predict = net.detach().cpu().reshape(-1) + exact = u(x).detach().cpu().reshape(-1) + l2_norm = torch.sqrt(sum((predict-exact)**2)) + return l2_norm.detach().cpu().numpy() + +def l2_norm_fourier(net, x): + x = x.to(torch.device('cuda:0')) + predict = net(x).detach().cpu().reshape(-1) + exact = u(x).detach().cpu().reshape(-1) + l2_norm = torch.sqrt(sum((predict-exact)**2)) + return l2_norm.detach().cpu().numpy() + + + + +def kdv_problem_formulation(grid_res): + + domain = Domain() + domain.variable('x', [-10, 10], grid_res) + domain.variable('t', [0, 1], grid_res) + + boundaries = Conditions() + + + # u(0,t) = u(1,t) + boundaries.periodic([{'x': -10, 't': [0, 1]}, {'x': 10, 't': [0, 1]}]) + + + """ + Initial conditions at t=0 + """ + + x = domain.variable_dict['x'] + + boundaries.dirichlet({'x': [-10, 10], 't': 0}, value=soliton(x,torch.tensor([0]))) + + equation = Equation() + + # operator is du/dt+6u*(du/dx)+d3u/dx3-sin(x)*cos(t)=0 + kdv = { + '1*du/dt**1': + { + 'coeff': 1, + 'du/dt': [1], + 'pow': 1, + 'var': 0 + }, + '6*u**1*du/dx**1': + { + 'coeff': 6, + 'u*du/dx': [[None], [0]], + 'pow': [1,1], + 'var':[0,0] + }, + 'd3u/dx3**1': + { + 'coeff': 1, + 'd3u/dx3': [0, 0, 0], + 'pow': 1, + 'var':0 + } + } + + equation.add(kdv) + + grid = domain.build('autograd') + + return grid,domain,equation,boundaries + + + + + + +def experiment_data_amount_kdv_PSO(grid_res,exp_name='kdv_PSO',save_plot=True): + solver_device('cuda') + exp_dict_list = [] + + grid,domain,equation,boundaries = kdv_problem_formulation(grid_res) + + net = torch.nn.Sequential( + torch.nn.Linear(2, 32), + torch.nn.Tanh(), + torch.nn.Linear(32, 32), + torch.nn.Tanh(), + torch.nn.Linear(32, 1) + ) + + + model = Model(net, domain, equation, boundaries) + + model.compile('autograd', lambda_operator=1, lambda_bound=100) + + cb_es = early_stopping.EarlyStopping(eps=1e-6, + loss_window=100, + no_improvement_patience=1000, + patience=5, + randomize_parameter=1e-6, + info_string_every=500) + + optim = Optimizer('Adam', {'lr': 1e-3}) + + start=time.time() + model.train(optim, 2e5, callbacks=[cb_es]) + end = time.time() + + time_adam = end - start + + grid = domain.build('autograd') + + grid_test = torch.cartesian_prod(torch.linspace(-10, 10, 100), torch.linspace(0, 1, 100)) + + u_exact_train = u(grid).reshape(-1) + + u_exact_test = u(grid_test).reshape(-1) + + error_adam_train = torch.sqrt(torch.mean((u_exact_train - net(grid).reshape(-1)) ** 2)) + + error_adam_test = torch.sqrt(torch.mean((u_exact_test - net(grid_test).reshape(-1)) ** 2)) + + loss_adam = model.solution_cls.evaluate()[0].detach().cpu().numpy() + + lu_f = model.solution_cls.operator.operator_compute() + + lu_f, gr = integration(lu_f, grid) + + lu_f_adam, _ = integration(lu_f, gr) + + ######## + + cb_es = early_stopping.EarlyStopping(eps=1e-6, + loss_window=100, + no_improvement_patience=100, + patience=2, + randomize_parameter=1e-5, + verbose=False, + info_string_every=500) + + optim = Optimizer('PSO', {'pop_size': 20, #30 + 'b': 0.4, #0.5 + 'c2': 0.5, #0.05 + 'c1': 0.5, + 'variance': 5e-4, + 'lr': 1e-4}) + start = time.time() + model.train(optim, 2e4, save_model=False, callbacks=[cb_es], info_string_every=20) + end = time.time() + time_pso = end - start + + error_pso_train = torch.sqrt(torch.mean((u_exact_train - net(grid).reshape(-1)) ** 2)) + + error_pso_test = torch.sqrt(torch.mean((u_exact_test - net(grid_test).reshape(-1)) ** 2)) + + loss_pso = model.solution_cls.evaluate()[0].detach().cpu().numpy() + + lu_f = model.solution_cls.operator.operator_compute() + + grid = domain.build('autograd') + + lu_f, gr = integration(lu_f, grid) + + lu_f_pso, _ = integration(lu_f, gr) + + ######### + + + + exp_dict={'grid_res': grid_res, + 'error_adam_train': error_adam_train.item(), + 'error_adam_test': error_adam_test.item(), + 'error_PSO_train': error_pso_train.item(), + 'error_PSO_test': error_pso_test.item(), + 'loss_adam': loss_adam.item(), + 'loss_pso': loss_pso.item(), + "lu_f_adam": lu_f_adam.item(), + "lu_f_pso": lu_f_pso.item(), + 'time_adam': time_adam, + 'time_pso': time_pso, + 'type': exp_name} + + print('Time taken {}= {}'.format(grid_res, end - start)) + print('RMSE_adam {}= {}'.format(grid_res, error_adam_test)) + print('RMSE_pso {}= {}'.format(grid_res, error_pso_test)) + + exp_dict_list.append(exp_dict) + + return exp_dict_list + +def experiment_data_amount_kdv_CSO(grid_res,exp_name='kdv_CSO',save_plot=True): + solver_device('cuda') + exp_dict_list = [] + + grid,domain,equation,boundaries = kdv_problem_formulation(grid_res) + + net = torch.nn.Sequential( + torch.nn.Linear(2, 32), + torch.nn.Tanh(), + torch.nn.Linear(32, 32), + torch.nn.Tanh(), + torch.nn.Linear(32, 1) + ) + + + model = Model(net, domain, equation, boundaries) + + model.compile('autograd', lambda_operator=1, lambda_bound=100) + + cb_es = early_stopping.EarlyStopping(eps=1e-6, + loss_window=100, + no_improvement_patience=1000, + patience=5, + randomize_parameter=1e-6, + info_string_every=500) + + optim = Optimizer('Adam', {'lr': 1e-3}) + + start=time.time() + model.train(optim, 2e5, callbacks=[cb_es]) + end = time.time() + + time_adam = end - start + + grid = domain.build('autograd') + + grid_test = torch.cartesian_prod(torch.linspace(-10, 10, 100), torch.linspace(0, 1, 100)) + + u_exact_train = u(grid).reshape(-1) + + u_exact_test = u(grid_test).reshape(-1) + + error_adam_train = torch.sqrt(torch.mean((u_exact_train - net(grid).reshape(-1)) ** 2)) + + error_adam_test = torch.sqrt(torch.mean((u_exact_test - net(grid_test).reshape(-1)) ** 2)) + + loss_adam = model.solution_cls.evaluate()[0].detach().cpu().numpy() + + lu_f = model.solution_cls.operator.operator_compute() + + lu_f, gr = integration(lu_f, grid) + + lu_f_adam, _ = integration(lu_f, gr) + + ######## + + cb_es = early_stopping.EarlyStopping(eps=1e-6, + loss_window=100, + no_improvement_patience=100, + patience=2, + randomize_parameter=1e-5, + verbose=False, + info_string_every=20) + + optim = Optimizer('CSO', {'pop_size': 20, #30 + 'variance': 5e-4, + 'lr': 1e-4}) + start = time.time() + model.train(optim, 2e4, save_model=False, callbacks=[cb_es]) + end = time.time() + time_pso = end - start + + error_pso_train = torch.sqrt(torch.mean((u_exact_train - net(grid).reshape(-1)) ** 2)) + + error_pso_test = torch.sqrt(torch.mean((u_exact_test - net(grid_test).reshape(-1)) ** 2)) + + loss_pso = model.solution_cls.evaluate()[0].detach().cpu().numpy() + + lu_f = model.solution_cls.operator.operator_compute() + + grid = domain.build('autograd') + + lu_f, gr = integration(lu_f, grid) + + lu_f_pso, _ = integration(lu_f, gr) + + ######### + + + + exp_dict={'grid_res': grid_res, + 'error_adam_train': error_adam_train.item(), + 'error_adam_test': error_adam_test.item(), + 'error_PSO_train': error_pso_train.item(), + 'error_PSO_test': error_pso_test.item(), + 'loss_adam': loss_adam.item(), + 'loss_pso': loss_pso.item(), + "lu_f_adam": lu_f_adam.item(), + "lu_f_pso": lu_f_pso.item(), + 'time_adam': time_adam, + 'time_pso': time_pso, + 'type': exp_name} + + print('Time taken {}= {}'.format(grid_res, end - start)) + print('RMSE_adam {}= {}'.format(grid_res, error_adam_test)) + print('RMSE_pso {}= {}'.format(grid_res, error_pso_test)) + + exp_dict_list.append(exp_dict) + + return exp_dict_list + + + +if __name__ == '__main__': + + if not os.path.isdir('examples\\results'): + os.mkdir('examples\\results') + + + exp_dict_list=[] + + nruns = 1 + + + for grid_res in range(100, 101, 10): + for _ in range(nruns): + exp_dict_list.append(experiment_data_amount_kdv_CSO(grid_res)) + exp_dict_list_flatten = [item for sublist in exp_dict_list for item in sublist] + df = pd.DataFrame(exp_dict_list_flatten) + df.to_csv('examples\\results\\kdv_CSO_adaptive_Z_V_UP_20_{}.csv'.format(grid_res)) + + + + diff --git a/tedeous/data.py b/tedeous/data.py index 21bdbbf6..0ce272e4 100644 --- a/tedeous/data.py +++ b/tedeous/data.py @@ -80,8 +80,6 @@ def build(self, var_lst = list(self.variable_dict.values()) var_lst = [i.cpu() for i in var_lst] - grid = None - if mode in ('autograd', 'NN'): if len(self.variable_dict) == 1: grid = check_device(var_lst[0].reshape(-1, 1)) @@ -106,9 +104,9 @@ def build(self, grid = csg_domain_difference(grid, geom_figure) else: grid = np.meshgrid(*var_lst, indexing='ij') - grid = check_device(torch.tensor(np.array(grid))) + grid = check_device(torch.tensor(grid.cpu().numpy())) - grid = check_device(torch.tensor(np.array(grid))) + grid = check_device(torch.tensor(grid.cpu().numpy())) return grid diff --git a/tedeous/input_preprocessing.py b/tedeous/input_preprocessing.py index c94014a6..270b2eb5 100644 --- a/tedeous/input_preprocessing.py +++ b/tedeous/input_preprocessing.py @@ -27,7 +27,7 @@ def lambda_prepare(val: torch.Tensor, if isinstance(lambda_, torch.Tensor): return lambda_ - if isinstance(lambda_, int): + if isinstance(lambda_, (int, float)): try: lambdas = torch.ones(val.shape[-1]) * lambda_ except: diff --git a/tedeous/model.py b/tedeous/model.py index d3a1962e..7449f2a0 100644 --- a/tedeous/model.py +++ b/tedeous/model.py @@ -97,8 +97,8 @@ def compile( boundary_order=boundary_order).set_strategy(mode) if self.batch_size != None: - if len(grid) < self.batch_size: - self.batch_size = None + if len(grid) torch.Tensor: + """ Method for converting model parameters *NN and autograd* + or model values *mat* to vector. + + Returns: + torch.Tensor: model parameters/model values vector. + """ + if not isinstance(self.params, torch.Tensor): + vec = parameters_to_vector(self.params) + else: + self.model_shape = self.params.shape + vec = self.params.reshape(-1) + + return vec + + def vec_to_params(self, vec: torch.Tensor) -> None: + """Method for converting vector to model parameters (NN, autograd) + or model values (mat) + + Args: + vec (torch.Tensor): The particle of swarm. + """ + if not isinstance(self.params, torch.Tensor): + vector_to_parameters(vec, self.params) + else: + self.params.data = vec.reshape(self.params).data + + + def build_swarm(self): + """Creates the swarm based on solution class model. + + Returns: + torch.Tensor: The PSO swarm population. + Each particle represents a neural network (NN, autograd) or model values (mat). + """ + vector = self.params_to_vec() + matrix = [] + for _ in range(self.pop_size): + matrix.append(vector.reshape(1, -1)) + matrix = torch.cat(matrix) + variance = torch.FloatTensor(self.pop_size, self.vec_shape).uniform_( + -self.variance, self.variance).to(device_type()) + swarm = matrix + variance + swarm[0] = matrix[0] + return swarm.clone().detach().requires_grad_(True) + + def start_velocities(self) -> torch.Tensor: + """Start the velocities of each particle in the population (swarm) as `0`. + + Returns: + torch.Tensor: The starting velocities. + """ + return torch.zeros((self.pop_size, self.vec_shape)) + + def gradient(self, loss: torch.Tensor) -> torch.Tensor: + """ Calculation of loss gradient by model parameters (NN, autograd) + or model values (mat). + + Args: + loss (torch.Tensor): result of loss calculation. + + Returns: + torch.Tensor: calculated gradient vector. + """ + dl_dparam = torch.autograd.grad(loss, self.params) + + grads = parameters_to_vector(dl_dparam) + + return grads + + def update_zero_v(self) -> Tuple[torch.Tensor, torch.Tensor]: + + idx = torch.where(abs(self.v) == 0) + if len(idx[0]) > 0: + rand = torch.rand_like(self.v[idx]) # Генерируем случайные значения той же формы, что и self.v + self.v[idx] = torch.where(rand > 0.5, rand * self.variance * (-self.V_max), rand * self.variance * self.V_max) + + def get_randoms(self) -> torch.Tensor: + """Generate random values to update the particles' positions. + + Returns: + torch.Tensor: random tensor + """ + return torch.rand((2, 1, self.vec_shape)) + + def update_p_best(self) -> None: + """Updates the *p-best* positions.""" + + idx = torch.where(self.loss_swarm < self.f_p) + + self.p[idx] = self.swarm[idx] + self.f_p[idx] = self.loss_swarm[idx].detach() + + def update_g_best(self) -> None: + """Update the *g-best* position.""" + self.g_best = self.p[torch.argmin(self.f_p)] + + def gradient_descent(self) -> torch.Tensor: + """ Gradiend descent based on Adam algorithm. + + Returns: + torch.Tensor: gradient term in velocities vector. + """ + self.m1 = self.beta1 * self.m1 + (1 - self.beta1) * self.grads_swarm + self.m2 = self.beta2 * self.m2 + (1 - self.beta2) * torch.square( + self.grads_swarm) + + update = self.lr * self.m1 / (torch.sqrt(torch.abs(self.m2)) + self.epsilon) + + return update + + def step(self, closure=None) -> torch.Tensor: + """ It runs ONE step on the competitive swarm optimization. + + Returns: + torch.Tensor: loss value for best particle of the swarm. + """ + self.loss_swarm, self.grads_swarm = closure() + if self.indicator: + self.f_p = copy(self.loss_swarm).detach() + self.g_best = self.p[torch.argmin(self.f_p)] + self.indicator = False + + fix_attempt=0 + while torch.any(self.loss_swarm!=self.loss_swarm): + self.swarm=self.swarm+0.001*torch.rand(size=self.swarm.shape) + self.loss_swarm, self.grads_swarm = closure() + fix_attempt+=1 + if fix_attempt>5: + break + + U = list(range(self.pop_size)) + while U: + i, j = np.random.choice(U, 2, replace=False) + X1, X2 = self.swarm[i], self.swarm[j] + + if self.loss_swarm[i] <= self.loss_swarm[j]: + Xw, Xl = X1, X2 + iw, il = i, j + else: + Xw, Xl = X2, X1 + iw, il = j, i + + R1, R2, R3 = torch.rand(self.vec_shape), torch.rand(self.vec_shape), torch.rand(self.vec_shape) + self.v[il] = R1 * self.v[il] + R2 * (Xw - Xl) + self.fi * R3 * ((Xl + Xw)/2 - Xl) + + with torch.no_grad(): + self.swarm[il] = Xl + self.v[il] + U.remove(i) + U.remove(j) + + if self.use_grad: + self.swarm = self.swarm - self.gradient_descent() + + self.update_p_best() + self.update_g_best() + + if self.t > 150: + self.update_zero_v() + self.vec_to_params(self.g_best) + min_loss = torch.min(self.f_p) + self.t += 1 + return min_loss diff --git a/tedeous/optimizers/closure.py b/tedeous/optimizers/closure.py index 5e318f2e..f2e80c7a 100644 --- a/tedeous/optimizers/closure.py +++ b/tedeous/optimizers/closure.py @@ -74,7 +74,7 @@ def loss_grads(): if self.optimizer.use_grad: grads = self.optimizer.gradient(loss) - grads = torch.where(grads == float('nan'), torch.zeros_like(grads), grads) + grads = torch.where(grads != grads, torch.zeros_like(grads), grads) else: grads = torch.tensor([0.]) @@ -89,6 +89,7 @@ def loss_grads(): grads_swarm.append(grads.reshape(1, -1)) losses = torch.stack(loss_swarm).reshape(-1) + gradients = torch.vstack(grads_swarm) self.model.cur_loss = min(loss_swarm) @@ -115,10 +116,39 @@ def _closure_ngd(self): return int_res, bval, true_bval, loss, self.model.solution_cls.evaluate + def _closure_nncg(self): + self.optimizer.zero_grad() + with torch.autocast(device_type=self.device, + dtype=self.dtype, + enabled=self.mixed_precision): + loss, loss_normalized = self.model.solution_cls.evaluate() + + + + + + # if self.optimizer.use_grad: + grads = self.optimizer.gradient(loss) + grads = torch.where(grads != grads, torch.zeros_like(grads), grads) + + #this fellow moved to model.py since it called several times a row + #if (self.model.t-1) % self.optimizer.precond_update_frequency == 0: + # print('here t={} and freq={}'.format(self.model.t-1,self.optimizer.precond_update_frequency)) + # self.optimizer.update_preconditioner(grads) + + + self.model.cur_loss = loss_normalized if self.normalized_loss_stop else loss + + return loss, grads + + + def get_closure(self, _type: str): - if _type == 'PSO': + if _type in ('PSO', 'CSO'): return self._closure_pso elif _type == 'NGD': return self._closure_ngd + elif _type == 'NNCG': + return self._closure_nncg else: return self._closure diff --git a/tedeous/optimizers/nys_newton_cg.py b/tedeous/optimizers/nys_newton_cg.py new file mode 100644 index 00000000..bb7530a1 --- /dev/null +++ b/tedeous/optimizers/nys_newton_cg.py @@ -0,0 +1,304 @@ +"""The code is a copy from https://github.com/pratikrathore8/opt_for_pinns""" + + +import torch +from torch.optim import Optimizer +from torch.func import vmap +from functools import reduce +from torch.nn.utils import parameters_to_vector + +def _armijo(f, x, gx, dx, t, alpha=0.1, beta=0.5): + """Line search to find a step size that satisfies the Armijo condition.""" + f0 = f(x, 0, dx) + f1 = f(x, t, dx) + while f1 > f0 + alpha * t * gx.dot(dx): + t *= beta + f1 = f(x, t, dx) + return t + +def _apply_nys_precond_inv(U, S_mu_inv, mu, lambd_r, x): + """Applies the inverse of the Nystrom approximation of the Hessian to a vector.""" + z = U.T @ x + z = (lambd_r + mu) * (U @ (S_mu_inv * z)) + (x - U @ z) + return z + +def _nystrom_pcg(hess, b, x, mu, U, S, r, tol, max_iters): + """Solves a positive-definite linear system using NyströmPCG. + + `Frangella et al. Randomized Nyström Preconditioning. + SIAM Journal on Matrix Analysis and Applications, 2023. + `""" + lambd_r = S[r - 1] + S_mu_inv = (S + mu) ** (-1) + + resid = b - (hess(x) + mu * x) + with torch.no_grad(): + z = _apply_nys_precond_inv(U, S_mu_inv, mu, lambd_r, resid) + p = z.clone() + + i = 0 + + while torch.norm(resid) > tol and i < max_iters: + v = hess(p) + mu * p + with torch.no_grad(): + alpha = torch.dot(resid, z) / torch.dot(p, v) + x += alpha * p + + rTz = torch.dot(resid, z) + resid -= alpha * v + z = _apply_nys_precond_inv(U, S_mu_inv, mu, lambd_r, resid) + beta = torch.dot(resid, z) / rTz + + p = z + beta * p + + i += 1 + + if torch.norm(resid) > tol: + print(f"Warning: PCG did not converge to tolerance. Tolerance was {tol} but norm of residual is {torch.norm(resid)}") + + return x + +class NysNewtonCG(Optimizer): + """Implementation of NysNewtonCG, a damped Newton-CG method that uses Nyström preconditioning. + + `Rathore et al. Challenges in Training PINNs: A Loss Landscape Perspective. + Preprint, 2024. ` + + .. warning:: + This optimizer doesn't support per-parameter options and parameter + groups (there can be only one). + + NOTE: This optimizer is currently a beta version. + + Our implementation is inspired by the PyTorch implementation of `L-BFGS + `. + + The parameters rank and mu will probably need to be tuned for your specific problem. + If the optimizer is running very slowly, you can try one of the following: + - Increase the rank (this should increase the accuracy of the Nyström approximation in PCG) + - Reduce cg_tol (this will allow PCG to terminate with a less accurate solution) + - Reduce cg_max_iters (this will allow PCG to terminate after fewer iterations) + + Args: + params (iterable): iterable of parameters to optimize or dicts defining + parameter groups + lr (float, optional): learning rate (default: 1.0) + rank (int, optional): rank of the Nyström approximation (default: 10) + mu (float, optional): damping parameter (default: 1e-4) + chunk_size (int, optional): number of Hessian-vector products to be computed in parallel (default: 1) + cg_tol (float, optional): tolerance for PCG (default: 1e-16) + cg_max_iters (int, optional): maximum number of PCG iterations (default: 1000) + line_search_fn (str, optional): either 'armijo' or None (default: None) + verbose (bool, optional): verbosity (default: False) + + """ + def __init__(self, params, lr=1.0, rank=10, mu=1e-4, chunk_size=1, + cg_tol=1e-16, cg_max_iters=1000, line_search_fn=None, verbose=False,precond_update_frequency=20,eigencdecomp_shift_attepmt_count=20): + + defaults = dict(lr=lr, rank=rank, chunk_size=chunk_size, mu=mu, cg_tol=cg_tol, + cg_max_iters=cg_max_iters, line_search_fn=line_search_fn, precond_update_frequency=precond_update_frequency,eigencdecomp_shift_attepmt_count=eigencdecomp_shift_attepmt_count) + self.rank = rank + self.mu = mu + self.chunk_size = chunk_size + self.cg_tol = cg_tol + self.cg_max_iters = cg_max_iters + self.line_search_fn = line_search_fn + self.precond_update_frequency=precond_update_frequency + self.eigencdecomp_shift_attepmt_count=eigencdecomp_shift_attepmt_count + + self.verbose = verbose + self.U = None + self.S = None + self.n_iters = 0 + super(NysNewtonCG, self).__init__(params, defaults) + + if len(self.param_groups) > 1: + raise ValueError( + "NysNewtonCG doesn't currently support per-parameter options (parameter groups)") + + if self.line_search_fn is not None and self.line_search_fn != 'armijo': + raise ValueError("NysNewtonCG only supports Armijo line search") + + self._params = self.param_groups[0]['params'] + self._params_list = list(self._params) + self._numel_cache = None + + + def gradient(self, loss: torch.Tensor) -> torch.Tensor: + """ Calculation of loss gradient by model parameters (NN, autograd) + or model values (mat). + + Args: + loss (torch.Tensor): result of loss calculation. + + Returns: + torch.Tensor: calculated gradient vector. + """ + dl_dparam = torch.autograd.grad(loss, self._params, create_graph=True) + + grads = parameters_to_vector(dl_dparam) + + return grads + + + def step(self, closure=None): + """Perform a single optimization step. + + Args: + closure (callable, optional): A closure that reevaluates the model and returns (i) the loss and (ii) gradient w.r.t. the parameters. + The closure can compute the gradient w.r.t. the parameters by calling torch.autograd.grad on the loss with create_graph=True. + """ + if self.n_iters == 0: + # Store the previous direction for warm starting PCG + self.old_dir = torch.zeros( + self._numel(), device=self._params[0].device) + + # NOTE: The closure must return both the loss and the gradient + loss = None + if closure is not None: + with torch.enable_grad(): + loss, grad_tuple = closure() + + g = torch.cat([grad.view(-1) for grad in grad_tuple if grad is not None]) + + # One step update + for group_idx, group in enumerate(self.param_groups): + def hvp_temp(x): + return self._hvp(g, self._params_list, x) + + # Calculate the Newton direction + d = _nystrom_pcg(hvp_temp, g, self.old_dir, + self.mu, self.U, self.S, self.rank, self.cg_tol, self.cg_max_iters) + + # Store the previous direction for warm starting PCG + self.old_dir = d + + # Check if d is a descent direction + if torch.dot(d, g) <= 0: + print("Warning: d is not a descent direction") + + if self.line_search_fn == 'armijo': + x_init = self._clone_param() + + def obj_func(x, t, dx): + self._add_grad(t, dx) + loss = float(closure()[0]) + self._set_param(x) + return loss + + # Use -d for convention + t = _armijo(obj_func, x_init, g, -d, group['lr']) + else: + t = group['lr'] + + self.state[group_idx]['t'] = t + + # update parameters + ls = 0 + for p in group['params']: + np = torch.numel(p) + dp = d[ls:ls+np].view(p.shape) + ls += np + p.data.add_(-dp, alpha=t) + + self.n_iters += 1 + + return loss, g + + def update_preconditioner(self, grad_tuple): + """Update the Nystrom approximation of the Hessian. + + Args: + grad_tuple (tuple): tuple of Tensors containing the gradients of the loss w.r.t. the parameters. + This tuple can be obtained by calling torch.autograd.grad on the loss with create_graph=True. + """ + + # Flatten and concatenate the gradients + gradsH = torch.cat([gradient.view(-1) + for gradient in grad_tuple if gradient is not None]) + + # Generate test matrix (NOTE: This is transposed test matrix) + p = gradsH.shape[0] + Phi = torch.randn( + (self.rank, p), device=gradsH.device) / (p ** 0.5) + Phi = torch.linalg.qr(Phi.t(), mode='reduced')[0].t() + + Y = self._hvp_vmap(gradsH, self._params_list)(Phi) + + # Calculate shift + shift = torch.finfo(Y.dtype).eps + Y_shifted = Y + shift * Phi + + # Calculate Phi^T * H * Phi (w/ shift) for Cholesky + choleskytarget = torch.mm(Y_shifted, Phi.t()) + + # Perform Cholesky, if fails, do eigendecomposition + # The new shift is the abs of smallest eigenvalue (negative) plus the original shift + try: + C = torch.linalg.cholesky(choleskytarget) + except: + shift_attempt_count=0 + while shift_attempt_count \ - Union[torch.optim.Adam, torch.optim.SGD, torch.optim.LBFGS, PSO]: + Union[torch.optim.Adam, torch.optim.SGD, torch.optim.LBFGS, PSO, CSO, NysNewtonCG]: """ Setting optimizer. If optimizer is string type, it will get default settings, or it may be custom optimizer defined by user. @@ -41,10 +43,15 @@ def optimizer_choice( torch_optim = torch.optim.SGD elif self.optimizer == 'LBFGS': torch_optim = torch.optim.LBFGS + elif self.optimizer == 'NNCG': + torch_optim = NysNewtonCG elif self.optimizer == 'PSO': torch_optim = PSO elif self.optimizer == 'NGD': torch_optim = NGD + elif self.optimizer == 'CSO': + torch_optim = CSO + if mode in ('NN', 'autograd'): optimizer = torch_optim(model.parameters(), **self.params) diff --git a/tedeous/version.py b/tedeous/version.py index b35bf60f..8a7c7e58 100644 --- a/tedeous/version.py +++ b/tedeous/version.py @@ -1 +1 @@ -__version__ = '0.4.6' \ No newline at end of file +__version__ = '0.4.8' \ No newline at end of file