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| import numpy as np | |
| from scipy.integrate import solve_ivp | |
| # Constants for integration | |
| DEFAULT_SOLVER_METHOD = 'DOP853' | |
| DEFAULT_TOLERANCE = 1e-9 | |
| class BaseSolver: | |
| """ | |
| Base class for ODE solvers. | |
| """ | |
| def solve(self, rhs, x0, t_eval): | |
| raise NotImplementedError("Subclasses must implement solve method") | |
| class SciPySolver(BaseSolver): | |
| """ | |
| Solver using scipy.integrate.solve_ivp | |
| """ | |
| def __init__(self, method=DEFAULT_SOLVER_METHOD, rtol=DEFAULT_TOLERANCE, atol=DEFAULT_TOLERANCE): | |
| self.method = method | |
| self.rtol = rtol | |
| self.atol = atol | |
| def solve(self, rhs, x0, t_eval): | |
| """ | |
| Solve ODE using scipy.integrate.solve_ivp | |
| Args: | |
| rhs: Right-hand side function of the ODE system | |
| x0: Initial conditions | |
| t_eval: Time points to evaluate the solution | |
| Returns: | |
| Tuple of (solution_successful, x_solution, y_solution) | |
| """ | |
| try: | |
| sol = solve_ivp(rhs, (t_eval[0], t_eval[-1]), x0, method=self.method, | |
| rtol=self.rtol, atol=self.atol, t_eval=t_eval) | |
| if sol.success: | |
| return True, sol.y[0], sol.y[1] | |
| else: | |
| return False, None, None | |
| except Exception: | |
| return False, None, None | |
| class NeuralFlowSolver(BaseSolver): | |
| """ | |
| Neural network solver that learns the vector field (x, y) -> (dx/dt, dy/dt) | |
| """ | |
| def __init__(self, model=None, epochs=2000, lr=1e-3): | |
| self.model = model | |
| self.epochs = epochs | |
| self.lr = lr | |
| self.trained = False | |
| def train(self, rhs, x0, t_train, y_train): | |
| """ | |
| Train the neural network to learn the vector field | |
| Args: | |
| rhs: Right-hand side function of the ODE system (used for generating training data) | |
| x0: Initial conditions | |
| t_train: Time points for training | |
| y_train: Target values for training (derivatives) | |
| """ | |
| # This is a placeholder implementation - a real implementation would involve | |
| # training a neural network to approximate the vector field | |
| # For now, we'll just store the target data | |
| self.t_train = t_train | |
| self.y_train = y_train | |
| self.trained = True | |
| def solve(self, rhs, x0, t_eval): | |
| """ | |
| Solve ODE using the trained neural network | |
| Args: | |
| rhs: Right-hand side function of the ODE system | |
| x0: Initial conditions | |
| t_eval: Time points to evaluate the solution | |
| Returns: | |
| Tuple of (solution_successful, x_solution, y_solution) | |
| """ | |
| if not self.trained: | |
| raise ValueError("Model must be trained before solving") | |
| # This is a placeholder implementation | |
| # A real implementation would use the trained neural network to solve the ODE | |
| # For now, we'll fall back to scipy solver if model is not implemented | |
| try: | |
| sol = solve_ivp(rhs, (t_eval[0], t_eval[-1]), x0, method=DEFAULT_SOLVER_METHOD, t_eval=t_eval) | |
| if sol.success: | |
| return True, sol.y[0], sol.y[1] | |
| else: | |
| return False, None, None | |
| except Exception: | |
| return False, None, None |