Source code for pybamm.solvers.casadi_solver

#
# CasADi Solver class
#
import casadi
import pybamm
import numpy as np
import warnings
from scipy.interpolate import interp1d
from .lrudict import LRUDict


[docs] class CasadiSolver(pybamm.BaseSolver): """Solve a discretised model, using CasADi. Parameters ---------- mode : str How to solve the model (default is "safe"): - "fast": perform direct integration, without accounting for events. \ Recommended when simulating a drive cycle or other simulation where \ no events should be triggered. - "fast with events": perform direct integration of the whole timespan, \ then go back and check where events were crossed. Experimental only. - "safe": perform step-and-check integration in global steps of size \ dt_max, checking whether events have been triggered. Recommended for \ simulations of a full charge or discharge. - "safe without grid": perform step-and-check integration step-by-step. \ Takes more steps than "safe" mode, but doesn't require creating the grid \ each time, so may be faster. Experimental only. rtol : float, optional The relative tolerance for the solver (default is 1e-6). atol : float, optional The absolute tolerance for the solver (default is 1e-6). root_method : str or pybamm algebraic solver class, optional The method to use to find initial conditions (for DAE solvers). If a solver class, must be an algebraic solver class. If "casadi", the solver uses casadi's Newton rootfinding algorithm to find initial conditions. Otherwise, the solver uses 'scipy.optimize.root' with method specified by 'root_method' (e.g. "lm", "hybr", ...) root_tol : float, optional The tolerance for root-finding. Default is 1e-6. max_step_decrease_count : float, optional The maximum number of times step size can be decreased before an error is raised. Default is 5. dt_max : float, optional The maximum global step size (in seconds) used in "safe" mode. If None the default value is 600 seconds. extrap_tol : float, optional The tolerance to assert whether extrapolation occurs or not. Default is 0. extra_options_setup : dict, optional Any options to pass to the CasADi integrator when creating the integrator. Please consult `CasADi documentation <https://tinyurl.com/y5rk76os>`_ for details. Some useful options: - "max_num_steps": Maximum number of integrator steps - "print_stats": Print out statistics after integration extra_options_call : dict, optional Any options to pass to the CasADi integrator when calling the integrator. Please consult `CasADi documentation <https://tinyurl.com/y5rk76os>`_ for details. return_solution_if_failed_early : bool, optional Whether to return a Solution object if the solver fails to reach the end of the simulation, but managed to take some successful steps. Default is False. perturb_algebraic_initial_conditions : bool, optional Whether to perturb algebraic initial conditions to avoid a singularity. This can sometimes slow down the solver, but is kept True as default for "safe" mode as it seems to be more robust (False by default for other modes). integrators_maxcount : int, optional The maximum number of integrators that the solver will retain before ejecting past integrators using an LRU methodology. A value of 0 or None leaves the number of integrators unbound. Default is 100. """ def __init__( self, mode="safe", rtol=1e-6, atol=1e-6, root_method="casadi", root_tol=1e-6, max_step_decrease_count=5, dt_max=None, extrap_tol=None, extra_options_setup=None, extra_options_call=None, return_solution_if_failed_early=False, perturb_algebraic_initial_conditions=None, integrators_maxcount=100, ): super().__init__( "problem dependent", rtol, atol, root_method, root_tol, extrap_tol, ) if mode in ["safe", "fast", "fast with events", "safe without grid"]: self.mode = mode else: raise ValueError( f"invalid mode '{mode}'. Must be 'safe', for solving with events, " "'fast', for solving quickly without events, or 'safe without grid' or " "'fast with events' (both experimental)" ) self.max_step_decrease_count = max_step_decrease_count self.dt_max = dt_max or 600 self.extra_options_setup = extra_options_setup or {} self.extra_options_call = extra_options_call or {} self.return_solution_if_failed_early = return_solution_if_failed_early self._on_extrapolation = "error" # Decide whether to perturb algebraic initial conditions, True by default for # "safe" mode, False by default for other modes if perturb_algebraic_initial_conditions is None: if mode == "safe": self.perturb_algebraic_initial_conditions = True else: self.perturb_algebraic_initial_conditions = False else: self.perturb_algebraic_initial_conditions = ( perturb_algebraic_initial_conditions ) self.name = f"CasADi solver with '{mode}' mode" # Initialize self.integrators_maxcount = integrators_maxcount self.integrators = LRUDict(maxsize=self.integrators_maxcount) self.integrator_specs = LRUDict(maxsize=self.integrators_maxcount) self.y_sols = {} pybamm.citations.register("Andersson2019") def _integrate(self, model, t_eval, inputs_dict=None): """ Solve a DAE model defined by residuals with initial conditions y0. Parameters ---------- model : :class:`pybamm.BaseModel` The model whose solution to calculate. t_eval : numeric type The times at which to compute the solution inputs_dict : dict, optional Any input parameters to pass to the model when solving """ # Record whether there are any symbolic inputs inputs_dict = inputs_dict or {} # convert inputs to casadi format inputs = casadi.vertcat(*[x for x in inputs_dict.values()]) if self.mode in ["fast", "fast with events"] or not model.events: if not model.events: pybamm.logger.info("No events found, running fast mode") if self.mode == "fast with events": # Create the integrator with an event switch that will set the rhs to # zero when voltage limits are crossed use_event_switch = True else: use_event_switch = False # Create an integrator with the grid (we just need to do this once) self.create_integrator( model, inputs, t_eval, use_event_switch=use_event_switch ) solution = self._run_integrator( model, model.y0, inputs_dict, inputs, t_eval ) # Check if the sign of an event changes, if so find an accurate # termination point and exit solution = self._solve_for_event(solution) solution.check_ys_are_not_too_large() return solution elif self.mode in ["safe", "safe without grid"]: y0 = model.y0 # Step-and-check t = t_eval[0] t_f = t_eval[-1] pybamm.logger.debug(f"Start solving {model.name} with {self.name}") if self.mode == "safe without grid": # in "safe without grid" mode, # create integrator once, without grid, # to avoid having to create several times self.create_integrator(model, inputs) # Initialize solution solution = pybamm.Solution( np.array([t]), y0, model, inputs_dict, sensitivities=False, ) solution.solve_time = 0 solution.integration_time = 0 use_grid = False else: solution = None use_grid = True # Try to integrate in global steps of size dt_max. Note: dt_max must # be at least as big as the the biggest step in t_eval (multiplied # by some tolerance, here 1.01) to avoid an empty integration window below dt_max = self.dt_max dt_eval_max = np.max(np.diff(t_eval)) * 1.01 if dt_max < dt_eval_max: pybamm.logger.debug( "Setting dt_max to be as big as the largest step in " f"t_eval ({dt_eval_max})" ) dt_max = dt_eval_max termination_due_to_small_dt = False first_ts_solved = False while t < t_f: # Step solved = False count = 0 dt = dt_max while not solved: # Get window of time to integrate over (so that we return # all the points in t_eval, not just t and t+dt) t_window = np.concatenate( ([t], t_eval[(t_eval > t) & (t_eval < t + dt)]) ) # Sometimes near events the solver fails between two time # points in t_eval (i.e. no points t < t_i < t+dt for t_i # in t_eval), so we simply integrate from t to t+dt if len(t_window) == 1: t_window = np.array([t, t + dt]) if self.mode == "safe": # update integrator with the grid self.create_integrator(model, inputs, t_window) # Try to solve with the current global step, if it fails then # halve the step size and try again. try: pybamm.logger.debug( "Running integrator for " f"{t_window[0]:.2f} < t < {t_window[-1]:.2f}" ) current_step_sol = self._run_integrator( model, y0, inputs_dict, inputs, t_window, use_grid=use_grid, extract_sensitivities_in_solution=False, ) first_ts_solved = True solved = True except pybamm.SolverError as error: pybamm.logger.debug("Failed, halving step size") dt /= 2 count += 1 # also reduce maximum step size for future global steps, # but skip them in the beginning # sometimes, for the first integrator smaller timesteps are # needed, but this won't affect the global timesteps. The # global timestep will only be reduced after the first timestep. if first_ts_solved: dt_max = dt if count > self.max_step_decrease_count: message = ( "Maximum number of decreased steps occurred at " f"t={t} (final SolverError: '{error}'). " "For a full solution try reducing dt_max (currently, " f"dt_max={dt_max}) and/or reducing the size of the " "time steps or period of the experiment." ) if first_ts_solved and self.return_solution_if_failed_early: warnings.warn(message, pybamm.SolverWarning) termination_due_to_small_dt = True break else: raise pybamm.SolverError( message + " Set `return_solution_if_failed_early=True` to " "return the solution object up to the point where " "failure occured." ) if termination_due_to_small_dt: break # Check if the sign of an event changes, if so find an accurate # termination point and exit current_step_sol = self._solve_for_event(current_step_sol) # assign temporary solve time current_step_sol.solve_time = np.nan # append solution from the current step to solution solution = solution + current_step_sol if current_step_sol.termination == "event": break else: # update time as time # from which to start the new casadi integrator t = t_window[-1] # update y0 as initial_values # from which to start the new casadi integrator y0 = solution.all_ys[-1][:, -1] # now we extract sensitivities from the solution if bool(model.calculate_sensitivities): solution.sensitivities = True solution.check_ys_are_not_too_large() return solution def _solve_for_event(self, coarse_solution): """ Check if the sign of an event changes, if so find an accurate termination point and exit Locate the event time using a root finding algorithm and event state using interpolation. The solution is then truncated so that only the times up to the event are returned """ pybamm.logger.debug("Solving for events") model = coarse_solution.all_models[-1] inputs_dict = coarse_solution.all_inputs[-1] inputs = casadi.vertcat(*[x for x in inputs_dict.values()]) def find_t_event(sol, typ): # Check most recent y to see if any events have been crossed if model.terminate_events_eval: y_last = sol.all_ys[-1][:, -1] crossed_events = np.sign( np.concatenate( [ event(sol.t[-1], y_last, inputs) for event in model.terminate_events_eval ] ) - 1e-5 ) else: crossed_events = np.sign([]) # Return None if no events have been triggered if (crossed_events == 1).all(): return None, None, None # get the index of the events that have been crossed event_idx = np.where(crossed_events != 1)[0] active_events = [model.terminate_events_eval[i] for i in event_idx] # loop over events to compute the time at which they were triggered t_events = [None] * len(active_events) event_idcs_lower = [None] * len(active_events) for i, event in enumerate(active_events): # Implement our own bisection algorithm for speed # This is used to find the time range in which the event is triggered # Evaluations of the "event" function are (relatively) expensive f_eval = {} def f(idx): try: return f_eval[idx] except KeyError: # We take away 1e-5 to deal with the case where the event sits # exactly on zero, as can happen when the event switch is used # (fast with events mode) f_eval[idx] = event(sol.t[idx], sol.y[:, idx], inputs) - 1e-5 return f_eval[idx] def integer_bisect(): a_n = 0 b_n = len(sol.t) - 1 for _ in range(len(sol.t)): if a_n + 1 == b_n: return a_n m_n = (a_n + b_n) // 2 f_m_n = f(m_n) if np.isnan(f_m_n): a_n = a_n b_n = m_n elif f_m_n < 0: a_n = a_n b_n = m_n elif f_m_n > 0: a_n = m_n b_n = b_n event_idx_lower = integer_bisect() if typ == "window": event_idcs_lower[i] = event_idx_lower elif typ == "exact": # Linear interpolation between the two indices to find the root time # We could do cubic interpolation here instead but it would be # slower t_lower = sol.t[event_idx_lower] t_upper = sol.t[event_idx_lower + 1] event_lower = abs(f(event_idx_lower)) event_upper = abs(f(event_idx_lower + 1)) t_events[i] = (event_lower * t_upper + event_upper * t_lower) / ( event_lower + event_upper ) if typ == "window": event_idx_lower = np.nanmin(event_idcs_lower) return event_idx_lower, None, None elif typ == "exact": # t_event is the earliest event triggered t_event = np.nanmin(t_events) # create interpolant to evaluate y in the current integration # window y_sol = interp1d(sol.t, sol.y, kind="linear") y_event = y_sol(t_event) closest_event_idx = event_idx[np.nanargmin(t_events)] return t_event, y_event, closest_event_idx # Find the interval in which the event was triggered event_idx_lower, _, _ = find_t_event(coarse_solution, "window") # Return the existing solution if no events have been triggered if event_idx_lower is None: # Flag "final time" for termination coarse_solution.termination = "final time" return coarse_solution # If events have been triggered, we solve for a dense window in the interval # where the event was triggered, then find the precise location of the event # Solve again with a more dense idx_window, starting from the start of the # window where the event was triggered t_window_event_dense = np.linspace( coarse_solution.t[event_idx_lower], coarse_solution.t[event_idx_lower + 1], 100, ) if self.mode == "safe without grid": use_grid = False else: self.create_integrator(model, inputs, t_window_event_dense) use_grid = True y0 = coarse_solution.y[:, event_idx_lower] dense_step_sol = self._run_integrator( model, y0, inputs_dict, inputs, t_window_event_dense, use_grid=use_grid, extract_sensitivities_in_solution=False, ) # Find the exact time at which the event was triggered t_event, y_event, closest_event_idx = find_t_event(dense_step_sol, "exact") # If this returns None, no event was crossed in dense_step_sol. This can happen # if the event crossing was right at the end of the interval in the coarse # solution. In this case, return the t and y from the end of the interval # (i.e. next point in the coarse solution) if y_event is None: # pragma: no cover # This is extremely rare, it's difficult to find a test that triggers this # hence no coverage check t_event = coarse_solution.t[event_idx_lower + 1] y_event = coarse_solution.y[:, event_idx_lower + 1].full().flatten() # Return solution truncated at the first coarse event time # Also assign t_event t_sol = coarse_solution.t[: event_idx_lower + 1] y_sol = coarse_solution.y[:, : event_idx_lower + 1] solution = pybamm.Solution( t_sol, y_sol, model, inputs_dict, np.array([t_event]), y_event[:, np.newaxis], "event", sensitivities=bool(model.calculate_sensitivities), ) solution.integration_time = ( coarse_solution.integration_time + dense_step_sol.integration_time ) solution.closest_event_idx = closest_event_idx return solution
[docs] def create_integrator(self, model, inputs, t_eval=None, use_event_switch=False): """ Method to create a casadi integrator object. If t_eval is provided, the integrator uses t_eval to make the grid. Otherwise, the integrator has grid [0,1]. """ pybamm.logger.debug("Creating CasADi integrator") # Use grid if t_eval is given use_grid = t_eval is not None if use_grid is True: t_eval_shifted = t_eval - t_eval[0] t_eval_shifted_rounded = np.round(t_eval_shifted, decimals=12).tobytes() # Only set up problem once if model in self.integrators: # If we're not using the grid, we don't need to change the integrator if use_grid is False: return self.integrators[model]["no grid"] # Otherwise, create new integrator with an updated grid # We don't need to update the grid if reusing the same t_eval # (up to a shift by a constant) else: if t_eval_shifted_rounded in self.integrators[model]: return self.integrators[model][t_eval_shifted_rounded] else: method, problem, options, time_args = self.integrator_specs[model] time_args = [t_eval_shifted[0], t_eval_shifted[1:]] integrator = casadi.integrator( "F", method, problem, *time_args, options ) self.integrators[model][t_eval_shifted_rounded] = integrator return integrator else: rhs = model.casadi_rhs algebraic = model.casadi_algebraic options = { "show_eval_warnings": False, **self.extra_options_setup, "reltol": self.rtol, "abstol": self.atol, } # set up and solve t = casadi.MX.sym("t") p = casadi.MX.sym("p", inputs.shape[0]) y0 = model.y0 y_diff = casadi.MX.sym("y_diff", rhs(0, y0, p).shape[0]) y_alg = casadi.MX.sym("y_alg", algebraic(0, y0, p).shape[0]) y_full = casadi.vertcat(y_diff, y_alg) if use_grid is False: time_args = [] # rescale time t_min = casadi.MX.sym("t_min") t_max = casadi.MX.sym("t_max") t_max_minus_t_min = t_max - t_min t_scaled = t_min + (t_max - t_min) * t # add time limits as inputs p_with_tlims = casadi.vertcat(p, t_min, t_max) else: time_args = [t_eval_shifted[0], t_eval_shifted[1:]] # rescale time t_min = casadi.MX.sym("t_min") # Set dummy parameters for consistency with rescaled time t_max_minus_t_min = 1 t_scaled = t_min + t p_with_tlims = casadi.vertcat(p, t_min) # define the event switch as the point when an event is crossed # we don't do this for ODE models # see #1082 event_switch = 1 if use_event_switch is True and not algebraic(0, y0, p).is_empty(): for event in model.casadi_switch_events: event_switch *= event(t_scaled, y_full, p) problem = { "t": t, "x": y_diff, # rescale rhs by (t_max - t_min) "ode": (t_max_minus_t_min) * rhs(t_scaled, y_full, p) * event_switch, "p": p_with_tlims, } if algebraic(0, y0, p).is_empty(): method = "cvodes" else: method = "idas" problem.update( { "z": y_alg, "alg": algebraic(t_scaled, y_full, p), } ) integrator = casadi.integrator("F", method, problem, *time_args, options) self.integrator_specs[model] = method, problem, options, time_args if use_grid is False: self.integrators[model] = {"no grid": integrator} else: self.integrators[model] = {t_eval_shifted_rounded: integrator} return integrator
def _run_integrator( self, model, y0, inputs_dict, inputs, t_eval, use_grid=True, extract_sensitivities_in_solution=None, ): """ Run the integrator. Parameters ---------- model : :class:`pybamm.BaseModel` The model whose solution to calculate. y0: casadi vector of initial conditions inputs_dict : dict, optional Any input parameters to pass to the model when solving inputs: Casadi vector of inputs t_eval : numeric type The times at which to compute the solution use_grid: bool, optional Determines whether the casadi solver uses a grid or rescales time to (0,1) extract_sensitivities_in_solution: bool or None If None, then the sensitivities are extracted within the :class:`pybamm.Solution` object returned, only if present in the solution. Setting to True or False will override this behaviour, forcing the sensitivities to be extracted or not (it is up to the caller to determine if the sensitivities are in fact present) """ pybamm.logger.debug("Running CasADi integrator") # are we solving explicit forward equations? explicit_sensitivities = bool(model.calculate_sensitivities) # by default we extract sensitivities in the solution if we # are calculating the sensitivities if extract_sensitivities_in_solution is None: extract_sensitivities_in_solution = explicit_sensitivities if use_grid is True: pybamm.logger.spam("Calculating t_eval_shifted") t_eval_shifted = t_eval - t_eval[0] t_eval_shifted_rounded = np.round(t_eval_shifted, decimals=12).tobytes() pybamm.logger.spam("Finished calculating t_eval_shifted") integrator = self.integrators[model][t_eval_shifted_rounded] else: integrator = self.integrators[model]["no grid"] len_rhs = model.concatenated_rhs.size len_alg = model.concatenated_algebraic.size # Check y0 to see if it includes sensitivities if explicit_sensitivities: num_parameters = model.len_rhs_sens // model.len_rhs len_rhs = len_rhs * (num_parameters + 1) len_alg = len_alg * (num_parameters + 1) y0_diff = y0[:len_rhs] y0_alg_exact = y0[len_rhs:] if self.perturb_algebraic_initial_conditions and len_alg > 0: # Add a tiny perturbation to the algebraic initial conditions # For some reason this helps with convergence # The actual value of the initial conditions for the algebraic variables # doesn't matter y0_alg = y0_alg_exact * (1 + 1e-6 * casadi.DM(np.random.rand(len_alg))) else: y0_alg = y0_alg_exact pybamm.logger.spam("Finished preliminary setup for integrator run") # Solve # Try solving if use_grid is True: t_min = t_eval[0] inputs_with_tmin = casadi.vertcat(inputs, t_min) # Call the integrator once, with the grid timer = pybamm.Timer() pybamm.logger.debug("Calling casadi integrator") try: casadi_sol = integrator( x0=y0_diff, z0=y0_alg, p=inputs_with_tmin, **self.extra_options_call ) except RuntimeError as error: # If it doesn't work raise error pybamm.logger.debug(f"Casadi integrator failed with error {error}") raise pybamm.SolverError(error.args[0]) pybamm.logger.debug("Finished casadi integrator") integration_time = timer.time() # Manually add initial conditions and concatenate x_sol = casadi.horzcat(y0_diff, casadi_sol["xf"]) if len_alg > 0: z_sol = casadi.horzcat(y0_alg_exact, casadi_sol["zf"]) y_sol = casadi.vertcat(x_sol, z_sol) else: y_sol = x_sol sol = pybamm.Solution( t_eval, y_sol, model, inputs_dict, sensitivities=extract_sensitivities_in_solution, check_solution=False, ) sol.integration_time = integration_time return sol else: # Repeated calls to the integrator x = y0_diff z = y0_alg_exact y_diff = x y_alg = z for i in range(len(t_eval) - 1): t_min = t_eval[i] t_max = t_eval[i + 1] inputs_with_tlims = casadi.vertcat(inputs, t_min, t_max) timer = pybamm.Timer() try: casadi_sol = integrator( x0=x, z0=z, p=inputs_with_tlims, **self.extra_options_call ) except RuntimeError as error: # If it doesn't work raise error pybamm.logger.debug(f"Casadi integrator failed with error {error}") raise pybamm.SolverError(error.args[0]) integration_time = timer.time() x = casadi_sol["xf"] z = casadi_sol["zf"] y_diff = casadi.horzcat(y_diff, x) if not z.is_empty(): y_alg = casadi.horzcat(y_alg, z) if z.is_empty(): y_sol = y_diff else: y_sol = casadi.vertcat(y_diff, y_alg) sol = pybamm.Solution( t_eval, y_sol, model, inputs_dict, sensitivities=extract_sensitivities_in_solution, check_solution=False, ) sol.integration_time = integration_time return sol