adding gradient checks for HyperViscoelastiticy; needs to be updated

optimism/inverse/test/test_HyperViscoelastic_gradient_checks.py

@@ -0,0 +1,241 @@
+import unittest
+
+import jax
+import jax.numpy as np
+import numpy as onp
+from scipy.sparse import linalg
+
+from optimism import EquationSolver as EqSolver
+from optimism import QuadratureRule
+from optimism import FunctionSpace
+from optimism import Mechanics
+from optimism import Objective
+from optimism import Mesh
+from optimism.material import HyperViscoelastic as Visco
+
+from optimism.inverse.test.FiniteDifferenceFixture import FiniteDifferenceFixture
+
+from optimism.Timer import Timer
+
+# misc. modules in test directory for now while I test
+import adjoint_problem_function_space as AdjointFunctionSpace
+import MechanicsInverse
+
+class HyperViscoelasticGlobalMeshAdjointSolveFixture(FiniteDifferenceFixture):
+    def setUp(self):
+        dispGrad0 =  np.array([[0.4, -0.2],
+                               [-0.04, 0.68]])
+        self.initialMesh, self.U = self.create_mesh_and_disp(4,4,[0.,1.],[0.,1.],
+                                            lambda x: dispGrad0@x)
+
+        K_eq  = 1.e2
+        G_eq  = 1.0
+        G_neq_1 = 5.0
+        tau_1   = 0.1
+        props = {
+            'equilibrium bulk modulus'     : K_eq,
+            'equilibrium shear modulus'    : G_eq,
+            'non equilibrium shear modulus': G_neq_1,
+            'relaxation time'              : tau_1,
+        } 
+        self.materialModel = Visco.create_material_model_functions(props)
+
+        self.quadRule = QuadratureRule.create_quadrature_rule_on_triangle(degree=1)
+
+        self.EBCs = [FunctionSpace.EssentialBC(nodeSet='all_boundary', component=0),
+                FunctionSpace.EssentialBC(nodeSet='all_boundary', component=1)]
+
+        self.dt = 0.01
+        self.steps = 2
+
+    def forward_solve(self, parameters):
+        self.mesh = Mesh.construct_mesh_from_basic_data(parameters.reshape(self.initialMesh.coords.shape),\
+                                                        self.initialMesh.conns, self.initialMesh.blocks,\
+                                                        self.initialMesh.nodeSets, self.initialMesh.sideSets)
+
+        functionSpace = FunctionSpace.construct_function_space(self.mesh, self.quadRule)
+        mechFuncs = Mechanics.create_mechanics_functions(functionSpace,
+                                                         "plane strain",
+                                                         self.materialModel, 
+                                                         dt=self.dt)
+        self.dofManager = FunctionSpace.DofManager(functionSpace, 2, self.EBCs)
+        Ubc = self.dofManager.get_bc_values(self.U)
+
+        Ubc_inc = Ubc / self.steps
+        ivs = mechFuncs.compute_initial_state()
+        p = Objective.Params(bc_data=np.zeros(Ubc.shape), state_data=ivs)
+
+        def compute_energy(Uu, p):
+            U = self.dofManager.create_field(Uu, p.bc_data)
+            internalVariables = p.state_data
+            return mechFuncs.compute_strain_energy(U, internalVariables)
+
+        Uu = 0.0*self.dofManager.get_unknown_values(self.U) 
+        self.objective = Objective.Objective(compute_energy, Uu, p)
+
+        storedState = []
+        storedState.append((Uu, p))
+
+        with Timer(name="forward solve"):
+            for step in range(1, self.steps+1):
+                p = Objective.param_index_update(p, 0, step*Ubc_inc)
+                Uu = EqSolver.nonlinear_equation_solve(self.objective, Uu, p, EqSolver.get_settings(), useWarmStart=False)
+                U = self.dofManager.create_field(Uu, p.bc_data)
+                ivs = mechFuncs.compute_updated_internal_variables(U, p.state_data)
+                p = Objective.param_index_update(p, 1, ivs)
+                storedState.append((Uu, p))
+
+        return storedState
+
+    def total_work_increment(self, Uu, Uu_prev, ivs, ivs_prev, p, p_prev, coordinates):
+        coords = coordinates.reshape(self.mesh.coords.shape)
+        internal_vars = ivs.reshape(p.state_data.shape)
+        internal_vars_prev = ivs_prev.reshape(p_prev.state_data.shape)
+
+        adjoint_func_space = AdjointFunctionSpace.construct_function_space_for_adjoint(coords, self.mesh, self.quadRule)
+        mech_funcs = Mechanics.create_mechanics_functions(adjoint_func_space, mode2D='plane strain', materialModel=self.materialModel,dt=self.dt)
+
+        def energy_function_all_dofs(U, ivs):
+            return mech_funcs.compute_strain_energy(U, ivs)
+
+        nodal_forces = jax.grad(energy_function_all_dofs, argnums=0)
+
+        index = (self.mesh.nodeSets['left'], 1) # arbitrarily choosing left side nodeset for reaction force
+
+        U = self.dofManager.create_field(Uu, p.bc_data)
+        force = np.array(nodal_forces(U, internal_vars).at[index].get())
+        disp = U.at[index].get()
+
+        U_prev = self.dofManager.create_field(Uu_prev, p_prev.bc_data)
+        force_prev = np.array(nodal_forces(U_prev, internal_vars_prev).at[index].get())
+        disp_prev = U_prev.at[index].get()
+
+        return 0.5*np.tensordot((force + force_prev),(disp - disp_prev), axes=1)
+
+    def total_work_objective(self, storedState, parameters):
+        val = 0.0
+        for step in range(1, self.steps+1):
+            Uu = storedState[step][0]
+            Uu_prev = storedState[step-1][0]
+            p = storedState[step][1]
+            p_prev = storedState[step-1][1]
+            ivs = p.state_data.ravel()
+            ivs_prev = p_prev.state_data.ravel()
+
+            # Can make a vmap or lax.scan, etc. (shouldn't affect this problem because only 2 steps)
+            with Timer(name="total_work_increment"):
+                val += self.total_work_increment(Uu, Uu_prev, ivs, ivs_prev, p, p_prev, parameters)
+
+        return val
+
+    def total_work_gradient_with_adjoint(self, storedState, parameters):
+
+        def energy_function_coords(Uu, ivs_prev, p, coordinates):
+            coords = coordinates.reshape(self.mesh.coords.shape)
+            internal_vars = ivs_prev.reshape(p.state_data.shape)
+            adjoint_func_space = AdjointFunctionSpace.construct_function_space_for_adjoint(coords, self.mesh, self.quadRule)
+            mech_funcs = Mechanics.create_mechanics_functions(adjoint_func_space, mode2D='plane strain', materialModel=self.materialModel,dt=self.dt)
+            U = self.dofManager.create_field(Uu, p.bc_data)
+            return mech_funcs.compute_strain_energy(U, internal_vars)
+
+        def update_internal_vars_test(Uu, ivs_prev, p, coordinates):
+            coords = coordinates.reshape(self.mesh.coords.shape)
+            internal_vars = ivs_prev.reshape(p.state_data.shape)
+            adjoint_func_space = AdjointFunctionSpace.construct_function_space_for_adjoint(coords, self.mesh, self.quadRule)
+            mech_funcs = Mechanics.create_mechanics_functions(adjoint_func_space, mode2D='plane strain', materialModel=self.materialModel,dt=self.dt)
+            U = self.dofManager.create_field(Uu, p.bc_data)
+            return mech_funcs.compute_updated_internal_variables(U, internal_vars).ravel()
+
+        compute_df = jax.grad(self.total_work_increment, (0, 1, 2, 3, 6))
+
+        # Here I go trying some stuff out
+        #~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~#
+        # adjoint_func_space = AdjointFunctionSpace.construct_function_space_for_adjoint(parameters.reshape(self.mesh.coords.shape), self.mesh, self.quadRule)
+        functionSpace = FunctionSpace.construct_function_space(self.mesh, self.quadRule)
+        mechInverseFuncs = MechanicsInverse.create_mechanics_inverse_functions(functionSpace,
+                                                                              "plane strain",
+                                                                              self.materialModel,
+                                                                              dt=self.dt)
+
+        # ivs_update_jac_disp = jax.jit(lambda x, y, q, r, vx:
+        #                               jax.vjp(lambda z: update_internal_vars_test(z, y, q, r), x)[1](vx))
+
+        # compute_dc = jax.jacfwd(update_internal_vars_test, (0, 1, 3))
+        compute_dc = jax.jacfwd(update_internal_vars_test, (0, 3))
+
+        #~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~#
+
+        gradient = np.zeros(parameters.shape)
+        mu = np.zeros(np.prod(np.array(storedState[0][1].state_data.shape))) 
+        adjointLoad = np.zeros(storedState[0][0].shape)
+
+        for step in reversed(range(1, self.steps+1)):
+            Uu = storedState[step][0]
+            Uu_prev = storedState[step-1][0]
+            p = storedState[step][1]
+            p_prev = storedState[step-1][1]
+            ivs = p.state_data.ravel()
+            ivs_prev = p_prev.state_data.ravel()
+
+            with Timer(name="compute_dc"):
+                # dc_du, dc_dcn, dc_dx = compute_dc(Uu, ivs_prev, p, parameters)
+                dc_du, dc_dx = compute_dc(Uu, ivs_prev, p, parameters)
+                dc_dcn = mechInverseFuncs.ivs_update_jac_ivs_prev(self.dofManager.create_field(Uu, p.bc_data), ivs_prev.reshape(p_prev.state_data.shape))
+
+            with Timer(name="compute_df"):
+                df_du, df_dun, df_dc, df_dcn, df_dx = compute_df(Uu, Uu_prev, ivs, ivs_prev, p, p_prev, parameters)
+
+            with Timer(name="first mu and adjoint load updates"):
+                mu += df_dc
+                adjointLoad -= df_du
+                adjointLoad -= np.tensordot(mu, dc_du, axes=1) # mu^T dc/du
+                # adjointLoad -= ivs_update_jac_disp(Uu, ivs_prev, p, parameters, mu)[0]
+
+            with Timer(name="adjoint solve"):
+                n = self.dofManager.get_unknown_size()
+                p_objective = Objective.Params(bc_data=p.bc_data, state_data=p_prev.state_data) # remember R is a function of ivs_prev
+                self.objective.p = p_objective 
+                self.objective.update_precond(Uu) # update preconditioner for use in cg (will converge in 1 iteration as long as the preconditioner is not approximate)
+                dRdu = linalg.LinearOperator((n, n), lambda V: onp.asarray(self.objective.hessian_vec(Uu, V)))
+                dRdu_decomp = linalg.LinearOperator((n, n), lambda V: onp.asarray(self.objective.apply_precond(V)))
+                adjointVector = linalg.cg(dRdu, onp.array(adjointLoad, copy=False), tol=1e-10, atol=0.0, M=dRdu_decomp)[0]
+
+            with Timer(name="update gradient"):
+                gradient += df_dx
+                # The action dRdX * lambda (the same as lambda^T * dRdX)
+                gradient += jax.vjp(lambda z: jax.grad(energy_function_coords, 0)(Uu, ivs_prev, p, z), parameters)[1](adjointVector)[0]
+
+                # gradient += np.tensordot(mu, dc_dx, axes=1) # mu^T dc/dx
+                gradient += np.tensordot(mu, dc_dx, axes=1) # mu^T dc/dx
+
+            with Timer(name="update mu"):
+
+                # mu = np.tensordot(mu, dc_dcn, axes=1)
+                mu = np.einsum('ijk,ijkn->ijn', mu.reshape(p.state_data.shape), dc_dcn).ravel()
+
+                # The action dRdcn * lambda (the same as lambda^T * dRdcn) - Is the residual dependent on ivs_prev? Is this term needed?
+                mu += jax.vjp(lambda z: jax.grad(energy_function_coords, 0)(Uu, z, p, parameters), ivs_prev)[1](adjointVector)[0]
+                mu += df_dcn 
+
+            with Timer(name="update adjoint load"):
+                adjointLoad = -df_dun
+
+        return gradient
+
+
+    def test_gradient_with_adjoint_solve(self):
+
+        self.compute_objective_function = self.total_work_objective
+        self.compute_gradient = self.total_work_gradient_with_adjoint
+
+        initialStepSize = 1e-5
+        numSteps = 4
+
+        errors = self.compute_finite_difference_errors(initialStepSize, numSteps, self.initialMesh.coords.ravel())
+
+        self.assertFiniteDifferenceCheckHasVShape(errors)
+
+
+
+if __name__ == '__main__':
+    unittest.main()