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"zeta_1": 55, "zeta_i": 54, "zeta_psi": 57, "zeta_u_0": 57, "zeta_x": 54, "zeta_x_tlm": 54, "zeta_y_tlm": 54}, "titles": ["References and acknowledgements", "<code class=\"xref py py-mod docutils literal notranslate\"><span class=\"pre\">tlm_adjoint.adjoint</span></code>", "<code class=\"xref py py-mod docutils literal notranslate\"><span class=\"pre\">tlm_adjoint.alias</span></code>", "<code class=\"xref py py-mod docutils literal notranslate\"><span class=\"pre\">tlm_adjoint.block_system</span></code>", "<code class=\"xref py py-mod docutils literal notranslate\"><span class=\"pre\">tlm_adjoint.cached_hessian</span></code>", "<code class=\"xref py py-mod docutils literal notranslate\"><span class=\"pre\">tlm_adjoint.caches</span></code>", "<code class=\"xref py py-mod docutils literal notranslate\"><span class=\"pre\">tlm_adjoint.checkpoint_schedules.binomial</span></code>", "<code class=\"xref py py-mod docutils literal notranslate\"><span class=\"pre\">tlm_adjoint.checkpoint_schedules.checkpoint_schedules</span></code>", "<code class=\"xref py py-mod docutils literal notranslate\"><span class=\"pre\">tlm_adjoint.checkpoint_schedules.h_revolve</span></code>", "<code class=\"xref py py-mod docutils literal notranslate\"><span class=\"pre\">tlm_adjoint.checkpoint_schedules.memory</span></code>", "<code class=\"xref py py-mod docutils literal notranslate\"><span class=\"pre\">tlm_adjoint.checkpoint_schedules.mixed</span></code>", "<code class=\"xref py py-mod docutils literal notranslate\"><span class=\"pre\">tlm_adjoint.checkpoint_schedules.none</span></code>", "<code class=\"xref py py-mod docutils literal notranslate\"><span class=\"pre\">tlm_adjoint.checkpoint_schedules.periodic</span></code>", "<code class=\"xref py py-mod docutils literal notranslate\"><span class=\"pre\">tlm_adjoint.checkpoint_schedules.schedule</span></code>", "<code class=\"xref py py-mod docutils literal notranslate\"><span class=\"pre\">tlm_adjoint.checkpointing</span></code>", "<code class=\"xref py py-mod docutils literal notranslate\"><span class=\"pre\">tlm_adjoint.equation</span></code>", "<code class=\"xref py py-mod docutils literal notranslate\"><span class=\"pre\">tlm_adjoint.equations</span></code>", "<code class=\"xref py py-mod docutils literal notranslate\"><span class=\"pre\">tlm_adjoint.fenics.assembly</span></code>", "<code class=\"xref py py-mod docutils literal notranslate\"><span class=\"pre\">tlm_adjoint.fenics.backend_interface</span></code>", "<code class=\"xref py py-mod docutils literal notranslate\"><span class=\"pre\">tlm_adjoint.fenics.caches</span></code>", "<code class=\"xref py py-mod docutils literal notranslate\"><span class=\"pre\">tlm_adjoint.fenics.expr</span></code>", "<code class=\"xref py py-mod docutils literal notranslate\"><span class=\"pre\">tlm_adjoint.fenics.interpolation</span></code>", "<code class=\"xref py py-mod docutils literal notranslate\"><span class=\"pre\">tlm_adjoint.fenics.projection</span></code>", "<code class=\"xref py py-mod docutils literal notranslate\"><span class=\"pre\">tlm_adjoint.fenics.solve</span></code>", "<code class=\"xref py py-mod docutils literal notranslate\"><span class=\"pre\">tlm_adjoint.fenics.variables</span></code>", "<code class=\"xref py py-mod docutils literal notranslate\"><span class=\"pre\">tlm_adjoint.firedrake.assembly</span></code>", "<code class=\"xref py py-mod docutils literal notranslate\"><span class=\"pre\">tlm_adjoint.firedrake.assignment</span></code>", "<code class=\"xref py py-mod docutils literal notranslate\"><span class=\"pre\">tlm_adjoint.firedrake.backend_interface</span></code>", "<code class=\"xref py py-mod docutils literal notranslate\"><span class=\"pre\">tlm_adjoint.firedrake.block_system</span></code>", "<code class=\"xref py py-mod docutils literal notranslate\"><span class=\"pre\">tlm_adjoint.firedrake.caches</span></code>", "<code class=\"xref py py-mod docutils literal notranslate\"><span class=\"pre\">tlm_adjoint.firedrake.expr</span></code>", "<code class=\"xref py py-mod docutils literal notranslate\"><span class=\"pre\">tlm_adjoint.firedrake.interpolation</span></code>", "<code class=\"xref py py-mod docutils literal notranslate\"><span class=\"pre\">tlm_adjoint.firedrake.projection</span></code>", "<code class=\"xref py py-mod docutils literal notranslate\"><span class=\"pre\">tlm_adjoint.firedrake.solve</span></code>", "<code class=\"xref py py-mod docutils literal notranslate\"><span class=\"pre\">tlm_adjoint.firedrake.variables</span></code>", "<code class=\"xref py py-mod docutils literal notranslate\"><span class=\"pre\">tlm_adjoint.fixed_point</span></code>", "<code class=\"xref py py-mod docutils literal notranslate\"><span class=\"pre\">tlm_adjoint.functional</span></code>", "<code class=\"xref py py-mod docutils literal notranslate\"><span class=\"pre\">tlm_adjoint.hessian</span></code>", "<code class=\"xref py py-mod docutils literal notranslate\"><span class=\"pre\">tlm_adjoint.hessian_system</span></code>", "<code class=\"xref py py-mod docutils literal notranslate\"><span class=\"pre\">tlm_adjoint</span></code>", "<code class=\"xref py py-mod docutils literal notranslate\"><span class=\"pre\">tlm_adjoint.instructions</span></code>", "<code class=\"xref py py-mod docutils literal notranslate\"><span class=\"pre\">tlm_adjoint.interface</span></code>", "<code class=\"xref py py-mod docutils literal notranslate\"><span class=\"pre\">tlm_adjoint.jax</span></code>", "<code class=\"xref py py-mod docutils literal notranslate\"><span class=\"pre\">tlm_adjoint.linear_equation</span></code>", "<code class=\"xref py py-mod docutils literal notranslate\"><span class=\"pre\">tlm_adjoint.manager</span></code>", "<code class=\"xref py py-mod docutils literal notranslate\"><span class=\"pre\">tlm_adjoint.markers</span></code>", "<code class=\"xref py py-mod docutils literal notranslate\"><span class=\"pre\">tlm_adjoint.optimization</span></code>", "<code class=\"xref py py-mod docutils literal notranslate\"><span class=\"pre\">tlm_adjoint.overloaded_float</span></code>", "<code class=\"xref py py-mod docutils literal notranslate\"><span class=\"pre\">tlm_adjoint.storage</span></code>", "<code class=\"xref py py-mod docutils literal notranslate\"><span class=\"pre\">tlm_adjoint.tangent_linear</span></code>", "<code class=\"xref py py-mod docutils literal notranslate\"><span class=\"pre\">tlm_adjoint.tlm_adjoint</span></code>", "<code class=\"xref py py-mod docutils literal notranslate\"><span class=\"pre\">tlm_adjoint.torch</span></code>", "<code class=\"xref py py-mod docutils literal notranslate\"><span class=\"pre\">tlm_adjoint.verification</span></code>", "Dependencies", "Getting started with tlm_adjoint", "Time-independent example", "Verifying derivative calculations", "Time-dependent example", "Visualizing derivatives", "Functional minimization", "Defining custom operations", "JAX integration", "Hessian-based uncertainty quantification", "tlm_adjoint"], "titleterms": {"A": 54, "The": 55, "__init__": 60, "acknowledg": 0, "action": 58, "ad": [54, 55, 57, 60, 61], "adjoint": [0, 1, 54, 55, 57, 58], "adjoint_derivative_act": 60, "adjoint_jacobian_solv": 60, "advanc": 63, "alia": 2, "an": [54, 55, 57], "annot": 57, "approxim": 62, "assembli": [17, 25, 55], "assign": 26, "backend": 53, "backend_interfac": [18, 27], "base": 62, "binomi": [0, 6], "block_system": [3, 28], "cach": [5, 19, 29, 55], "cached_hessian": 4, "calcul": 56, "checkpoint": [0, 14, 57], "checkpoint_schedul": [6, 7, 8, 9, 10, 11, 12, 13], "cite": 0, "comput": [54, 55, 57, 62], "content": [1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52], "converg": [0, 56], "custom": 60, "data": 55, "defin": 60, "depend": [53, 57], "deriv": [54, 55, 56, 57, 58], "differenti": 0, "direct": 55, "dolfin": 0, "drop": 60, "equat": [15, 16, 60], "equationsolv": 55, "estim": 62, "exampl": [54, 55, 57, 63], "expr": [20, 30], "featur": 63, "fenic": [17, 18, 19, 20, 21, 22, 23, 24], "find": 62, "firedrak": [25, 26, 27, 28, 29, 30, 31, 32, 33, 34], "first": [56, 58], "fix": 0, "fixed_point": 35, "flag": 55, "float": 54, "forward": [55, 56, 57, 58, 59, 60, 61, 62], "forward_solv": 60, "full": 62, "function": [36, 59], "fund": 0, "get": 54, "h_revolv": 8, "hessian": [37, 55, 57, 58, 62], "hessian_system": 38, "higher": [54, 56], "independ": 55, "indic": 63, "inform": [55, 57], "instruct": 40, "integr": 61, "interest": 62, "interfac": 41, "interpol": [21, 31], "invers": [59, 62], "jax": [42, 60, 61], "licens": 63, "linear": [54, 55, 57], "linear_equ": 43, "low": 62, "manag": 44, "marker": 45, "maxim": 62, "memori": 9, "method": 60, "minim": 59, "mix": 10, "modul": [1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52], "multipl": 55, "none": 11, "oper": 60, "optim": [46, 57], "option": 53, "order": [54, 56, 58], "overloaded_float": 47, "period": 12, "point": [0, 54], "posterior": 62, "problem": [0, 55, 56, 57, 58, 59, 60, 61, 62], "project": [22, 32], "pytorch": 0, "quantif": 62, "quantiti": 62, "rank": 62, "refer": [0, 60], "remaind": [0, 56], "requir": 53, "schedul": [13, 57], "second": [54, 56], "singl": 55, "solv": [23, 33], "solver": 55, "sourc": 63, "start": 54, "static": 55, "storag": 48, "submodul": 39, "tangent": [54, 55, 57], "tangent_linear": [49, 60], "taylor": [0, 56], "test": [0, 56], "third": 54, "time": [55, 57], "tlm_adjoint": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 54, 55, 57, 60, 61, 63], "torch": 51, "tutori": 63, "uncertainti": 62, "updat": 62, "us": [54, 55, 57, 60], "variabl": [24, 34], "verif": 52, "verifi": 56, "visual": 58}})