Optimizations.cpp

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#include "Optimizations.hpp"
 
#include <polyfem/mesh/GeometryReader.hpp>
#include <jse/jse.h>
 
#include "AdjointNLProblem.hpp"
 
#include <polyfem/State.hpp>
#include <polyfem/solver/forms/adjoint_forms/SpatialIntegralForms.hpp>
#include <polyfem/solver/forms/adjoint_forms/SumCompositeForm.hpp>
#include <polyfem/solver/forms/adjoint_forms/CompositeForms.hpp>
#include <polyfem/solver/forms/adjoint_forms/TransientForm.hpp>
#include <polyfem/solver/forms/adjoint_forms/SmoothingForms.hpp>
#include <polyfem/solver/forms/adjoint_forms/AMIPSForm.hpp>
#include <polyfem/solver/forms/adjoint_forms/BarrierForms.hpp>
#include <polyfem/solver/forms/adjoint_forms/SurfaceTractionForms.hpp>
#include <polyfem/solver/forms/adjoint_forms/TargetForms.hpp>
 
#include <polyfem/solver/forms/parametrization/Parametrizations.hpp>
#include <polyfem/solver/forms/parametrization/SplineParametrizations.hpp>
 
#include <polyfem/solver/forms/adjoint_forms/ParametrizedProductForm.hpp>
 
#include <polyfem/io/OBJReader.hpp>
#include <polyfem/utils/JSONUtils.hpp>
#include <polyfem/io/MatrixIO.hpp>
 
#include <polysolve/nonlinear/BoxConstraintSolver.hpp>
 
namespace spdlog::level
{
    NLOHMANN_JSON_SERIALIZE_ENUM(
        spdlog::level::level_enum,
        {{spdlog::level::level_enum::trace, "trace"},
         {spdlog::level::level_enum::debug, "debug"},
         {spdlog::level::level_enum::info, "info"},
         {spdlog::level::level_enum::warn, "warning"},
         {spdlog::level::level_enum::err, "error"},
         {spdlog::level::level_enum::critical, "critical"},
         {spdlog::level::level_enum::off, "off"},
         {spdlog::level::level_enum::trace, 0},
         {spdlog::level::level_enum::debug, 1},
         {spdlog::level::level_enum::info, 2},
         {spdlog::level::level_enum::warn, 3},
         {spdlog::level::level_enum::err, 3},
         {spdlog::level::level_enum::critical, 4},
         {spdlog::level::level_enum::off, 5}})
}
 
namespace polyfem::solver
{
    namespace
    {
        bool load_json(const std::string &json_file, json &out)
        {
            std::ifstream file(json_file);
 
            if (!file.is_open())
                return false;
 
            file >> out;
 
            out["root_path"] = json_file;
 
            return true;
        }
    } // namespace
 
    std::shared_ptr<polysolve::nonlinear::Solver> AdjointOptUtils::make_nl_solver(const json &solver_params, const json &linear_solver_params, const double characteristic_length)
    {
        auto names = polysolve::nonlinear::Solver::available_solvers();
        if (std::find(names.begin(), names.end(), solver_params["solver"]) != names.end())
            return polysolve::nonlinear::Solver::create(solver_params, linear_solver_params, characteristic_length, adjoint_logger());
 
        names = polysolve::nonlinear::BoxConstraintSolver::available_solvers();
        if (std::find(names.begin(), names.end(), solver_params["solver"]) != names.end())
            return polysolve::nonlinear::BoxConstraintSolver::create(solver_params, linear_solver_params, characteristic_length, adjoint_logger());
 
        log_and_throw_adjoint_error("Invalid nonlinear solver name!");
    }
 
    std::shared_ptr<AdjointForm> AdjointOptUtils::create_simple_form(const std::string &obj_type, const std::string &param_type, const std::shared_ptr<State> &state, const json &args)
    {
        std::shared_ptr<AdjointForm> obj;
        VariableToSimulationGroup var2sim;
        var2sim.push_back(VariableToSimulation::create(param_type, {state}, CompositeParametrization()));
        if (obj_type == "compliance")
            obj = std::make_shared<ComplianceForm>(var2sim, *state, args);
        else if (obj_type == "acceleration")
            obj = std::make_shared<AccelerationForm>(var2sim, *state, args);
        else if (obj_type == "kinetic")
            obj = std::make_shared<AccelerationForm>(var2sim, *state, args);
        else if (obj_type == "position")
            obj = std::make_shared<PositionForm>(var2sim, *state, args);
        else if (obj_type == "stress")
            obj = std::make_shared<StressForm>(var2sim, *state, args);
        else if (obj_type == "stress_norm")
            obj = std::make_shared<StressNormForm>(var2sim, *state, args);
        else if (obj_type == "elastic_energy")
            obj = std::make_shared<ElasticEnergyForm>(var2sim, *state, args);
        else if (obj_type == "max_stress")
            obj = std::make_shared<MaxStressForm>(var2sim, *state, args);
        else if (obj_type == "volume")
            obj = std::make_shared<VolumeForm>(var2sim, *state, args);
        else if (obj_type == "min_jacobian")
            obj = std::make_shared<MinJacobianForm>(var2sim, *state);
        else if (obj_type == "AMIPS")
            obj = std::make_shared<AMIPSForm>(var2sim, *state);
        else if (obj_type == "function-target")
        {
            std::shared_ptr<TargetForm> tmp = std::make_shared<TargetForm>(var2sim, *state, args);
            tmp->set_reference(args["target_function"], args["target_function_gradient"]);
            obj = tmp;
        }
        else if (obj_type == "boundary_smoothing")
        {
            if (args["surface_selection"].is_array())
                obj = std::make_shared<BoundarySmoothingForm>(var2sim, *state, args["scale_invariant"], args["power"], args["surface_selection"].get<std::vector<int>>());
            else
                obj = std::make_shared<BoundarySmoothingForm>(var2sim, *state, args["scale_invariant"], args["power"], std::vector<int>{args["surface_selection"].get<int>()});
        }
        else
            log_and_throw_adjoint_error("Invalid simple form type {}!", obj_type);
        
        return obj;
    }
 
    std::shared_ptr<AdjointForm> AdjointOptUtils::create_form(const json &args, const VariableToSimulationGroup &var2sim, const std::vector<std::shared_ptr<State>> &states)
    {
        std::shared_ptr<AdjointForm> obj;
        if (args.is_array())
        {
            std::vector<std::shared_ptr<AdjointForm>> forms;
            for (const auto &arg : args)
                forms.push_back(create_form(arg, var2sim, states));
 
            obj = std::make_shared<SumCompositeForm>(var2sim, forms);
        }
        else
        {
            const std::string type = args["type"];
            if (type == "transient_integral")
            {
                std::shared_ptr<StaticForm> static_obj = std::dynamic_pointer_cast<StaticForm>(create_form(args["static_objective"], var2sim, states));
                if (!static_obj)
                    log_and_throw_adjoint_error("Transient integral objective must have a static objective!");
                const auto &state = states[args["state"]];
                obj = std::make_shared<TransientForm>(var2sim, state->args["time"]["time_steps"], state->args["time"]["dt"], args["integral_type"], args["steps"].get<std::vector<int>>(), static_obj);
            }
            else if (type == "proxy_transient_integral")
            {
                std::shared_ptr<StaticForm> static_obj = std::dynamic_pointer_cast<StaticForm>(create_form(args["static_objective"], var2sim, states));
                if (!static_obj)
                    log_and_throw_adjoint_error("Transient integral objective must have a static objective!");
                if (args["steps"].size() == 0)
                    log_and_throw_adjoint_error("ProxyTransientForm requires non-empty \"steps\"!");
                const auto &state = states[args["state"]];
                obj = std::make_shared<ProxyTransientForm>(var2sim, state->args["time"]["time_steps"], state->args["time"]["dt"], args["integral_type"], args["steps"].get<std::vector<int>>(), static_obj);
            }
            else if (type == "power")
            {
                std::shared_ptr<AdjointForm> obj_aux = create_form(args["objective"], var2sim, states);
                obj = std::make_shared<PowerForm>(obj_aux, args["power"]);
            }
            else if (type == "divide")
            {
                std::shared_ptr<AdjointForm> obj1 = create_form(args["objective"][0], var2sim, states);
                std::shared_ptr<AdjointForm> obj2 = create_form(args["objective"][1], var2sim, states);
                std::vector<std::shared_ptr<AdjointForm>> objs({obj1, obj2});
                obj = std::make_shared<DivideForm>(objs);
            }
            else if (type == "plus-const")
            {
                obj = std::make_shared<PlusConstCompositeForm>(create_form(args["objective"], var2sim, states), args["value"]);
            }
            else if (type == "compliance")
            {
                obj = std::make_shared<ComplianceForm>(var2sim, *(states[args["state"]]), args);
            }
            else if (type == "acceleration")
            {
                obj = std::make_shared<AccelerationForm>(var2sim, *(states[args["state"]]), args);
            }
            else if (type == "kinetic")
            {
                obj = std::make_shared<AccelerationForm>(var2sim, *(states[args["state"]]), args);
            }
            else if (type == "target")
            {
                std::shared_ptr<TargetForm> tmp = std::make_shared<TargetForm>(var2sim, *(states[args["state"]]), args);
                auto reference_cached = args["reference_cached_body_ids"].get<std::vector<int>>();
                tmp->set_reference(states[args["target_state"]], std::set(reference_cached.begin(), reference_cached.end()));
                obj = tmp;
            }
            else if (type == "displacement-target")
            {
                std::shared_ptr<TargetForm> tmp = std::make_shared<TargetForm>(var2sim, *(states[args["state"]]), args);
                Eigen::VectorXd target_displacement;
                target_displacement.setZero(states[args["state"]]->mesh->dimension());
                if (target_displacement.size() != args["target_displacement"].size())
                    log_and_throw_error("Target displacement shape must match the dimension of the simulation");
                for (int i = 0; i < target_displacement.size(); ++i)
                    target_displacement(i) = args["target_displacement"][i].get<double>();
                if (args["active_dimension"].size() > 0)
                {
                    if (target_displacement.size() != args["active_dimension"].size())
                        log_and_throw_error("Active dimension shape must match the dimension of the simulation");
                    std::vector<bool> active_dimension_mask(args["active_dimension"].size());
                    for (int i = 0; i < args["active_dimension"].size(); ++i)
                        active_dimension_mask[i] = args["active_dimension"][i].get<bool>();
                    tmp->set_active_dimension(active_dimension_mask);
                }
                tmp->set_reference(target_displacement);
                obj = tmp;
            }
            else if (type == "center-target")
            {
                obj = std::make_shared<BarycenterTargetForm>(var2sim, args, states[args["state"]], states[args["target_state"]]);
            }
            else if (type == "sdf-target")
            {
                std::shared_ptr<SDFTargetForm> tmp = std::make_shared<SDFTargetForm>(var2sim, *(states[args["state"]]), args);
                double delta = args["delta"].get<double>();
                if (!states[args["state"]]->mesh->is_volume())
                {
                    int dim = 2;
                    Eigen::MatrixXd control_points(args["control_points"].size(), dim);
                    for (int i = 0; i < control_points.rows(); ++i)
                        for (int j = 0; j < control_points.cols(); ++j)
                            control_points(i, j) = args["control_points"][i][j].get<double>();
                    Eigen::VectorXd knots(args["knots"].size());
                    for (int i = 0; i < knots.size(); ++i)
                        knots(i) = args["knots"][i].get<double>();
                    tmp->set_bspline_target(control_points, knots, delta);
                }
                else
                {
                    int dim = 3;
                    Eigen::MatrixXd control_points_grid(args["control_points_grid"].size(), dim);
                    for (int i = 0; i < control_points_grid.rows(); ++i)
                        for (int j = 0; j < control_points_grid.cols(); ++j)
                            control_points_grid(i, j) = args["control_points_grid"][i][j].get<double>();
                    Eigen::VectorXd knots_u(args["knots_u"].size());
                    for (int i = 0; i < knots_u.size(); ++i)
                        knots_u(i) = args["knots_u"][i].get<double>();
                    Eigen::VectorXd knots_v(args["knots_v"].size());
                    for (int i = 0; i < knots_v.size(); ++i)
                        knots_v(i) = args["knots_v"][i].get<double>();
                    tmp->set_bspline_target(control_points_grid, knots_u, knots_v, delta);
                }
 
                obj = tmp;
            }
            else if (type == "mesh-target")
            {
                std::shared_ptr<MeshTargetForm> tmp = std::make_shared<MeshTargetForm>(var2sim, *(states[args["state"]]), args);
                double delta = args["delta"].get<double>();
                Eigen::MatrixXd V;
                Eigen::MatrixXi E, F;
                bool read = polyfem::io::OBJReader::read(args["mesh_path"], V, E, F);
                if (!read)
                    log_and_throw_error(fmt::format("Could not read mesh! {}", args["mesh"]));
                tmp->set_surface_mesh_target(V, F, delta);
                obj = tmp;
            }
            else if (type == "function-target")
            {
                std::shared_ptr<TargetForm> tmp = std::make_shared<TargetForm>(var2sim, *(states[args["state"]]), args);
                tmp->set_reference(args["target_function"], args["target_function_gradient"]);
                obj = tmp;
            }
            else if (type == "node-target")
            {
                obj = std::make_shared<NodeTargetForm>(*(states[args["state"]]), var2sim, args);
            }
            else if (type == "min-dist-target")
            {
                obj = std::make_shared<MinTargetDistForm>(var2sim, args["steps"], args["target"], args, states[args["state"]]);
            }
            else if (type == "position")
            {
                obj = std::make_shared<PositionForm>(var2sim, *(states[args["state"]]), args);
            }
            else if (type == "stress")
            {
                obj = std::make_shared<StressForm>(var2sim, *(states[args["state"]]), args);
            }
            else if (type == "stress_norm")
            {
                obj = std::make_shared<StressNormForm>(var2sim, *(states[args["state"]]), args);
            }
            else if (type == "elastic_energy")
            {
                obj = std::make_shared<ElasticEnergyForm>(var2sim, *(states[args["state"]]), args);
            }
            else if (type == "quadratic_contact_force_norm")
            {
                obj = std::make_shared<ProxyContactForceForm>(var2sim, *(states[args["state"]]), args["dhat"], true, args);
            }
            else if (type == "log_contact_force_norm")
            {
                obj = std::make_shared<ProxyContactForceForm>(var2sim, *(states[args["state"]]), args["dhat"], false, args);
            }
            else if (type == "max_stress")
            {
                obj = std::make_shared<MaxStressForm>(var2sim, *(states[args["state"]]), args);
            }
            else if (type == "volume")
            {
                obj = std::make_shared<VolumeForm>(var2sim, *(states[args["state"]]), args);
            }
            else if (type == "soft_constraint")
            {
                std::vector<std::shared_ptr<AdjointForm>> forms({create_form(args["objective"], var2sim, states)});
                Eigen::VectorXd bounds = args["soft_bound"];
                obj = std::make_shared<InequalityConstraintForm>(forms, bounds, args["power"]);
            }
            else if (type == "min_jacobian")
            {
                obj = std::make_shared<MinJacobianForm>(var2sim, *(states[args["state"]]));
            }
            else if (type == "AMIPS")
            {
                obj = std::make_shared<AMIPSForm>(var2sim, *(states[args["state"]]));
            }
            else if (type == "boundary_smoothing")
            {
                if (args["surface_selection"].is_array())
                    obj = std::make_shared<BoundarySmoothingForm>(var2sim, *(states[args["state"]]), args["scale_invariant"], args["power"], args["surface_selection"].get<std::vector<int>>());
                else
                    obj = std::make_shared<BoundarySmoothingForm>(var2sim, *(states[args["state"]]), args["scale_invariant"], args["power"], std::vector<int>{args["surface_selection"].get<int>()});
            }
            else if (type == "collision_barrier")
            {
                obj = std::make_shared<CollisionBarrierForm>(var2sim, *(states[args["state"]]), args["dhat"]);
            }
            else if (type == "layer_thickness")
            {
                obj = std::make_shared<LayerThicknessForm>(var2sim, *(states[args["state"]]), args["boundary_ids"].get<std::vector<int>>(), args["dhat"]);
            }
            else if (type == "layer_thickness_log")
            {
                obj = std::make_shared<LayerThicknessForm>(var2sim, *(states[args["state"]]), args["boundary_ids"].get<std::vector<int>>(), args["dhat"], true, args["dmin"]);
            }
            else if (type == "deformed_collision_barrier")
            {
                obj = std::make_shared<DeformedCollisionBarrierForm>(var2sim, *(states[args["state"]]), args["dhat"]);
            }
            else if (type == "parametrized_product")
            {
                std::vector<std::shared_ptr<Parametrization>> map_list;
                for (const auto &arg : args["parametrization"])
                    map_list.push_back(create_parametrization(arg, states, {}));
                obj = std::make_shared<ParametrizedProductForm>(CompositeParametrization(std::move(map_list)));
            }
            else
                log_and_throw_adjoint_error("Objective not implemented!");
 
            obj->set_weight(args["weight"]);
            if (args["print_energy"].get<std::string>() != "")
                obj->enable_energy_print(args["print_energy"]);
        }
 
        return obj;
    }
 
    std::shared_ptr<Parametrization> AdjointOptUtils::create_parametrization(const json &args, const std::vector<std::shared_ptr<State>> &states, const std::vector<int> &variable_sizes)
    {
        std::shared_ptr<Parametrization> map;
        const std::string type = args["type"];
        if (type == "per-body-to-per-elem")
        {
            map = std::make_shared<PerBody2PerElem>(*(states[args["state"]]->mesh));
        }
        else if (type == "per-body-to-per-node")
        {
            map = std::make_shared<PerBody2PerNode>(*(states[args["state"]]->mesh), states[args["state"]]->bases, states[args["state"]]->n_bases);
        }
        else if (type == "E-nu-to-lambda-mu")
        {
            map = std::make_shared<ENu2LambdaMu>(args["is_volume"]);
        }
        else if (type == "slice")
        {
            if (args["from"] != -1 || args["to"] != -1)
                map = std::make_shared<SliceMap>(args["from"], args["to"], args["last"]);
            else if (args["parameter_index"] != -1)
            {
                int idx = args["parameter_index"].get<int>();
                int from, to, last;
                int cumulative = 0;
                for (int i = 0; i < variable_sizes.size(); ++i)
                {
                    if (i == idx)
                    {
                        from = cumulative;
                        to = from + variable_sizes[i];
                    }
                    cumulative += variable_sizes[i];
                }
                last = cumulative;
                map = std::make_shared<SliceMap>(from, to, last);
            }
            else
                log_and_throw_adjoint_error("Incorrect spec for SliceMap!");
        }
        else if (type == "exp")
        {
            map = std::make_shared<ExponentialMap>(args["from"], args["to"]);
        }
        else if (type == "scale")
        {
            map = std::make_shared<Scaling>(args["value"]);
        }
        else if (type == "power")
        {
            map = std::make_shared<PowerMap>(args["power"]);
        }
        else if (type == "append-values")
        {
            Eigen::VectorXd vals = args["values"];
            map = std::make_shared<InsertConstantMap>(vals, args["start"]);
        }
        else if (type == "append-const")
        {
            map = std::make_shared<InsertConstantMap>(args["size"], args["value"], args["start"]);
        }
        else if (type == "linear-filter")
        {
            map = std::make_shared<LinearFilter>(*(states[args["state"]]->mesh), args["radius"]);
        }
        else if (type == "bounded-biharmonic-weights")
        {
            map = std::make_shared<BoundedBiharmonicWeights2Dto3D>(args["num_control_vertices"], args["num_vertices"], *states[args["state"]], args["allow_rotations"]);
        }
        else if (type == "scalar-velocity-parametrization")
        {
            map = std::make_shared<ScalarVelocityParametrization>(args["start_val"], args["dt"]);
        }
        else
            log_and_throw_adjoint_error("Unkown parametrization!");
 
        return map;
    }
 
    std::unique_ptr<VariableToSimulation> AdjointOptUtils::create_variable_to_simulation(const json &args, const std::vector<std::shared_ptr<State>> &states, const std::vector<int> &variable_sizes)
    {
        const std::string type = args["type"];
 
        std::vector<std::shared_ptr<State>> cur_states;
        if (args["state"].is_array())
            for (int i : args["state"])
                cur_states.push_back(states[i]);
        else
            cur_states.push_back(states[args["state"]]);
 
        std::vector<std::shared_ptr<Parametrization>> map_list;
        for (const auto &arg : args["composition"])
            map_list.push_back(create_parametrization(arg, states, variable_sizes));
 
        std::unique_ptr<VariableToSimulation> var2sim = VariableToSimulation::create(type, cur_states, CompositeParametrization(std::move(map_list)));
        var2sim->set_output_indexing(args);
 
        return var2sim;
    }
 
    Eigen::VectorXd AdjointOptUtils::inverse_evaluation(const json &args, const int ndof, const std::vector<int> &variable_sizes, VariableToSimulationGroup &var2sim)
    {
        Eigen::VectorXd x;
        x.setZero(ndof);
        int accumulative = 0;
        int var = 0;
        for (const auto &arg : args)
        {
            const auto &arg_initial = arg["initial"];
            Eigen::VectorXd tmp(variable_sizes[var]);
            if (arg_initial.is_array() && arg_initial.size() > 0)
            {
                tmp = arg_initial;
                x.segment(accumulative, tmp.size()) = tmp;
            }
            else if (arg_initial.is_number())
            {
                tmp.setConstant(arg_initial.get<double>());
                x.segment(accumulative, tmp.size()) = tmp;
            }
            else // arg["initial"] is empty array
                x += var2sim[var]->inverse_eval();
 
            accumulative += tmp.size();
            var++;
        }
 
        return x;
    }
 
    std::shared_ptr<State> AdjointOptUtils::create_state(const json &args, CacheLevel level, const size_t max_threads)
    {
        std::shared_ptr<State> state = std::make_shared<State>();
        state->set_max_threads(max_threads);
 
        json in_args = args;
        in_args["solver"]["max_threads"] = max_threads;
        if (!args.contains("output") || !args["output"].contains("log") || !args["output"]["log"].contains("level"))
        {
            const json tmp = R"({
                    "output": {
                        "log": {
                            "level": "error"
                        }
                    }
                })"_json;
 
            in_args.merge_patch(tmp);
        }
 
        state->optimization_enabled = level;
        state->init(in_args, true);
        state->load_mesh();
        Eigen::MatrixXd sol, pressure;
        state->build_basis();
        state->assemble_rhs();
        state->assemble_mass_mat();
 
        return state;
    }
 
    std::vector<std::shared_ptr<State>> AdjointOptUtils::create_states(const json &state_args, const CacheLevel &level, const size_t max_threads)
    {
        std::vector<std::shared_ptr<State>> states(state_args.size());
        int i = 0;
        for (const json &args : state_args)
        {
            json cur_args;
            if (!load_json(args["path"], cur_args))
                log_and_throw_adjoint_error("Can't find json for State {}", i);
 
            states[i++] = AdjointOptUtils::create_state(cur_args, level, max_threads);
        }
        return states;
    }
 
    void AdjointOptUtils::solve_pde(State &state)
    {
        state.assemble_rhs();
        state.assemble_mass_mat();
        Eigen::MatrixXd sol, pressure;
        state.solve_problem(sol, pressure);
    }
 
    void apply_objective_json_spec(json &args, const json &rules)
    {
        if (args.is_array())
        {
            for (auto &arg : args)
                apply_objective_json_spec(arg, rules);
        }
        else if (args.is_object())
        {
            jse::JSE jse;
            const bool valid_input = jse.verify_json(args, rules);
 
            if (!valid_input)
            {
                logger().error("invalid objective json:\n{}", jse.log2str());
                throw std::runtime_error("Invald objective json file");
            }
 
            args = jse.inject_defaults(args, rules);
 
            for (auto &it : args.items())
            {
                if (it.key().find("objective") != std::string::npos)
                    apply_objective_json_spec(it.value(), rules);
            }
        }
    }
 
    json AdjointOptUtils::apply_opt_json_spec(const json &input_args, bool strict_validation)
    {
        json args_in = input_args;
 
        // CHECK validity json
        json rules;
        jse::JSE jse;
        {
            jse.strict = strict_validation;
            std::ifstream file(POLYFEM_OPT_INPUT_SPEC);
 
            if (file.is_open())
                file >> rules;
            else
            {
                logger().error("unable to open {} rules", POLYFEM_OPT_INPUT_SPEC);
                throw std::runtime_error("Invald spec file");
            }
 
            jse.include_directories.push_back(POLYFEM_JSON_SPEC_DIR);
            jse.include_directories.push_back(POLYSOLVE_JSON_SPEC_DIR);
            rules = jse.inject_include(rules);
 
            // polysolve::linear::Solver::apply_default_solver(rules, "/solver/linear");
        }
 
        // polysolve::linear::Solver::select_valid_solver(args_in["solver"]["linear"], logger());
 
        const bool valid_input = jse.verify_json(args_in, rules);
 
        if (!valid_input)
        {
            logger().error("invalid input json:\n{}", jse.log2str());
            throw std::runtime_error("Invald input json file");
        }
 
        json args = jse.inject_defaults(args_in, rules);
 
        json obj_rules;
        {
            const std::string polyfem_objective_spec = POLYFEM_OBJECTIVE_INPUT_SPEC;
            std::ifstream file(polyfem_objective_spec);
 
            if (file.is_open())
                file >> obj_rules;
            else
            {
                logger().error("unable to open {} rules", polyfem_objective_spec);
                throw std::runtime_error("Invald spec file");
            }
        }
        apply_objective_json_spec(args["functionals"], obj_rules);
 
        if (args.contains("stopping_conditions"))
            apply_objective_json_spec(args["stopping_conditions"], obj_rules);
 
        return args;
    }
 
    int AdjointOptUtils::compute_variable_size(const json &args, const std::vector<std::shared_ptr<State>> &states)
    {
        if (args["number"].is_number())
        {
            return args["number"].get<int>();
        }
        else if (args["number"].is_null() && args["initial"].size() > 0)
        {
            return args["initial"].size();
        }
        else if (args["number"].is_object())
        {
            auto selection = args["number"];
            if (selection.contains("surface_selection"))
            {
                auto surface_selection = selection["surface_selection"].get<std::vector<int>>();
                auto state_id = selection["state"];
                std::set<int> node_ids = {};
                for (const auto &surface : surface_selection)
                {
                    std::vector<int> ids;
                    states[state_id]->compute_surface_node_ids(surface, ids);
                    for (const auto &i : ids)
                        node_ids.insert(i);
                }
                return node_ids.size() * states[state_id]->mesh->dimension();
            }
            else if (selection.contains("volume_selection"))
            {
                auto volume_selection = selection["volume_selection"].get<std::vector<int>>();
                auto state_id = selection["state"];
                std::set<int> node_ids = {};
                for (const auto &volume : volume_selection)
                {
                    std::vector<int> ids;
                    states[state_id]->compute_volume_node_ids(volume, ids);
                    for (const auto &i : ids)
                        node_ids.insert(i);
                }
 
                if (selection["exclude_boundary_nodes"])
                {
                    std::vector<int> ids;
                    states[state_id]->compute_total_surface_node_ids(ids);
                    for (const auto &i : ids)
                        node_ids.erase(i);
                }
 
                return node_ids.size() * states[state_id]->mesh->dimension();
            }
        }
 
        log_and_throw_adjoint_error("Incorrect specification for parameters.");
        return -1;
    }
} // namespace polyfem::solver