TransientForm.cpp

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#include <polyfem/optimization/forms/TransientForm.hpp>
 
#include <polyfem/varforms/diff/DifferentiableVarForm.hpp>
#include <polyfem/optimization/DiffCache.hpp>
 
#include <Eigen/Core>
 
#include <cassert>
#include <vector>
 
namespace polyfem::solver
{
    std::vector<double> TransientForm::get_transient_quadrature_weights() const
    {
        std::vector<double> weights;
        weights.assign(time_steps_ + 1, dt_);
        if (transient_integral_type_ == "uniform")
        {
            weights[0] = 0;
        }
        else if (transient_integral_type_ == "trapezoidal")
        {
            weights[0] = dt_ / 2.;
            weights[weights.size() - 1] = dt_ / 2.;
        }
        else if (transient_integral_type_ == "simpson")
        {
            weights[0] = dt_ / 3.;
            weights[weights.size() - 1] = dt_ / 3.;
            for (int i = 1; i < weights.size() - 1; i++)
            {
                if (i % 2)
                    weights[i] = dt_ * 4. / 3.;
                else
                    weights[i] = dt_ * 2. / 4.;
            }
        }
        else if (transient_integral_type_ == "final")
        {
            weights.assign(time_steps_ + 1, 0);
            weights[time_steps_] = 1;
        }
        else if (transient_integral_type_ == "steps")
        {
            weights.assign(time_steps_ + 1, 0);
            for (const int step : steps_)
            {
                assert(step > 0 && step < weights.size());
                weights[step] += 1. / steps_.size();
            }
        }
        else
            assert(false);
 
        return weights;
    }
 
    double TransientForm::value_unweighted(const Eigen::VectorXd &x) const
    {
        std::vector<double> weights = get_transient_quadrature_weights();
 
        double value = 0;
        for (int i = 0; i < time_steps_ + 1; i++)
        {
            if (weights[i] == 0)
                continue;
            const double tmp = obj_->value_unweighted_step(i, x);
            value += (weights[i] * obj_->weight()) * tmp;
        }
 
        return value;
    }
    Eigen::MatrixXd TransientForm::compute_adjoint_rhs(const Eigen::VectorXd &x, const varform::DifferentiableVarForm &varform, const DiffCache &diff_cache) const
    {
        Eigen::MatrixXd terms;
        terms.setZero(varform.primary_space().ndof(), time_steps_ + 1);
        std::vector<double> weights = get_transient_quadrature_weights();
 
        for (int i = 0; i < time_steps_ + 1; i++)
        {
            if (weights[i] == 0)
                continue;
            terms.col(i) = weights[i] * obj_->compute_adjoint_rhs_step(i, x, varform, diff_cache);
            if (obj_->depends_on_step_prev() && i > 0)
                terms.col(i - 1) = weights[i] * obj_->compute_adjoint_rhs_step_prev(i, x, varform, diff_cache);
        }
 
        return terms * weight();
    }
    void TransientForm::compute_partial_gradient(const Eigen::VectorXd &x, Eigen::VectorXd &gradv) const
    {
        gradv.setZero(x.size());
        std::vector<double> weights = get_transient_quadrature_weights();
 
        Eigen::VectorXd tmp;
        for (int i = 0; i < time_steps_ + 1; i++)
        {
            if (weights[i] == 0)
                continue;
            obj_->compute_partial_gradient_step(i, x, tmp);
            gradv += weights[i] * tmp;
        }
 
        gradv *= weight();
    }
 
    void TransientForm::init(const Eigen::VectorXd &x)
    {
        obj_->init(x);
    }
 
    bool TransientForm::is_step_valid(const Eigen::VectorXd &x0, const Eigen::VectorXd &x1) const
    {
        return obj_->is_step_valid(x0, x1);
    }
 
    double TransientForm::max_step_size(const Eigen::VectorXd &x0, const Eigen::VectorXd &x1) const
    {
        return obj_->max_step_size(x0, x1);
    }
 
    void TransientForm::line_search_begin(const Eigen::VectorXd &x0, const Eigen::VectorXd &x1)
    {
        obj_->line_search_begin(x0, x1);
    }
 
    void TransientForm::line_search_end()
    {
        obj_->line_search_end();
    }
 
    void TransientForm::post_step(const polysolve::nonlinear::PostStepData &data)
    {
        obj_->post_step(data);
    }
 
    void TransientForm::solution_changed(const Eigen::VectorXd &new_x)
    {
        AdjointForm::solution_changed(new_x);
        // obj_->solution_changed(new_x);
        std::vector<double> weights = get_transient_quadrature_weights();
        for (int i = 0; i <= time_steps_; i++)
        {
            if (weights[i] == 0)
                continue;
            obj_->solution_changed_step(i, new_x);
        }
    }
    bool TransientForm::is_step_collision_free(const Eigen::VectorXd &x0, const Eigen::VectorXd &x1) const
    {
        return obj_->is_step_collision_free(x0, x1);
    }
 
    double ProxyTransientForm::value_unweighted(const Eigen::VectorXd &x) const
    {
        Eigen::VectorXd vals(steps_.size());
        int j = 0;
        for (int i : steps_)
        {
            vals(j++) = obj_->value_unweighted_step(i, x);
        }
 
        return eval(vals);
    }
    Eigen::MatrixXd ProxyTransientForm::compute_adjoint_rhs(const Eigen::VectorXd &x, const varform::DifferentiableVarForm &varform, const DiffCache &diff_cache) const
    {
        Eigen::VectorXd vals(steps_.size());
        Eigen::MatrixXd terms;
        terms.setZero(varform.primary_space().ndof(), steps_.size());
 
        int j = 0;
        for (int i : steps_)
        {
            vals(j) = obj_->value_unweighted_step(i, x);
            terms.col(j++) = obj_->compute_adjoint_rhs_step(i, x, varform, diff_cache);
        }
 
        const Eigen::VectorXd g = eval_grad(vals);
        Eigen::MatrixXd out;
        out.setZero(varform.primary_space().ndof(), time_steps_ + 1);
        j = 0;
        for (int i : steps_)
        {
            out.col(i) = terms.col(j) * (g(j) * weight());
            j++;
        }
 
        return out;
    }
    void ProxyTransientForm::compute_partial_gradient(const Eigen::VectorXd &x, Eigen::VectorXd &gradv) const
    {
        Eigen::VectorXd vals(steps_.size());
        Eigen::MatrixXd terms;
        terms.setZero(x.size(), steps_.size());
 
        int j = 0;
        Eigen::VectorXd tmp;
        for (int i : steps_)
        {
            vals(j) = obj_->value_unweighted_step(i, x);
            obj_->compute_partial_gradient_step(i, x, tmp);
            terms.col(j++) = tmp;
        }
 
        gradv = terms * eval_grad(vals) * weight();
    }
 
    double ProxyTransientForm::eval(const Eigen::VectorXd &y) const
    {
        return 1. / y.array().inverse().sum();
    }
 
    Eigen::VectorXd ProxyTransientForm::eval_grad(const Eigen::VectorXd &y) const
    {
        return y.array().pow(-2.0) * pow(eval(y), 2);
    }
} // namespace polyfem::solver