Using std::valarray in numerical simulation

I posted a simple n-body class that I have written in C++ here in Code Review.

There I was told to use std::valarray instead of plain std::array with the goal that I can rewrite some code that looks currently like this

void Particle::update_position() {
    for (unsigned int d = 0; d < DIM; ++d) {
        position[d] += dt*(velocity[d] + a*force_new[d]);
        force_old[d] = force_new[d];
    }
}

to this

void Particle::update_position() {
    position += 0.1*(velocity + force_new);
    force_old = force_new;
}

Since I am a beginner in C++ I wrote a short program that uses the std::valarray such that I can learn how to use this data structure. The compiler, however, throws a lot of errors and I do not know why. I hope you can help me with this. Here is the small program I wrote:

#include <iostream>
#include <vector>
#include <array>
#include <valarray>

constexpr unsigned int DIM = 2;

struct Particle{
    std::array<std::valarray<double>, DIM> position; 
    std::array<std::valarray<double>, DIM> velocity;
    std::array<std::valarray<double>, DIM> force_new;
    std::array<std::valarray<double>, DIM> force_old;
    void update_position();
};

void Particle::update_position() {
    position += 0.1*(velocity + force_new);
    force_old = force_new;
}

void compute_position(std::vector<Particle>& particles) {
    for (auto& particle: particles) { 
        particle.update_position();
    }
}

void print_data(const std::vector<Particle>& particles) {
    for (const auto& particle: particles) {
        for (const auto& x: particle.position) std::cout << x << " ";
        for (const auto& v: particle.position) std::cout << v << " ";
        for (const auto& F: particle.position) std::cout << F << " ";
        std::cout << std::endl;
    }
}

void init_data(std::vector<Particle>& particles) {
    for (auto& particle: particles) {
        for (const auto& p: particle) {
            p.position = 1.0
            p.velocity = 2.0
            p.force_new = 3.0
            p.force_old = 4.0
        }
    }
}

int main() { 
    const unsigned int n = 10;
    std::vector<Particle> particles(n);
    init_data(particles);
    compute_position(particles);
    print_data(particles); 
    return 0;
}

When I try to compile this code, I get the following errors:

so.cpp: In member function ‘void Particle::update_position()’:
so.cpp:17:31: error: no match for ‘operator+’ (operand types are ‘std::array<std::valarray<double>, 2>’ and ‘std::array<std::valarray<double>, 2>’)
     position += 0.1*(velocity + force_new);

so.cpp: In function ‘void print_data(const std::vector<Particle>&)’:
so.cpp:29:58: error: no match for ‘operator<<’ (operand types are ‘std::ostream’ {aka ‘std::basic_ostream<char>’} and ‘const std::valarray<double>’)
         for (const auto& x: particle.position) std::cout << x << " ";


so.cpp: In function ‘void init_data(std::vector<Particle>&)’:
so.cpp:38:29: error: ‘begin’ was not declared in this scope
         for (const auto& p: particle) {
                             ^~~~~~~~
so.cpp:38:29: note: suggested alternative:
In file included from so.cpp:4:
/usr/include/c++/8/valarray:1211:5: note:   ‘std::begin’
     begin(const valarray<_Tp>& __va)
     ^~~~~
so.cpp:38:29: error: ‘end’ was not declared in this scope
         for (const auto& p: particle) {