How can hidden fields be utilized to preserve form data in PHP scripts?

Hidden fields can be utilized in HTML forms to store data that should be preserved between form submissions. In PHP scripts, hidden fields can be used to pass information from one page to another without displaying it to the user. This can be useful for preserving form data, such as user input or session information, across multiple form submissions.

```php
<form action="process_form.php" method="post">
  <input type="hidden" name="user_id" value="<?php echo $user_id; ?>">
  <!-- Other form fields -->
  <button type="submit">Submit</button>
</form>
```

In the above code snippet, the hidden input field "user_id" is used to store the value of the variable $user_id. When the form is submitted, the value of "user_id" will be passed to the "process_form.php" script along with the other form data. This allows the script to access and process the preserved data.