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css - How to add animated gradient to an svg path?

I have a heart svg path like so:

<svg viewBox="0 0 100 100">
<path className="" d="M20,31 C15.4189994,27.2225585 12.5023327,24.2225585 11.25,22 C10.2743515,20.6156479 10,19.6181623 10,18.1428571 C10,15.5113854 12.4883456,13 15,13 C17.3176009,13 18.9621484,13.8491346 20,15.5714286 C21.0382977,13.8491346 22.6828452,13 25,13 C27.5116544,13 30,15.5113854 30,18.1428571 C30,19.6181623 29.7256485,20.6156479 28.75,22 C27.497816,24.2225585 24.5811493,27.2225585 20,31 Z" />
</svg>

And I'd like to add a gradient effect on it and move the gradient from left to right, as if the heart is shimmering.

However, path doesn't accept a background property and if I use fill, it doesn't accept gradient as a value. It also doesn't have a background-position property (so that I can move the background-position from left to right by using @keyframes).

Is there a way to achieve this?

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You can use the SMIL animation of SVG. The idea is to animate the color-stop or the offset of the gradient to create the needed effect:

svg {
 border:1px solid;
 width:200px;
}
<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" 
   viewBox="10 10 24 24">
    <defs>
        <linearGradient id="linear-gradient" x1="-100%" y1="0" x2="200%" y2="0" >
            <stop offset="0" stop-color="red">
               <animate attributeName="offset" values="0;0.2;0.5" dur="2s" repeatCount="indefinite"  /> 
            </stop>
            <stop offset="0.5" stop-color="yellow">
                <animate attributeName="offset" values="0.5;0.7;0.8;1" dur="2s" repeatCount="indefinite"  /> 
            </stop>
        </linearGradient>
    </defs>
<path fill="url(#linear-gradient)" d="M20,31 C15.4189994,27.2225585 12.5023327,24.2225585 11.25,22 C10.2743515,20.6156479 10,19.6181623 10,18.1428571 C10,15.5113854 12.4883456,13 15,13 C17.3176009,13 18.9621484,13.8491346 20,15.5714286 C21.0382977,13.8491346 22.6828452,13 25,13 C27.5116544,13 30,15.5113854 30,18.1428571 C30,19.6181623 29.7256485,20.6156479 28.75,22 C27.497816,24.2225585 24.5811493,27.2225585 20,31 Z" />
</svg>

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