Beyond all the wasm/webgpu approaches other folks have linked (mostly in the transformers.js ecosystem), there's been a standardized API brewing since 2019: https://webmachinelearning.github.io/webnn-intro/

Demos here: https://webmachinelearning.github.io/webnn-samples/ I'm not sure any of them allow you to select a model file from disk, but that should be entirely straightforward.