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I have seen the following formula when writing an academic article:

To the best of our knowledge, this is the first work that shows how to optimize a non-submodular function for ....

I like this construction in a paper, and I am wondering if there is a way to replace "To the best of our knowledge" by a similar expression that conveys a similar message, i.e. novelty, as far as one can tell from the literature.

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When you say "to the best of my/our knowledge," you're saying that "you think your statement is true, because it is based on what you know/believe, but you are not completely sure" [Macmillan].

So any phrase that expresses that lack of complete certainty that fits the context will do. In the context of an academic paper, you might say:

We believe that this is the first work that shows how to optimize a non-submodular function...

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  • +1, as "We believe" is an excellent replacement to the phrase in OP in scientific settings.
    – Ilonpilaaja
    Sep 21, 2020 at 12:19
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What about "As far as I/we know" or "As far as I/we can tell"

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    In conversation, "as far as we can tell" would be fine. I'd avoid that form in an academic paper, however.
    – J.R.
    Apr 25, 2012 at 23:46
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    This is more of a variation, but I have heard it as "To the extent of our knowledge"
    – Ian
    Apr 26, 2012 at 0:04
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You may use as far as we know.

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