You should have a decent size professional network given your many years in academia. Assuming you can narrow down which companies could benefit from your innovation, maybe you already know someone in industry who can make the introduction to an R&D person with hiring abilities at their company. To answer your second question, I have personally seen companies hire smart people and let them work on their own pet research projects and some suggest it is at times done to ensure the competition doesn't hire them. For extra fun (or stress), get at least two companies interested and let them bid on you.

On a personal note, the amazing opportunities in my career have come from the outliers of my professional network. As in people who I didn't even think would remember me. So don't be too shy in reaching out.

But as another commenter mentioned, getting a patent would be great. Is the cost of filing preventing you from doing that ?

I hadn't considered a patent at all. Will definitely think about it, although i suspect it could get complicated with respect to my current institution.

It's not filing a patent that is the issue. If granted, you will need to defend it. Often deep-pocketed firms willfully abuse patents knowing that the patent holder can't afford the legal costs of defending it.

As an individual, in most cases, you are better off being the co-holder of a patent together with a substantial entity who can better protect your mutual interests.

This is silly and false. If there’s a good case that someone is willfully infringing your patent, lawyers will happily take the case on contingency.

Some details.

I've often seen patent applications, particularly provisional patent applications, as an "ace in the hole" for real and potential commercial disputes. If you are afraid you might get screwed the patent gives you a weapon to screw back.

Your university might be able to force you to assign the patent to the university and I wouldn't worry about it.

If you are filing your first patent and not (initially) putting the name of any big organization on it you can get 1/2 or 1/4 off the filing fee. I got 1/2 off the last time I filed one I spent a day gathering together my notes and I paid $65. A real patent is going to cost you somewhere in the low $1000s. The PPA starts the clock and gives you 1 year to file a real application which is enough time if you're serious. It also will keep anybody else from filing a patent.

You could go to the technology transfer office at your uni but I don't reccommend it because (1) the folks involved know some aspects of the subject very well but they are clueless in others, so they might not have good judgement about "is this worth filing a patent for?" and (2) they are going to spend more money determining if it is worth filing a patent than you are going to spend on filing fees.

You are better off begging forgiveness than asking permission I think, particularly if your first step is filing the provisional patent. Even if you are forced to assign the patent to your uni, you are much better off getting into a commercial dispute over something valuable than you are not having anything valuable to begin with.

Nolo press has some very good books on patent law that tell you all you need to know to file patents. Go get one from the library.

I work like you, and my advice would be to not get super attached to a particular idea, or it can cause tunnel vision and frustration at how slow the world is to adopt your insight, be patient.

Good ideas are relatively common, what is less common is an environment where you can change the world with an idea, that is what you are searching for now.

Apply for work at some corporate research lab for the job security and leverage your new insights to solve some cool problems.

yeah, this is pretty much my view on it also. I am not so much frustrated, but wondering if there is a way of progressing a research career outside of typical research institutions with actual research

Why not try starting a company? Here's a good primer: How to spin your scientific research out of a university and into a startup[0]

[0] - https://blog.ycombinator.com/how-to-spin-your-scientific-res...

It's not likely to get it in the exact way you want - but you could get close. There would likely be alot of your time being allocated and your project being a 'side project' ancillary to the actual work. The only way to change that balance is to get in using your professional network or someone more senior who is willing to take a bet on whatever it is that you've made.

Since it does carry an element of risk it's not likely to be able to be hired on it alone. If you see fit to develop it you could make a research company and raise money on it.

Does your new technique solve any ... business problems? With an appreciable market?

May be worth taking a stab starting your own company (or at least a consulting business) rather than wait for one of the big companies to suck you up into their intake vents. Or even if that's your preferred destination, this approach might help you get there (and better positioned for the kind of role you'd prefer to have).

I think there would definitely be a market for it, but right now I have a prototype, and the amount of engineering effort required to turn it into a reliable product would be immense. Not sure how it would fit into a startup timeline.

AFAIK, Microsoft, Google, etc have areas of research interest. Your knowledge of the literature might help you identify if there are any industry based projects that are relevant to your research. Another option might be to found a startup based upon your research. The proposals to VCs is similar to grant applications.

Would Google Research be interested? This sounds like an intersection between physical and computational engineering and as far as I am aware there are some folks at GR who are working in that intersection -- awkward enough that no one academic discipline would be a good fit.

I would expect so. I think one of the things which makes places like GR not so great for me is that I don't have a ML background. I have done little bits here and there, and am pretty comfortable with the tools, but I am not really interested in using ML to solve problems unless it is kind of obvious, if you know what I mean.

Why don’t you apply to become a PI in academia?

If it’s published, can you explain your idea of using auto differentiation infrastructure to better see how good an idea actually it is?!

not published yet, but I am going to start writing the paper soon. I addressed the PI route in my post, but essentially, my career has not been focused enough which makes applying to be a PI very difficult.

If you mean important in the sense of potential economic impact, this seems like a case where you should form a company to develop the idea.

Can you file a patent?