Intelligence,
Bound by Physics

I build AI tools for small scientific and engineering companies. They learn from your own measurements and simulations, and the physics limits what they're allowed to tell you. A model that only conserves energy some of the time isn't much use to an engineer.

Fig. 1  The first four modes of a string fixed at both ends, ψn(x) = sin(nπx/L). The boundaries decide which solutions are allowed.

Why I started Eigenbound

Most of the work on physics and AI is aimed at large aerospace and automotive firms, with the contracts and timelines to match. Meanwhile, plenty of smaller instrument and testing companies have years of measurements and simulation runs that nobody has had time to do much with.

General AI tools are easy to get hold of, but they know nothing about your system. They'll happily fit a curve that goes negative where it physically can't, or hand you a number with no idea how uncertain it is.

I think there's room for something in between. Small projects on a single problem, built by a physicist, with the physics in from the start.

What I build

Faster models of slow simulations

If a simulation takes hours to run, a surrogate model can get you close in seconds. I test it against conservation laws and against the cases where you already know the answer.

Analysis pipelines

Code that takes raw measurements through to a result, with an honest estimate of the uncertainty attached to it.

LLM tools that check their working

If you use language models for analysis or reporting, the numbers they produce can be checked for units and dimensions before anyone relies on them.

Projects are usually one dataset and one problem, so there's nothing to roll out across the company.

You'll know where it works and where it doesn't

Every tool comes with a written validation report. For me it's the most important part of the job, because a model that looks good on its training data can fall apart the first time it sees something new. Your engineers should be able to read the report and decide for themselves how far to trust the tool.

What the report covers
CheckWhat it shows
1ResidualsError against measurements the model hasn't seen, and where it grows
2Limiting casesBehaviour where the physics has a known answer
3DimensionsUnits agree from input to output
4UncertaintyWhether the error bars match the errors you actually see
5Valid rangeThe inputs it has been tested on, and what happens outside them

Where it fits

So far I've mostly been talking to companies in instrumentation and metrology, non-destructive testing, photonics and lasers, and space and Earth observation. If your work involves physical measurements and you have more data than time to look at it, I'd like to hear about it.

How a project works

  1. 1 to 2 weeks

    Data diagnostic

    I look through your data, work out where AI would actually help, and build a small prototype so you can judge it on something real.

  2. 4 to 6 weeks

    Pilot

    If the prototype is worth pursuing, I turn it into a proper tool with its validation report and hand it over to your team.

  3. Ongoing

    Support

    If the tool ends up in your product or your day-to-day work, I can keep it maintained as your data changes.

We agree the scope in writing before each stage, and you're only ever committed to the stage you're in. Your data and results stay yours, and I'm happy to sign an NDA before seeing anything.

About me

I'm Declan Tuohy. I study physics at the University of Bath, and during an internship at the European Space Agency I worked on AI tools for satellite navigation.

Eigenbound is just me for now. If you get in touch, you'll be talking to the person who does the work.

Get in touch

If you've got data you think could be doing more, send me a couple of lines about what it is and what you'd want from it. It doesn't need to be formal.