What makes a useful prior?
Inverse problems often require knowledge beyond the measurements. We study how to represent, learn, and reuse that knowledge, and how the choice of prior affects a solution’s reliability.
toward
foundation models
for inverse problems
OpenInverse is a research initiative focused on AI methods for inverse problems. We study how models, learned priors, and evaluation methods can transfer across problems.
problem
Many inverse problems share a common mathematical form.
y = A(x) + ηmeasurement · operator · unknown · noise
Inverse problems start with observations and ask what produced them: reconstructing an image from measurements, estimating a material’s properties, or recovering the structure beneath the Earth. The challenge is that incomplete and noisy observations can support more than one answer.
The measurement process and the unknown differ between problems, but many require similar mathematical tools. Methods developed for one application often turn out to be useful in others.
For example, in seismic inversion, the measurements are recorded waves and the unknown is the structure beneath the surface. A forward model predicts how waves travel through a proposed structure. Inversion uses the recorded waves to estimate that structure.
question
How far can learning generalize across inverse problems?
There is more than one way for a method to generalize. It may be reusable within a single problem, portable across measurement setups, or transferable between different physical systems, and each of those claims requires different evidence. Our research spans the directions below.
task-specific models
One problem, one setup, one dataset.
reusable models
A model or prior can be reused on new measurements of the same problem.
across operators and domains
Adapts to different forward operators and scientific domains.
foundation models
Pretrained models that adapt across operators, tasks, and domains.
research
How can learning and domain knowledge work together?
Our research combines AI and deep learning with physics, mathematical models, numerical methods, and domain knowledge to solve inverse problems across science and engineering.
How far can a model generalize?
We study what reusable and pretrained models can carry across tasks, operators, and domains, and develop ways to evaluate their capabilities and limitations.
benchmarks
OpenInverse Bench
OpenInverse Bench is a planned benchmark suite bringing together problem definitions, datasets, baselines, and evaluation protocols to study how inverse methods perform and how well they transfer.
Problem definitions
Code defining forward operators, noise models, and dataset splits.
Baselines
Classical and learned reference implementations, kept with the data.
Metrics
Reconstruction quality, measurement consistency, uncertainty, and computational cost.
Cross-problem evaluation
Trained on one operator family, tested on an unseen one.
programs
Work with us on inverse problems.
We plan to organize challenges, competitions, workshops, and fellowships around shared inverse problems, connecting method researchers with domain expertise.
- challenges
Research around a shared open problem.
- competitions
Ranked submissions on a fixed benchmark.
- workshops
Connecting inverse problem methods with scientific applications.
- fellowships
Sustained research on an open question.
contact
Tell us what you are trying to recover,
and what you can measure.
Working on an inverse problem? We’d like to hear about your research, your measurements, or a question you want to explore together.
contact@openinverse.com