CU Denver faculty are helping strengthen how researchers make sense of uncertainty in complex systems.
A new article by CU Denver's College of Liberal Arts and Science's Department of Mathematical and Statistical Sciences Troy Butler, Ph.D., and collaborators, “Iterative Data-Consistent Inversion with Multiple Push-Forward Constraints,” is now published in the International Journal for Uncertainty Quantification. The paper introduces a rigorous, scalable approach for solving modern stochastic inverse problems, especially when data arrives from multiple sources and in different forms.
What Problem Does This Research Solve
Many real-world questions start with outputs we can measure and end with inputs we need to infer.
For example:
- We observe sensor readings, test results, or system performance
- We want to estimate the uncertain parameters that produced those outcomes
- We need the inferred parameters to remain consistent with the data we actually observed
This “work backward from observations” challenge is called an inverse problem. In uncertainty quantification, the goal is often to estimate an entire probability distribution over the uncertain inputs, not just a single best guess. This is especially challenging when there are multiple datasets (or types of observations) that must all be matched at once.
What The Team Introduced
The paper presents an iterative data-consistent inversion (iDCI) method designed for multi-source data settings. In plain terms, iDCI is an approach that updates an estimated distribution step-by-step so it becomes consistent with observed datasets, even when there are multiple constraints coming from different observed quantities of interest (QoI).
Key contributions described in the article include:
- A convergent, measure-theoretic framework for handling multiple push-forward constraints (multiple observed datasets tied to different model outputs).
- A proof that the standard DCI solution is theoretically optimal in a precise sense: it minimizes an f-divergence among all solutions that satisfy the push-forward constraint.
- An iterative scheme that converges to a solution satisfying multiple constraints and minimizes cumulative divergence across them; under uniform initialization, the solution aligns with a maximal entropy (I-projection) viewpoint.
- Demonstrations on numerical examples, including high-dimensional parameter problems governed by partial differential equations, showing the method can avoid difficulties tied to approximating high-dimensional joint observed measures directly.
Why It Matters For Real-World Impact
Today’s data rarely comes in one clean, synchronized stream. In many fields, observations can be:
- Asynchronous (collected at different times)
- Heterogeneous (different sensors or measurement types)
- High-dimensional (many variables at once)
This work expands the computational reach of data-consistent inversion to better reflect that reality, helping position iDCI as a practical tool for modern uncertainty quantification and stochastic inverse problems.
Congratulations to Dr. Troy Butler and co-authors Tianyi Jiang, Timothy Wildey, Tim Kutta, and Haonan Wang on this publication and the continued advancement of uncertainty quantification research with real-world relevance.