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Research
Using data to understand the models we build.
Our programs span two modeling regimes: systems with more parameters than classical intuition expects, and interpretable systems whose mechanisms can be discovered from observations.
Generalization in complex models
Modern predictive models can behave in ways that classical bias–variance intuition does not explain. We develop mathematical tools for separating the effects of the model, the data, and their interaction—then use those tools to understand when added complexity helps rather than hurts.
In collaboration with Tyler Jarvis, Mark Transtrum, Gus Hart, and student researchers at BYU.
Questions we are asking
- What creates double- and multiple-descent behavior?
- Which aspects of a sampling design control generalization?
- Can model quality be assessed before labels are collected?
Published research highlights
Each highlight leads with the result, then provides the complete publication record.
Interpretable models from data
Rather than replace physics with a black box, this program asks how incoming observations can improve a model while preserving a form that scientists can interpret. Continuous data assimilation synchronizes a model with observations; optimization then turns the remaining mismatch into information about unknown parameters, forcing, or equations.
Questions we are asking
- Can state and parameters be recovered at the same time?
- How little of a complex system must be observed?
- Which optimization schemes remain reliable in chaotic dynamics?
Published research highlights
Each highlight leads with the result, then provides the complete publication record.
Research highlight
Continuous data assimilation turns online model discovery into a finite-dimensional optimization problem, enabling multiple unknown parameters to be updated as observations arrive.
Read the publicationResearch highlight
Relaxation least-squares and Newton schemes provide a general framework for recovering unknown state and parameters simultaneously in dissipative systems.
Read the publicationDiscovering cloud physics
Cloud models contain physical processes that occur below the scales a simulation can resolve. This project brings model discovery into that setting: use sparse, evolving observations to identify missing or misspecified processes while retaining equations that scientists can inspect and test.
A multi-institution effort with Michigan Technological University, the University of Utah, Brookhaven National Laboratory, Pacific Northwest National Laboratory, and NSF NCAR.
Questions we are asking
- Which unresolved processes leave identifiable signatures in observations?
- Can those processes be represented by interpretable equations?
- How do discoveries transfer across models and observing systems?
U.S. Department of Energy Awardee
DOE-supported research in progress
This program is supported through the U.S. Department of Energy's Genesis Mission. The project is now adapting the model-discovery methods developed in our interpretable-modeling program to cloud physics; no cloud-physics results have been published yet.
Logo was developed by the U.S. Department of Energy to indicate receipt of DOE funding. Not an endorsement by DOE.
Rolling publication highlights
Publications from the past two years
New journal articles and arXiv preprints are added automatically and leave this section after 24 months. Hand-edited summaries are preserved when the metadata refreshes.
· arXivPreprint
Asymptotic approximation of sensitivities in finite dimensional continuous data assimilation with application to parameter estimation
The authors develop a rigorous justification for a parameter estimation algorithm which couples continuous data assimilation to generic optimization.
Read the preprint· arXivPreprint
Continuous data assimilation in steady Navier-Stokes equations with unknown viscosity: robust and efficient solvers and fast parameter recovery
This work develops continuous-data-assimilation solvers that recover an unknown viscosity in the steady Navier–Stokes equations from partial flow observations, with quadratic convergence and strong numerical performance even from poor initial guesses.
Read the preprint· Physical Review Research
Generalized aliasing explains double descent and informs model design
This work separates prediction error into model insufficiency, data insufficiency, and generalized aliasing, providing an explanation for double descent and practical guidance for model and experimental design.
Read the publication· Journal of Geophysical Research Machine Learning and Computation
Embracing Uncertainty in “Small Data” Problems: Estimating Earthquakes From Historical Anecdotes
Bayesian inference and uncertainty analysis are used to reconstruct historical Indonesian earthquakes from anecdotal tsunami evidence and assess which conclusions remain robust under explicit modeling assumptions.
Read the publication· Journal of Computational Physics
Model discovery on the fly using continuous data assimilation
Continuous data assimilation turns online model discovery into a finite-dimensional optimization problem, allowing multiple unknown parameters to be updated as observations arrive.
Read the publication· Experiments in Fluids
Error propagation of direct pressure gradient integration and a Helmholtz–Hodge decomposition-based pressure field reconstruction method for image velocimetry
This work compares direct pressure-gradient integration with a Helmholtz–Hodge reconstruction method to characterize how measurement errors propagate into pressure fields recovered from image velocimetry.
Read the publication· Inverse Problems
Relaxation-based schemes for on-the-fly parameter estimation in dissipative dynamical systems
Relaxation least-squares and Newton schemes provide a general framework for recovering unknown states and parameters together in dissipative dynamical systems.
Read the publication
Research support
Supported by the U.S. National Science Foundation
This material is based upon work supported by the U.S. National Science Foundation under the following current and recent awards to Jared P. Whitehead at Brigham Young University.
DMS-2206762Data Assimilation for Turbulent Flows: Dynamic Model Learning and Solution CapturingView the NSF award record CCF-2343286XTRIPODS: Advances and Novel Applications of Closed-Loop Data Assimilation, and Educational Improvements to Data Science CoursesView the NSF award record DMS-2510495Augmenting Continuous Data Assimilation to Perform Equation Discovery with Applications in GeophysicsView the NSF award record
Any opinions, findings, conclusions, or recommendations expressed on this site are those of the authors and do not necessarily reflect the views of the U.S. National Science Foundation.