# Uncertainty Quantification and Multifidelity Modeling

Building on our established strengths in complex, multiscale science, PNNL facilitates a coordinated effort in uncertainty quantification and multiscale mathematics to develop the mathematical and computational theory and algorithms that will enable true multiscale simulation and analysis using probabilistic and mathematical models to represent and explore stochastic processes and phenomena, especially when lab experiments are too costly, difficult, hazardous, or time-consuming.

# Key Capabilities

- Adaptive Methods and Time-step Acceleration
- Hybrid
*ab initio*and quality control methods - New adaptive evolution algorithms
- Wavelets
- Multivariational analysis
- Adaptive multiscale particle methods
- Accelerated stochastic kinetic simulation with adaptive spatial meshing

- Hybrid
- Optimization, Inverse Modeling, and Data Integration
- Large-scale parameter estimation
- Clustering and probabilistic model selection
- Constrained stochastic optimization
- Multiscale likelihood calculations

# Significant Projects

### CM4 Website

## Collaboratory on Mathematics for Mesoscopic Modeling of Materials (CM4)

CM4 focuses on developing rigorous mathematical foundations for understanding and controlling fundamental mechanisms in mesoscale processes to enable scalable synthesis of complex materials through the design of efficient modeling methods and corresponding scalable algorithms.

Funding Source: DOE Office of Advanced Scientific Computing Research, Applied Mathematics Program

## Modeling Framework (MMF) for Climate Research

...MoreClimate modelers employ grid resolution developments in multiscale mathematics to connect the physics and chemistry of atmospheric processes across naturally occurring scales, from hundreds of nanometers to thousands of kilometers.

## Uncertainty Quantification: Design and Analysis of Computer Experiments

...MoreThis adaptive methodology will enable efficient, global analysis of uncertainty and sensitivity of predictions from large-scale scientific simulations. Computer models estimate the performance of real-world phenomenon because model input parameters can be simulated from probability distributions to measure the sensitivities within the model and uncertainties of the results.

## Crosscutting: Hierarchy Theory

...MoreThis concerns finding the mathematical conditions under which model reduction can be achieved by collapsing discrete collections of objects into continuous representation while retaining the accuracy of information flow across levels of scale and organization.

## Multiscale Modeling and Uncertainty Quantification for Bioremediation

...MoreAdvances in these mathematical methods will result in more accurate modeling of the wettability properties of various fluids, facilitating realistic subsurface flow predictions important for groundwater remediation and oil extraction efforts.

## Biology: Multicell Models of Cell-to-Cell Communication

...MoreThis software will facilitate linking stochastic receptor binding events with intercellular processes of protein-to-protein interactions, leading to the gene expression regulation.

## High-performance Computing

...MoreHPC efforts involve developing linear algebra software, including eigensolvers or parallel architectures.