Combining Data and Simulation to Predict the
Behavior of Complex Systems
IntroductionPredicting the behavior of complex physical systems is a key requirement for many important DOE applications. However, incomplete physical models and uncertain parameters limit the predictive capability of even high fidelity simulations. Model and parameter identification are typically done by finding models and parameter sets that accurately predict the results of controlled experiments. This often involves a combination of computation and optimization. 
Senior Investigators

Project GoalThe goal of this project is to develop new tools that allow us to use data from multiple experiments of different kinds in conjunction with simulation. It has become clear that traditional simulation and sampling methods do not suffice. The constraints that experiments put on parameters are ill conditioned and complex. Simulating highly nonlinear experiments is so slow that huge numbers of samples are not practical.
Measurements often reflect a complex, uncertain relationship between the system state and
measured quantities. For example, laser diagnostic measurements
of a chemical species in a reacting flow are modulated by statedependent quenching corrections.
Observations from cosmological surveys require modeling of photometric redshifts, corrections for telescope focal plane distortions, and a number of other systematic effects.
In some cases, the combination of imprecisely defined experiments and complex dynamics
means that it is appropriate to consider only
statistical properties of the experiments, not a detailed trajectory.

ApproachOur overall approach is based on Monte Carlo sampling within a Bayesian framework. Monte Carlo (MC) sampling provides a numerically sound implementation that respects the strong nonlinearity in the target applications. Our hierarchical approach in this project is based on a combination of implicit sampling (IS), Markov chain MC (MCMC), and reducedorder models (ROMs), with a focus on application to complex, high dimensional problems. In Implicit Sampling, sample generation is guided by the solution of an optimization problem that is based on the target model; this helps to identify regions of high probability with respect to the posterior (see Implicit Sampling inset below). For MCMC, we use techniques based on parallel marginalization to reduce correlation time in the sampling process, and use an affineinvariant sampling algorithm to improve the overall efficiency when the parameters span orders of magnitude in scale and variation. Reduced order models will play an increasingly important role in building a hierarchy of targets, particularly when the targets span a large range of computational complexities, and when observables are complex functions of the simulated state variables. 



As an example, combustion chemistry models are constructed and optimized with respect to available experimental data; typically including volumetric reactors (such as calormetric bombs, flow reactors, shock tubes), and counterflowing flame systems  all of which are lowdimensional idealized configurations providing fairly wellcharacterized data for limited parameter ranges. However the resulting "validated" combustion models are then applied to a wide range of systems, from zeroD and steady systems to fully turbulent combustion environments. Historically, there has been very little feedback from the more practical combustion systems to the improvements of the underlying models.
Ultimately, we would like to combine all of these technologies into an extensivle
hierarchical adaptive sampling scheme for highdimensional parameter space, where we
can directly exploit the wide range of computational expense associated with zeroD
systems through turbulent 3D reacting flow systems. The ultimate goal is to create the
methodology to incorporate increasingly complex, realistic and relevant experimentally
observable data into the development and improvement of the fundamental models that
underpin the computational predictions of complex multiphysics systems.

Applications 
Contact 