The main objective of the Caliente Project is to create and apply algorithms and software tools for on-line simulations that continuously (1) assimilate sensor data from dynamic physical processes, and (2) generate optimal strategies for their control. The critical step in both phases is the solution of a large-scale nonlinear optimization problem that is constrained by the simulation equations, typically partial differential equations (PDEs) or their reduced order models.

• The data assimilation phase seeks to minimize the mismatch between sensor data and model-based predictions by adjusting unknown parameters of the PDE simulation, typically initial/boundary conditions, model coefficients, sources, or the geometry.
• The optimal control phase finds an optimal control strategy based on the just-updated PDE model.

A number of critical industrial, scientific, and societal problems stand to benefit from our proposed research, including applications in aerodynamics, energy, the environment, geophysics, homeland security, infrastructure, manufacturing, and medicine. In these and many other cases, the underlying models have become capable of sufficient fidelity to yield meaningful predictions, provided unknown parameters can be estimated appropriately using observational data.

Incorporation of such high-resolution models into the decision-making process requires real-time data assimilation and optimal control of PDEs, a task that, until recently, could not even be contemplated. However, the past decade has witnessed a number of remarkable advances that collectively undergird and invite the research we propose. First, aggressive advances in processor and network speeds have made commodity-based multiprocessors with peak speeds of hundreds of gigaflop/s affordable for regional industrial and governmental sites, and several multi-teraflop/s systems have come on line at national laboratories and supercomputing centers. Second is the emergence of parallel PDE solvers capable of resolving complex physics and scaling to the thousands of processors that characterize these systems. Third, large-scale optimization algorithms are beginning to appear that are tailored to PDE constraints and exploit these PDE solvers. Finally, real-time optimization with simpler ODE models is in production use in several industries.

However, despite these advances in hardware, networks, parallel PDE solvers, large-scale optimization algorithms, and real-time ODE optimization, significant algorithmic and software challenges must be overcome before the ultimate goal of real-time PDE data assimilation and optimal control can be realized. We need fundamentally new PDE optimization algorithms that must: (1) run sufficiently quickly to permit decision-making at time scales of interest; (2) scale to the large numbers of variables and constraints that characterize PDE optimization and processors that characterize high-end systems; (3) adjust to different solution accuracy requirements; (4) target time-dependent objectives and constraints; (5) tolerate incomplete, uncertain, or errant data; (6) be capable of bootstrapping current solutions; (7) yield meaningful results when terminated prematurely; and (8) be robust in the face of ill-posedness.

To create, apply, and disseminate the enabling technologies for real-time PDE data assimilation and optimal control, we are working to:

• Develop algorithms and tools for real-time data assimilation and optimal control that meet the above specifications for a class of important applications.
• Implement and publicly distribute these algorithms within an object-oriented framework that (1) incorporates problem structure, (2) interfaces easily with high performance PDE solver libraries (such as PETSc and Trilinos), (3) fosters applicability of our tools to a broad range of real-time data assimilation and optimal control problems, and (4) enables extension of the algorithms without interfering with applications.
• Apply these algorithms and tools to critical environmental, industrial, and national problems, including inversion and control of wildland firespread, airborne chemical attacks, and groundwater pollutants.
• Interact with other user communities to ensure that the algorithms and software we produce are useful across a broad range of applications.

The Caliente Project receives major support from the National Science Foundation's Information Technology Research Program, through grants ACI-0121667 to Carnegie Mellon University, ACI-0121207 to Old Dominion University, and ACI-0121360 to Rice University.