Development of the adjoint of GEOS-Chem

We present the adjoint of the global chemical transport model GEOS-Chem, focusing on the chemical and thermodynamic relationships between sulfate – ammonium – nitrate aerosols and their gas-phase precursors. The adjoint model is constructed from a combination of manually and automatically derived discrete adjoint algorithms and numerical solutions to continuous adjoint equations. Explicit inclusion of the processes that govern secondary formation of inorganic aerosol is shown to afford efficient calculation of model sensitivities such as the dependence of sulfate and nitrate aerosol concentrations on emissions of SOx, NOx, and NH3. The adjoint model is extensively validated by comparing adjoint to finite difference sensitivities, which are shown to agree within acceptable tolerances; most sets of comparisons have a nearly 1:1 correlation and R2>0.9. We explore the robustness of these results, noting how insufficient observations or nonlinearities in the advection routine can degrade the adjoint model performance. The potential for inverse modeling using the adjoint of GEOS-Chem is assessed in a data assimilation framework through a series of tests using simulated observations, demonstrating the feasibility of exploiting gas- and aerosol-phase measurements for optimizing emission inventories of aerosol precursors

Forward, Tangent Linear, and Adjoint Runge Kutta Methods in KPP–2.2 for Efficient Chemical Kinetic Simulations

The Kinetic PreProcessor (KPP) is a widely used software environment which generates Fortran90, Fortran77, Matlab, or C code for the simulation of chemical kinetic systems. High computational efficiency is attained by exploiting the sparsity pattern of the Jacobian and Hessian. In this paper we report on the implementation of two new families of stiff numerical integrators in the new version 2.2 of KPP. One family is the fully implicit three-stage Runge Kutta methods, and the second family are singly diagonally-implicit Runge Kutta methods. For each family tangent linear models for direct decoupled sensitivity analysis, and adjoint models for adjoint sensitivity analysis of chemical kinetic systems are also implemented. To the best of our knowledge this work brings the first implementation of the direct decoupled sensitivity method and of the discrete adjoint sensitivity method with Runge Kutta methods. Numerical experiments with a chemical system used in atmospheric chemistry illustrate the power of the stiff Runge Kutta integrators and their tangent linear and discrete adjoint models. Through the integration with KPP–2.2. these numerical techniques become easily available to a wide community interested in the simulation of chemical kinetic systems

Energy-Aware High Performance Computing

High performance computing centres consume substantial amounts of energy to power large-scale supercomputers and the necessary building and cooling infrastructure. Recently, considerable performance gains resulted predominantly from developments in multi-core, many-core and accelerator technology. Computing centres rapidly adopted this hardware to serve the increasing demand for computational power. However, further performance increases in large-scale computing systems are limited by the aggregate energy budget required to operate them. Power consumption has become a major cost factor for computing centres. Furthermore, energy consumption results in carbon dioxide emissions, a hazard for the environment and public health; and heat, which reduces the reliability and lifetime of hardware components. Energy efficiency is therefore crucial in high performance computing

Cost-Effective Sulphur Reduction Under Uncertainty

The problem of reducing SO2 emissions in Europe is considered. The costs of reduction are assumed to be uncertain and are modeled by a set of possible scenarios. A mean-variance model of the problem is formulated and a specialized computational procedure is developed. The approach is applied to the transboundary air pollution model with real-world data

Hybrid Analog-Digital Co-Processing for Scientific Computation

In the past 10 years computer architecture research has moved to more heterogeneity and less adherence to conventional abstractions. Scientists and engineers hold an unshakable belief that computing holds keys to unlocking humanity's Grand Challenges. Acting on that belief they have looked deeper into computer architecture to find specialized support for their applications. Likewise, computer architects have looked deeper into circuits and devices in search of untapped performance and efficiency. The lines between computer architecture layers---applications, algorithms, architectures, microarchitectures, circuits and devices---have blurred. Against this backdrop, a menagerie of computer architectures are on the horizon, ones that forgo basic assumptions about computer hardware, and require new thinking of how such hardware supports problems and algorithms. This thesis is about revisiting hybrid analog-digital computing in support of diverse modern workloads. Hybrid computing had extensive applications in early computing history, and has been revisited for small-scale applications in embedded systems. But architectural support for using hybrid computing in modern workloads, at scale and with high accuracy solutions, has been lacking. I demonstrate solving a variety of scientific computing problems, including stochastic ODEs, partial differential equations, linear algebra, and nonlinear systems of equations, as case studies in hybrid computing. I solve these problems on a system of multiple prototype analog accelerator chips built by a team at Columbia University. On that team I made contributions toward programming the chips, building the digital interface, and validating the chips' functionality. The analog accelerator chip is intended for use in conjunction with a conventional digital host computer. The appeal and motivation for using an analog accelerator is efficiency and performance, but it comes with limitations in accuracy and problem sizes that we have to work around. The first problem is how to do problems in this unconventional computation model. Scientific computing phrases problems as differential equations and algebraic equations. Differential equations are a continuous view of the world, while algebraic equations are a discrete one. Prior work in analog computing mostly focused on differential equations; algebraic equations played a minor role in prior work in analog computing. The secret to using the analog accelerator to support modern workloads on conventional computers is that these two viewpoints are interchangeable. The algebraic equations that underlie most workloads can be solved as differential equations, and differential equations are naturally solvable in the analog accelerator chip. A hybrid analog-digital computer architecture can focus on solving linear and nonlinear algebra problems to support many workloads. The second problem is how to get accurate solutions using hybrid analog-digital computing. The reason that the analog computation model gives less accurate solutions is it gives up representing numbers as digital binary numbers, and instead uses the full range of analog voltage and current to represent real numbers. Prior work has established that encoding data in analog signals gives an energy efficiency advantage as long as the analog data precision is limited. While the analog accelerator alone may be useful for energy-constrained applications where inputs and outputs are imprecise, we are more interested in using analog in conjunction with digital for precise solutions. This thesis gives novel insight that the trick to do so is to solve nonlinear problems where low-precision guesses are useful for conventional digital algorithms. The third problem is how to solve large problems using hybrid analog-digital computing. The reason the analog computation model can't handle large problems is it gives up step-by-step discrete-time operation, instead allowing variables to evolve smoothly in continuous time. To make that happen the analog accelerator works by chaining hardware for mathematical operations end-to-end. During computation analog data flows through the hardware with no overheads in control logic and memory accesses. The downside is then the needed hardware size grows alongside problem sizes. While scientific computing researchers have for a long time split large problems into smaller subproblems to fit in digital computer constraints, this thesis is a first attempt to consider these divide-and-conquer algorithms as an essential tool in using the analog model of computation. As we enter the post-Moore’s law era of computing, unconventional architectures will offer specialized models of computation that uniquely support specific problem types. Two prominent examples are deep neural networks and quantum computers. Recent trends in computer science research show these unconventional architectures will soon have broad adoption. In this thesis I show another specialized, unconventional architecture is to use analog accelerators to solve problems in scientific computing. Computer architecture researchers will discover other important models of computation in the future. This thesis is an example of the discovery process, implementation, and evaluation of how an unconventional architecture supports specialized workloads

Coupling problem in thermal systems simulations

Building energy simulation is playing a key role in building design in order to reduce the energy consumption and, consequently, the CO2 emissions. An object-oriented tool called NEST is used to simulate all the phenomena that appear in a building. In the case of energy and momentum conservation and species transport, the current solver behaves well, but in the case of mass conservation it takes a lot of time to reach a solution. For this reason, in this work, instead of solving the continuity equations explicitly, an implicit method based on the Trust Region algorithm is proposed. Previously, a study of the properties of the model used by NEST-Building software has been done in order to simplify the requirements of the solver. For a building with only 9 rooms the new solver is a thousand times faster than the current method