Keywords
numerical techniques, simulation, executable models, intelligent solver configuration
Start Date
1-7-2006 12:00 AM
Abstract
The models considered in this work contain combinations of a large number of non-linear differential equations and algebraic equations, which have to be solved numerically. Because of this, running simulation experiments on a computer can be very time-consuming, i.e. it can last for days or even weeks. On top of that, some solvers are not appropriate for solving certain of these systems. For example, stiff solvers are only appropriate for stiff systems while they are not the best choice for non-stiff systems. Choosing the appropriate solver and solver settings for a certain initialized model can significantly shorten the computation time. In order to make this choice a scientist must combine the knowledge he/she has of the initialized model with the knowledge of certain solvers and their settings. Unfortunately, most environmental scientists do not have the opportunity to build up experience as modeller/mathematician and most of the time they rely on the default solver settings. The goal of intelligent configuration is to automate the selection of numerical solvers and their settings in order to get the "best result" for the solution of a certain initialized model. The "best result" is influenced by the time it takes to compute the model, as well as by the goal of the simulation experiment, e.g. the required accuracy of the model results. Our intelligent configuration system is developed in two steps: first it gathers and interprets information that enables us to select a certain solver (e.g. input data, parameter values, and properties of the differential equations); in a second step it generalizes this information from one model, so that it can be used to select solvers for other models that resemble the training model. Both steps are developed using machine learning techniques.
Intelligent configuration of numerical solvers of environmental ODE/DAE models using machine learning techniques
The models considered in this work contain combinations of a large number of non-linear differential equations and algebraic equations, which have to be solved numerically. Because of this, running simulation experiments on a computer can be very time-consuming, i.e. it can last for days or even weeks. On top of that, some solvers are not appropriate for solving certain of these systems. For example, stiff solvers are only appropriate for stiff systems while they are not the best choice for non-stiff systems. Choosing the appropriate solver and solver settings for a certain initialized model can significantly shorten the computation time. In order to make this choice a scientist must combine the knowledge he/she has of the initialized model with the knowledge of certain solvers and their settings. Unfortunately, most environmental scientists do not have the opportunity to build up experience as modeller/mathematician and most of the time they rely on the default solver settings. The goal of intelligent configuration is to automate the selection of numerical solvers and their settings in order to get the "best result" for the solution of a certain initialized model. The "best result" is influenced by the time it takes to compute the model, as well as by the goal of the simulation experiment, e.g. the required accuracy of the model results. Our intelligent configuration system is developed in two steps: first it gathers and interprets information that enables us to select a certain solver (e.g. input data, parameter values, and properties of the differential equations); in a second step it generalizes this information from one model, so that it can be used to select solvers for other models that resemble the training model. Both steps are developed using machine learning techniques.
