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AMPL – modelling language for large-scale linear, mixed integer and nonlinear optimization. ANTIGONE – a deterministic global optimization MINLP solver. APMonitor – modelling language and optimization suite for large-scale, nonlinear, mixed integer, differential, and algebraic equations with interfaces to MATLAB, Python, and Julia.
Rule-based modeling is a modeling approach that uses a set of rules that indirectly specifies a mathematical model. The rule-set can either be translated into a model such as Markov chains or differential equations, or be treated using tools that directly work on the rule-set in place of a translated model, as the latter is typically much bigger.
One of the popular examples in computer science is the mathematical models of various machines, an example is the deterministic finite automaton (DFA) which is defined as an abstract mathematical concept, but due to the deterministic nature of a DFA, it is implementable in hardware and software for solving various specific problems. For example ...
The mathematical model represents the physical model in virtual form, and conditions are applied that set up the experiment of interest. The simulation starts – i.e., the computer calculates the results of those conditions on the mathematical model – and outputs results in a format that is either machine- or human-readable, depending upon ...
A big step towards the modern modelling languages is found in UIMP, [8] where the structure of the mathematical programming models taken from real life is analyzed for the first time, to highlight the natural grouping of variables and constraints arising from such models. This led to data-structure features, which supported structured modelling ...
SageMath is an open-source math software, [12] with a unified Python interface which is available as a text interface or a graphical web-based one. Includes interfaces for open-source and proprietary general purpose CAS, and other numerical analysis programs, like PARI/GP, GAP, gnuplot, Magma, and Maple.
Model order reduction (MOR) is a technique for reducing the computational complexity of mathematical models in numerical simulations. As such it is closely related to the concept of metamodeling , with applications in all areas of mathematical modelling .
A surrogate model is an engineering method used when an outcome of interest cannot be easily measured or computed, so an approximate mathematical model of the outcome is used instead. Most engineering design problems require experiments and/or simulations to evaluate design objective and constraint functions as a function of design variables.