MARICI: A powerful software to predict materials
This website is launched to share my findings and passion on my research with the world when they can. The software MARICI implements the algorithm derived from my theory, which is formulated by the mixed-integer nonlinear programming to efficiently predict functional materials.
What is mathematical crystal chemistry?
Mathematical crystal chemistry formalizes the empirical rules of inorganic structural chemistry by generalized disjunctive programming (GDP) which is formulated using continuous and Boolean variables to involve the algebraic equations, disjunctions, and logic propositions. This theory combines the continuous and discrete aspects of crystal structures to develop an efficient solution method for crystal structure prediction.
Why generalized disjunctive programming (GDP)?
The typical form of generalized disjunctive programming (GDP) naturally formulates the empirical rules of inorganic structural chemistry. GDP is one of the specific forms of mixed-integer nonlinear programming, where all the integer variables are only used for indicating whether certain constraints on real variables are enforced or not. Since we have only to introduce a minimal number of constants, variables, and constraint equations, I believe that GDP is exactly suitable for the governing equation to design prototypes of crystal structures as optimal solutions.
Simple governing equation to design crystal structures
Owing to the simpleness of the governing equation formalized by a typical form of GDP, the practical user interface to design crystal structures is also very simple: The input parameters to design crystal structures are only the atomic radii and feasible coordination numbers of each atom. One of the most important discovery derived by mathematical crystal chemistry is that such a simple classcal model is enough to design prototypes of crystal structures.
Removing most of unstable structures
Boolean variables, which are True or False variables, are introduced to elucidate the “combinatorial backbone” of the original continuous optimization problem, which corresponds to the graphs describing crystal structures with clear chemical meanings. Owing to the Boolean variables, mathematical crystal chemistry extracts only the meaningful optimal solutions of the original continuous optimization problem for crystal structure prediction. Accordingly, the number of the optimal solutions, which correspond to prototypes of crystal structures, is getting very small.
High-speed design of crystal structures
The continuous variables represents the packing of atomic spheres with several kinds of atomic radii, while the Boolean variables represents the graphs describing crystal structures with clear chemical meanings. The former consists of lattice parameters, atomic position, and several kinds of atomic radii, while the latter assign one type of interatomic-distance constraints to every pair of atoms. Owing to the smallness of these data and the simple algorithm for structural optimization, the computational cost to design prototypes of crystal structures is very small. The crystal structures of not only simple ternary oxides but also simple quaternary oxides will be discovered in less than ten seconds on your laptop computer.
Mathematics capable of competing with AI performance
Since the feasibilities of continuous variables change drastically depending on Boolean variables and vice versa, iterative optimization of continuous and Boolean variables efficiently transforms a randomly generated initial structure into an optimal solution. This solution method is formulated based on the GDP Branch-and-Bound method and Logic-Based Outer Approximation, which are the conventional methods to solve GDPs. Besides, this solution method includes the subproblem containing the memories of the feasibilities of subgraphs, which is inspired by AI techniques. The efficiency of this solution method indicates that introducing integer variables to extract the “combinatorial backbone” of an original continuous optimization problem accelerates visiting every local optimum by iteratively optimizing the continuous and integer variables like the Logic Based Outer-Approximation and remembering infeasible subsets of integer variables to avoid precise optimization of continous variables with infeasible integer variables like the GDP Branch and Bound method.
What is Marici (Buddhism)?
Marici (Marishiten in Japanese) is the god/goddess of heat haze ("kagerou" in Japanese). Since Marici always walk in front of sun and moon, Marici is invisible illusion despite the huge supernatural power. Marici is never seen, captured, and injured by anyone. Marici rides on a few boars, and according to one theory, Marici murmurs "You have already been defeated" before a ruhing headlong for invisible attack. Marici has been invoked by samurai and ninja, because it has been said that anyone who rever Marici acquires the power of invisibility from Marici.