Systems and methods for material simulation

A method for material simulation with reduced computational requirements, the method comprising:

• training, by a computing device, a recurrent neural network (RNN) to predict an approximate total electronic charge density and a plurality of approximate energy levels for a plurality of grid points based on a provided structure fingerprint by mapping the provided structure fingerprint to stored atomic configurations, wherein the RNN comprises three hidden layers with a plurality of neurons in each layer, and wherein the plurality of grid points comprise arrangements of millions of atoms of a first material;
• receiving, by a transceiver of the computing device, an input structure for a second material, the input structure comprising arrangements of millions of atoms of the second material;
• identifying, by a processor of a computing device and based on the input structure, a first reference grid point (g) for the second material;
• determining, by the processor, a first scalar component for the second material, wherein the first scalar component comprises radial information of a plurality of atoms of the second material;
• determining, by the processor, a first vector component for the second material based on the first reference grid point;
• determining, by the processor, a first tensorial component for the second material based on the first reference grid point;
• generating, by the processor, a first structure fingerprint (G) for the second material based on the first scalar component, the first vector component, and the first tensorial component by applying one or more functions to the first scalar component, the first vector component, and the first tensorial component;
• sending, by the processor, the first structure fingerprint to the RNN;
• generating, using the trained RNN, a first approximate total electronic charge density and a first plurality of approximate energy levels for the first reference grid point g based on the first structure fingerprint G;
• receiving, by the processor, the first approximate total electronic charge density for the first reference grid point based on at least one corresponding stored atomic configuration, from the RNN;
• generating, by the processor, a predictive total electronic charge density for the first reference grid point based on the approximate total electronic charge density generated by the trained RNN;
• receiving, by the processor, the first plurality of approximate energy levels for the first reference grid point based on at least one corresponding stored atomic configuration, from the RNN;
• generating, by the processor, a first predictive local density of states for the first reference grid point based on the first plurality of approximate energy levels generated by the trained RNN;
• generating, by the processor, a first visual simulation of the second material based on the first predictive local density of states and the predictive total electronic charge density;
• displaying, by a graphical user interface of the computing device, the first visual simulation of the second material;
• and
• further training the RNN based on the generated predictive total electronic charge density for the first reference grid point g and the generated first predictive local density of states for the first reference grid point g to improve the accuracy of the RNN.

A system for material simulation with reduced computational requirements, the system comprising:

• a computing device comprising:
• a processor;
• a transceiver;
• and
• a graphical user interface;
• a recurrent neural network (RNN);
• and
• memory, in communication with the processor, the transceiver, the RNN, and the graphical user interface, storing instructions, that when executed, cause the system to:
• train, by the computing device, the RNN to predict an approximate total electronic charge density and a plurality of approximate energy levels for a plurality of grid points based on a provided structure fingerprint by mapping the provided structure fingerprint to stored atomic configurations, wherein the RNN comprises three hidden layers with a plurality of neurons in each layer, and wherein the plurality of grid points comprise arrangements of millions of atoms of a first material;
• receive, by the transceiver, an input structure for a second material, the input structure comprising arrangements of millions of atoms of the second material;
• identify, by the processor, a first reference grid point (g) for the second material;
• determine, by the processor, a first scalar component for the second material, wherein the first scalar component comprises radial information of a plurality of atoms of the second material;
• determine, by the processor, a first vector component for the second material based on the first reference grid point;
• determine, by the processor, a first tensorial component for the second material based on the first reference grid point;
• generate, by the processor, a first structure fingerprint (G) for the second material based on the first scalar component, the first vector component, and the first tensorial component;
• wherein one or more of:
• determining the first scalar component for the second material comprises applying an equation of:
• S_kQ=c_kΣ_(i=1){circumflex over ( )}(N_Ω)exp((−r_gi{circumflex over ( )}2)/2σ_k{circumflex over ( )}2)f_c(rgi), wherein rgi is an amount of distance between an atom (i) of a species Ω and the first reference grid point location is any cutoff function that decays to zero for the plurality of atoms at a distance greater than Rc from the first reference grid point g, ck is a normalization constant given by
• 1
• 2
• ⁢
• π
• ⁢
• σ
• k
• ,
• NΩ is a number or atoms or the species Ω, and an overall dimensionality of the first scalar component is based on a number of Gaussians k and a type of the species Ω;
• determining the first vector component for the second material comprises applying an equation of:
• V
• k
• ⁢
• Ω
• α
• =
• c
• k
• ⁢
• ∑
• i
• =
• 1
• N
• Ω
• ⁢
• r
• gi
• α
• r
• gi
• ⁢
• exp
• ⁡
• (
• -
• r
• gi
• 2
• 2
• ⁢
• σ
• k
• 2
• )
• ⁢
• f
• c
• (
• r
• g
• ⁢
• i
• )
• ,
• wherein α represents each of the x, y, or z directions;
• determining the first tensorial component for the second material comprises applying an equation of:
• T
• k
• ⁢
• Ω
• α
• ⁢
• β
• =
• c
• k
• ⁢
• ∑
• i
• =
• 1
• N
• Ω
• ⁢
• r
• gi
• α
• ⁢
• r
• gi
• β
• r
• gi
• 2
• ⁢
• exp
• ⁡
• (
• -
• r
• gi
• 2
• 2
• ⁢
• σ
• k
• 2
• )
• ⁢
• f
• c
• (
• r
• g
• ⁢
• i
• )
• ,
• wherein α represents each of the x, y, or z directions, and β represents each of the x, y, or z directions;
• and
• generating the first structure fingerprint comprises applying a function to the first scalar component, the first vector component, and the first tensorial component;
• generate, using the trained RNN, a first approximate total electronic charge density and a first plurality of approximate energy levels for the first reference grid point g based on the first structure fingerprint G;
• determine, by the processor, a total electronic charge density for the first reference grid point g based on the approximate total electronic charge density generated by the trained RNN;
• determine, by the processor, a first predictive local density of states for the first reference grid point g based on the first plurality of approximate energy levels generated by the trained RNN;
• generate, by the processor, a first visual simulation of the second material based on the total electronic charge density and the first predictive local density of states;
• display, by the graphical user interface, the first visual simulation;
• and
• further train the RNN based on the determined total electronic charge density for the first reference grid point g and the determined first predictive local density of states for the first reference grid point g to improve the accuracy of the RNN.