# US 12,596,854 B2 · Systems and methods for material simulation

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- Number: US 12,596,854 B2
- Document ID: US12596854B2
- Status: Granted
- Kind: B2
- Application number: 17/284,596
- Filed: 2019-10-11
- Published: 2021-08-26
- Granted: 2026-04-07
- Earliest claimed: 2018-10-11
- Assignees: Georgia Tech Research Corporation
- Applicants: Georgia Tech Research Corporation
- Inventors: Rampi Ramprasad; Anand Chandrasekaran
- Web page: https://patentgrep.com/patent/US12596854B2

## CPC

- G06F 30/25: using particle-based methods
- G06N 3/04: Architecture, e.g. interconnection topology
- G06N 3/044: Recurrent networks, e.g. Hopfield networks
- G06N 3/0442: characterised by memory or gating, e.g. long short-term memory [LSTM] or gated recurrent units [GRU]
- G06N 3/063: using electronic means
- G06N 3/08: Learning methods
- G06N 3/09: Supervised learning
- G16C 60/00: Computational materials science, i.e. ICT specially adapted for investigating the physical or chemical properties of materials or phenomena associated with their design, synthesis, processing, characterisation or utilisation
- G06F 2111/10: Numerical modelling
- G16C 20/30: Prediction of properties of chemical compounds, compositions or mixtures
- G16C 20/70: Machine learning, data mining or chemometrics
- G16C 20/80: Data visualisation
- G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N)
- G06N: COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
- G16C: COMPUTATIONAL CHEMISTRY; CHEMOINFORMATICS; COMPUTATIONAL MATERIALS SCIENCE

## Abstract

A system for a material simulation is disclosed. The system may receive an input structure for the material and identify a reference grid point for the material. The system may determine a scalar, vector, and tensorial component for the material. Further, the system may render the vector component and the tensorial component rotationally invariant. Next, the system may generate a first structure fingerprint for the material based on the scalar, vector component, and tensorial component. The system may map the structure fingerprint to stored atomic configurations and based on corresponding stored atomic configuration(s), may determine an approximate total electronic charge density and a plurality of approximate energy levels for the reference grid point. Based on the plurality of approximate energy levels, the system may determine a predictive local density of states for the reference grid point. The system may also generate and display a visual simulation of the material.

## Claims

### Claim 1

A method for material fingerprinting 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 the 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;
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 of atoms of 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;
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;
determining, 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;
determining, by the processor, a 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;
generating, by the processor, a first visual simulation of the second material based on the total electronic charge density and the local density of states;
displaying, by the computing device, the first visual simulation via a graphical user interface (GUI); and
further training the RNN based on the determined total electronic charge density for the first reference grid point g and the determined local density of states for the first reference grid point g to improve the accuracy of the RNN.

### Claim 2 (depends on 1)

The method of claim 1, wherein the first structure fingerprint for the second material is a numerical representation of the atomic arrangement around the first grid reference point of the second material.

### Claim 3 (depends on 2)

The method of claim 2, further comprising rendering the first vector component rotationally invariant by: applying an equation of: VkΩ=√{square root over ((VkΩx)2)}+(VkΩy)2+(VkΩz)2.

### Claim 4 (depends on 2)

The method of claim 2, further comprising rendering the first tensorial component rotationally invariant by:
applying an equation of: T′kΩ=TkΩxxTkΩyy+TkΩyyTkΩzz+TkΩxxTkΩzz−(TkΩxy)2−(TkΩyz)2−(TkΩzx)2; and
applying an equation of: T″kΩ=detTkΩαβ.

### Claim 5 (depends on 2)

The method of claim 2, further comprising rendering the first tensorial component rotationally invariant by: applying an equation of: T′″kΩ=TkΩxx+TkΩyy+TkΩzz.

### Claim 6 (depends on 2)

The method of claim 2, wherein the RNN is located on a remote device.

### Claim 7 (depends on 1)

The method of claim 1, further comprising sending, by the transceiver, instructions to a remote device that causes the remote device to display the first visual simulation as a second GUI.

### Claim 8 (depends on 1)

The method of claim 1, further comprising:
identifying, by the processor, a second reference grid point (g2) for the second material;
determining, by the processor, a second scalar component for the second material based on the second reference grid point;
determining, by the processor, a second vector component for the second material based on the second reference grid point;
determining, by the processor, a second tensorial component for the second material based on the second reference grid point;
generating, by the processor, a second structure fingerprint (G2) for the second material based on the second scalar component, the second vector component, and the second tensorial component, wherein the second structure fingerprint comprises a numerical representation of the second structure fingerprint;
sending, by the processor, the second structure fingerprint to the RNN, wherein the RNN maps the second structure fingerprint to stored atomic configurations;
receiving, by the processor, a second plurality of approximate energy levels for the second reference grid point based on at least one corresponding stored atomic configuration, from the RNN;
generating, by the processor, a second predictive local density of states for the second reference grid point based on the second plurality of approximate energy levels; and
calculating, by the processor, a total density of states (DOS) based on at least the local density of states for the first reference grid point and the second predictive local density of states.

### Claim 9

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.

### Claim 10 (depends on 9)

The method of claim 9, wherein 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;
wherein ck is a normalization constant given by
1
2
⁢
π
⁢
σ
k
;
wherein NΩ is a number of atoms of the species Ω; and
wherein an overall dimensionality of the scalar component is based on a number of Gaussians k and a type of the species Ω.

### Claim 11 (depends on 9)

The method of claim 9, wherein 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
)
;
and
wherein α represents each of the x, y, or z directions.

### Claim 12 (depends on 11)

The method of claim 11, further comprising rendering the first vector component rotationally invariant by: applying an equation of: VkΩ=√{square root over ((VkΩx)2)}+(VkΩy)2+(VkΩz)2.

### Claim 13 (depends on 9)

The method of claim 9, wherein 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
wherein β represents each of the x, y, or z directions.

### Claim 14 (depends on 13)

The method of claim 13, further comprising rendering the first tensorial component rotationally invariant by:
applying an equation of: T′kΩ=TkΩxxTkΩyy+TkΩyyTkΩzz+TkΩxxTkΩzz−(TkΩxy)2−(TkΩyz)2−(TkΩzx)2; and
applying an equation of: T″kΩ=detTkΩαβ.

### Claim 15 (depends on 13)

The method of claim 13, further comprising rendering the first tensorial component rotationally invariant by: applying an equation of:
T
k
⁢
Ω
′′′
=
T
k
⁢
Ω
xx
+
T
k
⁢
Ω
yy
+
T
k
⁢
Ω
zz
.

### Claim 16 (depends on 9)

The method of claim 9, further comprising:
identifying, by the processor, a second reference grid point (g2) for the second material;
determining, by the processor, a second scalar component for the second material based on the second reference grid point;
determining, by the processor, a second vector component for the second material based on the second reference grid point;
determining, by the processor, a second tensorial component for the second material based on the second reference grid point;
generating, by the processor, a second structure fingerprint (G2) for the second material based on the second scalar component, the second vector component, and the second tensorial component, wherein the second structure fingerprint comprises a numerical representation of the second structure fingerprint;
sending, by the processor, the second structure fingerprint to the RNN, wherein the RNN maps the second structure fingerprint to stored atomic configurations;
receiving, by the processor, a second plurality of approximate energy levels for the second reference grid point based on at least one corresponding stored atomic configuration, from the RNN;
generating, by the processor, a second predictive local density of states for the second reference grid point based on the second plurality of approximate energy levels; and
calculating, by the processor, a total density of states (DOS) based on at least the first predictive local density of states and the second predictive local density of states.

### Claim 17

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.

### Claim 18 (depends on 17)

The system of claim 17, wherein the system is further configured to:
identify, by the processor, a second reference grid point (g2) for the second material;
determine, by the processor, a second scalar component for the second material based on the second reference grid point;
determine, by the processor, a second vector component for the second material based on the second reference grid point;
determine, by the processor, a second tensorial component for the second material based on the second reference grid point;
generate, by the processor, a second structure fingerprint (G2) for the second material based on the second scalar component, the second vector component, and the second tensorial component, wherein the second structure fingerprint comprises a numerical representation of the second structure fingerprint;
map, by the RNN, the second structure fingerprint to stored atomic configurations;
determine, by the RNN, a second plurality of approximate energy levels for the second reference grid point based on at least one corresponding stored atomic configuration;
determine, by the processor, a second predictive local density of states for the second reference grid point based on the second plurality of approximate energy levels; and
calculate, by the processor, a total density of states (DOS) based on at least the first predictive local density of states for the first reference grid point and the second predictive local density of states.