Quantum mechanical Hamiltonian learning and temporal property prediction
View Patent ↗A machine learning system for predicting a time dependent property of a material system includes a processor and a memory communicably coupled to the processor. Stored in the memory is an acquisition module and a machine learning module. The machine learning module includes instructions that, when executed by the processor, cause the processor during each of one or more iterations, to train a machine learning model to learn an initial state vector, Hermitian operators encoding observables, and a Hamiltonian of a material system from the Schrödinger equation of the material system propagated in a time series. The machine learning model also predicts, based at least in part on the learned initial state vector, Hermitian operators, and Hamiltonian, at least one time dependent property of the material system at time not equal to zero.
1 . A system comprising:
a processor; and
a memory communicably coupled to the processor and storing machine-readable instructions that, when executed by the processor, cause the processor to:
select a material system from a candidate material system data set and select a training data set from an observables data set;
train a machine learning model with observables for the material system to learn: a) an initial state vector; b) Hermitian operators encoding each observable; and c) a Hamiltonian of the material system from a Schrödinger equation of the material system propagated in a time series, wherein the Schrödinger equation of the material system is represented in a Schrödinger picture; and
predict, based at least in part on the learned initial state vector of the material system, at least one time dependent property of the material system at time t≠0.
2 . The system according to claim 1 , wherein the Schrödinger equation of the material system is:
❘
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Ψ
S
(
t
)
〉
=
exp
(
-
i
H
^
t
ℏ
)
❘
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Ψ
S
(
0
)
〉
where |Ψ s (t) is the state vector of the material system at time t, i is complex number √{square root over (−1)}, Ĥ is a Hamiltonian, t is time, ℏ is Planck's constant divided by 2π, and |Ψ s (0) is the state vector of the material system at t=0.
3 . The system according to claim 2 further comprising training the machine learning model to learn the Hamiltonian Ĥ with the training data set for the material system.
4 . The system according to claim 1 , wherein the Schrödinger equation of the material system is:
❘
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Ψ
S
(
t
+
dt
)
〉
=
exp
(
-
i
H
^
dt
ℏ
)
❘
"\[LeftBracketingBar]"
Ψ
S
(
t
)
〉
where dt is a time interval, |Ψ s (t+dt) is the state vector of the material system at time t+dt, i is complex number √{square root over (−1)}, Ĥ is a Hamiltonian, t is time, ℏ is Planck's constant divided by 2π, and |Ψ s (t) is the state vector of the material system at time t.
5 . The system according to claim 4 further comprising training the machine learning model to learn the Hamiltonian Ĥ with the training data set for the material system for every timer interval dt.
6 . The system according to claim 1 , wherein the material system includes a battery material and the training data set include a plurality of states of charge.
7 . The system according to claim 6 , wherein the plurality of states of charge include states of charge as a function of time.
8 . The system according to claim 6 , wherein the plurality of states of charge include states of charge as a function of load.
9 . The system according to claim 6 , wherein the plurality of states of charge include states of charge as a function of time and load.
10 . The system according to claim 9 , wherein the at least one time dependent property of the material system is service life of the material system.
11 . The system according to claim 1 , wherein the material system includes a catalyst material and the training data set includes a plurality of catalyst activities.
12 . The system according to claim 11 , wherein the plurality of catalyst activities include catalyst activities as a function of time.
13 . The system according to claim 11 , wherein the plurality of catalyst activities include catalyst activities as a function of reactant.
14 . The system according to claim 11 , wherein the plurality of catalyst activities include catalyst activities as a function of time and reactant.
15 . The system according to claim 11 , wherein the plurality of catalyst activities includes catalyst activities as a function of time for which the catalyst material is not exposed to a reactant.
16 . The system according to claim 11 , wherein the plurality of catalyst activities includes catalyst activities as a function of time for which the catalyst material is exposed to a reactant.
17 . The system according to claim 11 , wherein the at least one time dependent property of the material system is catalyst life of the material system.
18 . A system comprising:
a processor; and
a memory communicably coupled to the processor, the memory storing:
an acquisition module including instructions that when executed by the processor cause the processor to select a material system from a candidate material system set and select a training data set for the material system from an observable data set by applying a training function to the observable data set;
a machine learning module including instructions that when executed by the processor cause the processor during each of one or more iterations, to:
train a machine learning model with the observables for the material system to learn: a) an initial state vector; b) Hermitian operators encoding each observable; and c) a Hamiltonian of the material system from a Schrödinger equation of the material system propagated in a time series, wherein the Schrödinger equation of the material system is represented in a Schrödinger picture by one of the equations:
❘
"\[LeftBracketingBar]"
Ψ
S
(
t
)
〉
=
exp
(
-
i
H
^
t
ℏ
)
❘
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Ψ
S
(
0
)
〉
and
❘
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Ψ
S
(
t
+
dt
)
〉
=
exp
(
-
i
H
^
dt
ℏ
)
❘
"\[LeftBracketingBar]"
Ψ
S
(
t
)
〉
where t is time, dt is a time interval, |Ψ s (t) is the state vector of the material system at time t, i is complex number √{square root over (−1)}, Ĥ is the Hamiltonian, ℏ is Planck's constant divided by 2π, |Ψ s (0) is the state vector of the material system at t=0, |Ψ s (t+dt) is the state vector of the material system at time t+dt, and |Ψ s (t) is the state vector of the material system at time t; and
predict, based at least in part on the learned initial state vector of the material system, at least one property of the material system at time t≠0.
19 . The system according to claim 18 , wherein the material system is selected from the group consisting of a battery material and a catalyst material, and observables in the training data set are selected from the group consisting of a plurality of states of charge and a plurality of catalyst activities, respectively, and the plurality of states of charge include the states of charge as a function of time and load, and the plurality of catalyst activities include catalyst activities as a function of time and reactant.
20 . A method comprising:
selecting a material system from a candidate material system set;
selecting a training data set for the material system from an observable data, the material system being selected from the group consisting of a battery material and a catalyst material, and the observable data set containing observables selected from the group consisting of a plurality of states of charge and a plurality of catalyst activities;
training a machine learning model with observables for the material system to learn: a) an initial state vector; b) Hermitian operators encoding each observable; and c) a Hamiltonian of the material system from a Schrödinger equation of the material system propagated in a time series, wherein the Schrödinger equation of the material system is represented in a Schrödinger picture by the equation:
❘
"\[LeftBracketingBar]"
Ψ
S
(
t
)
〉
=
exp
(
-
i
H
^
t
ℏ
)
❘
"\[LeftBracketingBar]"
Ψ
S
(
0
)
〉
where |Ψ s (t) is the state vector of the material system at time t, i is complex number √{square root over (−1)}, Ĥ is the Hamiltonian, t is time, ℏ is Planck's constant divided by 2π, and |Ψ s (0) is the state vector of the material system at t=0; and
predicting, based at least in part on the learned state vector of the material system, at least one time dependent property of the material system at time t≠0.