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US 2023/0267166 A1Published application
Parallel Simulation of Large-Scale Dynamical Systems Using Tensor Network
AssigneeEFSolutions GbR
InventorsStefano Elefante, Raffaele Iervolino
Life of this patent
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Abstract
A system includes a memory storing computer-readable instructions and at least one processor to execute the instructions to perform at least one tensor network method to numerically solve at least one differential equation.
Claims21
A system comprising:
- a memory storing computer-readable instructions;
- and
- at least one processor to execute the instructions to:
- perform at least one tensor network method to numerically solve at least one differential equation;
- build a mathematical representation of one of a physical, economic, and engineering problem using the at least one differential equation;
- determine a graph that defines connections between states of the problem and determine an adjacency matrix;
- subdivide a matrix into n sets of matrices whose elements commute with each other while at least one element of a set does not commute with at least one element of another set;
- implement a Suzuki Trotter decomposition using singular value decomposition to reduce data transfer among cores of the at least one processor on the n sets of matrices with a given time interval δ and a predefined p expansion order;
- evaluate the problem at a time T=Nδ by iteratively performing the Suzuki Trotter decomposition N times;
- and
- generate simulation results for the problem within an error of order of No (δp+1).
8 more elements
A method, comprising:
- performing, by at least one processor, at least one tensor network method to numerically solve at least one differential equation;
- building, by the at least one processor, a mathematical representation of one of a physical, economic, and engineering problem using the at least one differential equation;
- determining, by the at least one processor, a graph that defines connections between states of the problem and determining an adjacency matrix;
- subdividing, by the at least one processor, a matrix into n sets of matrices whose elements commute with each other while at least one element of a set does not commute with at least one element of another set;
- implementing, by the at least one processor, a Suzuki Trotter decomposition using singular value decomposition to reduce data transfer among cores of the at least one processor on the n sets of matrices with a given time interval δ and a predefined p expansion order;
- evaluating, by the at least one processor, the problem at a time T=Nδ by iteratively performing the Suzuki Trotter decomposition N times;
- and
- generating, by the at least one processor, simulation results for the problem within an error of order of No(δp+1).
5 more elements
A non-transitory computer-readable storage medium comprising instructions stored thereon that, when executed by a computing device cause the computing device to perform operations, the operations comprising:
- performing, at least one tensor network method to numerically solve at least one differential equation;
- building a mathematical representation of one of a physical, economic, and engineering problem using the at least one differential equation;
- determining a graph that defines connections between states of the problem and determining an adjacency matrix;
- subdividing a matrix into n sets of matrices whose elements commute with each other while at least one element of a set does not commute with at least one element of another set;
- implementing a Suzuki Trotter decomposition using singular value decomposition to reduce data transfer among cores of the at least one processor on the n sets of matrices with a given time interval δ and a predefined p expansion order;
- evaluating the problem at a time T=Nδ by iteratively performing the Suzuki Trotter decomposition N times;
- and
- generating simulation results for the problem within an error of order of No(δp+1).
5 more elements
Dependencies are inferred from the claim text.