# US 12,112,261 B2 · System and method for model parameter optimization

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- Number: US 12,112,261 B2
- Document ID: US12112261B2
- Status: Granted
- Kind: B2
- Application number: 16/714,347
- Filed: 2019-12-13
- Published: 2021-06-17
- Granted: 2024-10-08
- Earliest claimed: 2019-12-13
- Assignees: Hewlett Packard Enterprise Development LP
- Applicants: Cray Inc.
- Inventors: Samuel H. Partee; Benjamin J. Robbins; Michael F. Ringenburg
- Web page: https://patentgrep.com/patent/US12112261B2

## CPC

- G05B 17/02: electric
- G06N 3/08: Learning methods
- G01W 1/02: Instruments for indicating weather conditions by measuring two or more variables, e.g. humidity, pressure, temperature, cloud cover or wind speed (G01W1/10 takes precedence)
- G05B 13/0265: {the criterion being a learning criterion}
- G06F 30/20: Design optimisation, verification or simulation (optimisation, verification or simulation of circuit designs G06F30/30)
- G06F 30/27: using machine learning, e.g. artificial intelligence, neural networks, support vector machines [SVM] or training a model
- G06N 3/0499: Feedforward networks
- G06N 3/09: Supervised learning
- G06N 5/01: Dynamic search techniques; Heuristics; Dynamic trees; Branch-and-bound
- G06N 20/20: Ensemble learning
- G05B: CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS (systems for controlling or regulating non-electric variables G05D; systems for regulating electric or magnetic variables G05F; control devices or systems insofar as characterised by mechanical features only G05G)
- G06N: COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
- G01W: METEOROLOGY (radar, sonar, lidar or analogous systems, designed for meteorological use G01S13/95, G01S15/88, G01S17/95)
- G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N)

## Abstract

One embodiment can provide a method and system for tuning parameters of a numerical model of a physical system. During operation, the system can obtain, using a machine-learning technique, a parameter-transform model for mapping parameters of the numerical model at a first resolution to parameters of the numerical model at a second resolution, the second resolution being higher than the first resolution. The system can perform a parameter-tuning operation on the numerical model at a first resolution to obtain a first set of tuned parameters and apply the parameter-transform model on the first set of tuned parameters to obtain a second set of tuned parameters at a second resolution. The system can then generate behavior information associated with the physical system by running the numerical model at the second resolution using the second set of tuned parameters.

## Claims

### Claim 1

A computer-implemented method comprising:
obtaining, using a first machine-learning technique, a parameter-transform model for mapping parameters of a numerical model other than the parameter-transform model at a first resolution to parameters of the numerical model at a second resolution, wherein the second resolution is higher than the first resolution, and obtaining the parameter-transform model comprises:
obtaining parameter-transform training samples comprising a set of training parameters of the numerical model associated with the first resolution and a corresponding set of training parameters of the numerical model associated with the second resolution; and
training the parameter-transform model using the obtained parameter-transform training samples;
performing a parameter-tuning operation on the numerical model at the first resolution to obtain a first set of tuned parameters;
applying the parameter-transform model on the first set of tuned parameters to obtain a second set of tuned parameters at the second resolution;
generating behavior information associated with the physical system by running the numerical model at the second resolution using the second set of tuned parameters; and
obtaining, using a second machine-learning technique, a parameter-mapping model for mapping an output of the numerical model to actual parameters used for running the numerical model at the first resolution.

### Claim 2 (depends on 1)

The computer-implemented method of claim 1, wherein the set of training parameters of the numerical model associated with the first resolution is obtained by applying the parameter-mapping model to outputs of the numerical model running at the second resolution; and wherein the set of training parameters associated with the second resolution comprises actual parameters used for generating the outputs by executing the numerical model at the second resolution.

### Claim 3 (depends on 1)

The computer-implemented method of claim 1, wherein the parameter-mapping model comprises a deep neural network.

### Claim 4 (depends on 1)

The computer-implemented method of claim 1, further comprising:
obtaining parameter-mapping training samples, which comprise parameters within a predetermined parameter space and outputs of the numerical model generated by executing the numerical model at the first resolution using the parameters within the predetermined parameter space; and
training the parameter-mapping model using the obtained parameter-mapping training samples.

### Claim 5 (depends on 4)

The computer-implemented method of claim 4, wherein obtaining the parameter-mapping training samples further comprises up-mapping the outputs of the numerical model from the first resolution to the second resolution.

### Claim 6 (depends on 4)

The computer-implemented method of claim 4, wherein obtaining the parameter-mapping training samples further comprises preprocessing outputs of the numerical model to facilitate the training of the parameter-mapping model.

### Claim 7

A computer system comprising:
a processor; and
a storage device coupled to the processor and storing instructions which when executed by the processor cause the processor to perform a method, the method comprising:
obtaining, using a first machine-learning technique, a parameter-transform model for mapping parameters of a numerical model other than the parameter-transform model at a first resolution to parameters of the numerical model at a second resolution, wherein the second resolution is higher than the first resolution, and obtaining the parameter-transform model comprises:
obtaining parameter-transform training samples comprising a set of training parameters of the numerical model associated with the first resolution and a corresponding set of training parameters of the numerical model associated with the second resolution; and
training the parameter-transform model using the obtained parameter-transform training samples;
performing a parameter-tuning operation on the numerical model at the first resolution to obtain a first set of tuned parameters; and
applying the parameter-transform model on the first set of tuned parameters to obtain a second set of tuned parameters at the second resolution;
generating behavior information associated with the physical system by running the numerical model at the second resolution using the second set of tuned parameters; and
obtaining, using a second machine-learning technique, a parameter-mapping model for mapping an output of the numerical model to actual parameters used for running the numerical model at the first resolution.

### Claim 8 (depends on 7)

The computer system of claim 7, wherein the set of training parameters of the numerical model associated with the first resolution is obtained by applying the parameter-mapping model to outputs of the numerical model running at the second resolution; and wherein the set of training parameters associated with the second resolution comprises actual parameters used for generating the outputs by executing the numerical model at the second resolution.

### Claim 9 (depends on 7)

The computer system of claim 7, wherein the parameter-mapping model comprises a deep neural network.

### Claim 10 (depends on 7)

The computer system of claim 7, wherein the method further comprises:
obtaining parameter-mapping training samples, which comprise parameters within a predetermined parameter space and outputs of the numerical model generated by executing the numerical model at the first resolution using the parameters within the predetermined parameter space; and
training the parameter-mapping model using the obtained parameter-mapping training samples.

### Claim 11 (depends on 10)

The computer system of claim 10, wherein obtaining the parameter-mapping training samples further comprises up-mapping the outputs of the numerical model from the first resolution to the second resolution.

### Claim 12 (depends on 10)

The computer system of claim 10, wherein obtaining the parameter-mapping training samples further comprises preprocessing outputs of the numerical model to facilitate the training of the parameter-mapping model.

### Claim 13

A computer-implemented method comprising:
obtaining, using a machine-learning technique, a parameter-transform model for mapping parameters of a numerical model other than the parameter-transform model at a first resolution to parameters of the numerical model at a second resolution, wherein the second resolution is higher than the first resolution, the numerical model comprises a deep regression network, and the parameter-transform model comprises a gradient-boosting regression model;
performing a parameter-tuning operation on the numerical model at the first resolution to obtain a first set of tuned parameters;
applying the parameter-transform model on the first set of tuned parameters to obtain a second set of tuned parameters at the second resolution; and
generating behavior information associated with the physical system by running the numerical model at the second resolution using the second set of tuned parameters.