Grey-Box Surrogate Model for Reduced Computational Complexity
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Solution Overview
Problem
Existing mathematical models for time-dependent phenomena face limitations such as high computational complexity, epistemic uncertainties, and dataset errors, making them costly and inefficient for prediction and simulation.
Innovation Solution
A computer-implemented method generates a surrogate mathematical model with reduced computational complexity by combining experimental data with prior knowledge using a grey-box approach, employing artificial neural networks trained with a loss function that balances dataset accuracy and physical principles, thereby reducing uncertainties and computational costs.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If a white-box approach is used to develop mathematical models based on first principles, then the model reliability is improved, but the development time and computational complexity increase
Solution Approach 1:
The patent combines the white-box approach (first principles) and black-box approach (machine learning) into a grey-box approach. The mathematical model integrates physics-based equations with data-driven components, allowing the system to leverage both theoretical reliability and empirical accuracy while reducing overall development time through automated calibration procedures.
Solution Approach 2:
The patent transforms the model development process by changing from purely theoretical parameter selection to a hybrid approach where parameters are partially derived from first principles and partially optimized through machine learning algorithms. This parameter transformation enables faster calibration while maintaining physical consistency.
2Loss of time
If a black-box approach is used to automate model construction through machine learning, then the development time is reduced, but measurement errors and uncertainties increase
Solution Approach 1:
The patent introduces physics-based first principles as an intermediary layer between the raw data and the final model. This intermediary constrains the machine learning process to respect physical laws, thereby filtering out unphysical predictions and reducing the impact of measurement errors while maintaining the speed advantages of automated model construction.
3Measurement precision
If high-fidelity mathematical models are used to describe complex phenomena, then the prediction accuracy is improved, but the computational cost increases
Solution Approach 1:
The patent segments the mathematical model into distinct components: physics-based modules that capture essential phenomena and data-driven modules that handle complex nonlinear behaviors. This segmentation allows computationally intensive parts to be pre-computed or approximated, while retaining high prediction accuracy for the overall system behavior.
4Reliability
If the parametric complexity of mathematical models is increased to capture more phenomenon details, then the model reliability is improved, but the ease of operation deteriorates
Solution Approach 1:
The patent implements automated calibration and optimization procedures that allow the model to self-adjust its parameters based on available data. This self-service capability reduces the burden on users to manually tune complex parameters, making high-reliability models easier to operate while maintaining their sophisticated predictive capabilities.
Data Source
AI summary
A computer-implemented method for the generation of a mathematical model with reduced computational complexity comprises at least the following steps: receiving at input a dataset comprising a plurality of input-output pairs relating to a phenomenon under consideration; receiving at input a plurality of functions relating to principles governing the phenomenon under consideration; determining a first term starting from the dataset comprising a plurality of input-output pairs; determining a second term starting from the functions relating to principles; generating a mathematical model by means of at least one artificial neural network trained on the basis of a loss function obtained starting from the first term and the second term.