Time-Series Prediction With Hybrid SDE Drift for Controlled Systems
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Solution Overview
Problem
Existing trainable prediction models based on stochastic differential equations (SDEs) for computer-controlled systems are not sufficiently accurate, require large amounts of training data, are computationally inefficient, and lack explainability, making them difficult to debug and trust.
Innovation Solution
A method that combines a predefined drift component with a trainable part in the SDE model, using domain knowledge to improve training efficiency and accuracy, and incorporates Bayesian models for uncertainty representation, allowing for more accurate and interpretable time-series predictions with reduced data requirements.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If existing trainable SDE models are used for time-series predictions, then the model can be trained on real-world measurements, but the prediction accuracy is insufficient and large amounts of training data are required
Solution Approach 1:
The drift component is segmented into a predefined part (based on domain knowledge) and a trainable part (learned from data). This segmentation allows the model to leverage both physical insights and data-driven learning, improving prediction accuracy while reducing the amount of training data needed compared to fully trainable models.
Solution Approach 2:
Domain knowledge is incorporated beforehand into the predefined drift component before training begins. This preliminary action provides a strong foundation that guides the learning process, enabling the model to achieve high accuracy with fewer training samples.
2Productivity
If existing trainable SDE models are used, then the model can learn from observations, but training efficiency is low and convergence is slow or fails
Solution Approach 1:
By segmenting the drift component into predefined and trainable parts, the optimization landscape becomes more favorable. The predefined part provides a good initialization that reduces the search space, leading to faster convergence and improved training efficiency.
Solution Approach 2:
The predefined drift component serves as a preliminary action that pre-configures the model with domain knowledge. This preliminary configuration accelerates convergence by providing a better starting point for optimization, reducing or eliminating training time losses.
3Ease of operation
If existing trainable SDE models are used, then the model can make predictions, but the model is a black-box with little explainability
Solution Approach 1:
The drift component is segmented into a predefined part (based on domain knowledge) and a trainable part (learned from data). This segmentation provides interpretability by separating physically meaningful components from data-driven adjustments, allowing users to understand and verify the model's behavior while maintaining flexibility.
Data Source
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AI summary
The invention relates to a computer-implemented method (600) of training a model for making time-series predictions of a computer-controlled system. The model uses a stochastic differential equation (SDE) comprising a drift component and a diffusion component. The drift component has a predefined part representing domain knowledge, that is received as an input to the training; and a trainable part. When training the model, values of the set of SDE variables at a current time point are predicted based on their values at a previous time point, and based on this, the model is refined. In order to predict the values of the set of SDE variables, the predefined part of the drift component is evaluated to get a first drift, and the first drift is combined with a second drift obtained by evaluating the trainable part of the drift component.