SDE Time-Series Prediction with Domain-Guided Drift Modeling
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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 SDEs, 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
1Reliability
If existing trainable SDE models are used for time-series predictions, then the model can capture stochasticity in the system, but the prediction accuracy is insufficient and large amounts of training data are required
Solution Approach 1:
The drift component of the SDE is segmented into a predefined part (based on domain knowledge) and a trainable part (learned from data). This segmentation allows the model to leverage existing knowledge while only learning the unknown components, thereby improving prediction accuracy with less training data.
Solution Approach 2:
Domain knowledge is incorporated into the predefined drift component before training begins. This preliminary action provides a head start for the model, reducing the amount of training data needed to achieve accurate predictions by pre-establishing a reasonable baseline model.
2Productivity
If existing trainable SDE models are used, then the model can be trained on real-world measurements, 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 training process only needs to optimize the trainable part, significantly reducing the optimization complexity and training time while maintaining the ability to capture system stochasticity.
Solution Approach 2:
Instead of training the entire drift component from scratch, the model applies partial action by only training the unspecified portion of the drift that is not covered by domain knowledge. This reduces training time and computational resources while still achieving accurate predictions.
3Ease of operation
If existing trainable SDE models are used, then the model can make predictions without explicit physical models, but the model lacks explainability and is difficult to debug
Solution Approach 1:
The drift component is divided into a predefined part (based on domain knowledge) and a trainable part. This segmentation provides interpretability because the predefined part represents known physical relationships, while the trainable part captures unknown dynamics, making it easier to understand and debug the model's behavior.
Solution Approach 2:
The predefined drift component acts as an intermediary that bridges domain knowledge and data-driven learning. It provides a interpretable framework that mediates between physical understanding and empirical observations, enhancing model explainability while maintaining predictive accuracy.
Data Source
AI summary
A computer-implemented method 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.