State Prediction With Neural SDEs for Stable Uncertainty-Aware Control
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Solution Overview
Problem
Current methods for modeling stochastic differential equations (SDEs) in computer-controlled entities are unstable and lack accurate prediction uncertainties, leading to poor control decisions due to noise injection and complex physical processes that are difficult to model accurately.
Innovation Solution
A computer-implemented method using trained neural networks to approximate the drift and diffusion components of SDEs, discretizing the equations into time steps, and determining time-evolving mean and covariance functions to provide accurate state predictions and uncertainty estimates, allowing for improved control and monitoring of computer-controlled entities.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If current methods for modeling stochastic differential equations are used, then control decisions can be made, but the training process is unstable and prediction uncertainties are inaccurate
Solution Approach 1:
The patent applies preliminary action by pre-processing the stochastic differential equation model to separate drift and diffusion components before training. The drift component is modeled using a neural network while the diffusion component is handled through analytical solutions, preparing the model in advance to avoid training instability. This pre-structuring allows for more reliable predictions by establishing a stable foundation before the actual training process begins.
Solution Approach 2:
The patent substitutes the traditional mechanical training approach for SDEs with a hybrid method that replaces parts of the neural network training mechanism with analytical solutions. Specifically, the diffusion component is solved analytically rather than through iterative training, replacing the mechanical training loop with a more stable mathematical approach for that specific component while retaining neural networks for the drift component.
2Adaptability or versatility
If noise is injected into the SDE model to capture physical processes, then the model can represent complex real-world behavior, but the training becomes unstable and harder to control
Solution Approach 1:
The patent applies segmentation by dividing the stochastic differential equation into two distinct components: the drift component and the diffusion component. The drift component, which represents the deterministic part of the system, is modeled using a neural network. The diffusion component, which represents the stochastic noise, is handled separately through analytical solutions. This segmentation allows the model to capture complex physical processes while maintaining training stability and control.
Solution Approach 2:
The patent introduces an intermediary approach by using analytical solutions as a mediator between the noise injection requirement and training stability. Instead of directly injecting noise into the training process, the diffusion component is handled through analytical solutions that inherently account for noise while providing stable training. This intermediary method bridges the gap between model flexibility and ease of operation.
3Loss of information
If traditional SDE modeling approaches are used, then the model can capture stochastic behavior, but accurate prediction uncertainties cannot be provided
Solution Approach 1:
The patent implements feedback by incorporating uncertainty information from the analytical diffusion component back into the overall prediction process. The analytical solution for the diffusion component provides explicit uncertainty estimates that feed into the final prediction, allowing the system to maintain accurate uncertainty information. This feedback mechanism ensures that control decisions are made with reliable uncertainty quantification, improving both information retention and decision quality.
Data Source
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AI summary
The invention relates to a computer-implemented method (500) for enabling control or monitoring of a computer-controlled entity operating in an environment by predicting a future state of the computer-controlled entity and/or its environment using sensor data which is indicative of a current state of the computer-controlled entity and/or its environment. The method comprises using a first neural network for approximating a drift component of a stochastic differential equation and a second neural network for approximating a diffusion component of the stochastic differential equation, and discretizing the stochastic differential equation into time steps. The method further comprises obtaining time-evolving mean and covariance functions based on the discretization and determining a probability distribution of a second state of the computer-controlled entity and/or its environment therefrom. The control of the computer-controlled entity may thus be enhanced and made more efficient and reliable using the uncertainty information available from the determined probability distribution.