Neural SDE State Prediction With Mean-Covariance Uncertainty
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Solution Overview
Problem
Existing methods for predicting the state of computer-controlled entities and their environments using stochastic differential equations (SDEs) are unstable, lack accurate uncertainty estimation, and require computationally expensive sampling, leading to poor control decisions.
Innovation Solution
A method involving neural networks to approximate the drift and diffusion components of SDEs, combined with Euler-Maruyama or Milstein discretization, allows for the determination of time-evolving mean and covariance functions, providing stable and accurate predictions with uncertainty estimates.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If sampling methods are used to solve SDEs for state prediction, then prediction capability is achieved, but computational cost increases and training stability deteriorates
Solution Approach 1:
The patent replaces traditional mechanical sampling methods with a neural network-based continuous prediction system. The neural network learns to directly predict future states from current states and control inputs, substituting the discrete sampling approach with a continuous, differentiable function that can be trained efficiently using gradient-based optimization.
Solution Approach 2:
The patent transforms the discrete sampling parameters into continuous function parameters. Instead of using fixed sampling intervals and discrete state transitions, the system uses neural network parameters (weights and biases) that can be continuously optimized through backpropagation, enabling stable training and efficient prediction without computational sampling overhead.
2Measurement precision
If traditional SDE solving methods are used, then state prediction is possible, but training stability deteriorates
Solution Approach 1:
The patent replaces unstable traditional SDE solving methods with a neural network-based system. The neural network provides a smooth, differentiable approximation of the SDE solution that can be trained using standard gradient descent, eliminating the numerical instability inherent in discrete sampling and iterative solving methods.
Solution Approach 2:
The neural network is designed to be self-contained, learning the complete dynamics model from data without requiring external solvers or sampling procedures during prediction. The network internally captures the stochastic dynamics through its learned parameters, making the system self-sufficient and training-stable.
3Reliability
If uncertainty estimation is implemented using traditional methods, then prediction uncertainty can be assessed, but computational cost increases
Solution Approach 1:
The patent merges uncertainty estimation with the primary prediction function by using the same neural network to output both predicted states and uncertainty metrics. The network simultaneously learns the mean and variance (or confidence intervals) of predictions, combining two functions into a single efficient model rather than requiring separate computational processes.
Solution Approach 2:
The patent replaces computationally expensive traditional uncertainty quantification methods (such as Monte Carlo sampling or bootstrapping) with a neural network-based approach. The network directly predicts uncertainty measures as part of its output, substituting iterative sampling procedures with a single forward pass that provides both prediction and confidence assessment.
Data Source
AI summary
A computer-implemented method 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 includes 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, and 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.