Neural State-Space Control for Uncertainty-Aware Predictive Models
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Solution Overview
Problem
Current state-space models struggle to simultaneously capture both aleatoric and epistemic uncertainties inherent to real-world technical systems, which is crucial for robust predictive control, especially in safety-critical applications.
Innovation Solution
The integration of neural networks with state-space models to generate a stochastic representation of technical systems, encapsulating uncertainties in both hidden states and neural network parameters, using an augmented state that combines latent states with neural network weights, and approximating transition and observation functions with normal density functions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional state-space models are used to represent technical systems, then the model structure is simple and computationally efficient, but the model cannot simultaneously capture both aleatoric and epistemic uncertainties
Solution Approach 1:
The patent combines neural networks with state-space models to create a hybrid architecture. The neural network components capture complex non-linear relationships and uncertainties (both aleatoric and epistemic), while the state-space model provides the structural framework for temporal dynamics. This merging allows the model to simultaneously achieve high reliability in uncertainty representation and maintain computational tractability through the structured state-space formulation.
Solution Approach 2:
The patent creates a composite modeling approach by integrating two different modeling paradigms: traditional state-space modeling and modern neural network modeling. This composite model leverages the strengths of both approaches - the interpretability and computational efficiency of state-space models and the flexibility and uncertainty representation capabilities of neural networks - to achieve superior overall performance in capturing system uncertainties.
2Adaptability or versatility
If neural networks are used to capture system behaviors, then the model can learn intricate non-linearities, but the computational complexity increases significantly
Solution Approach 1:
The patent segments the neural network into specific functional components within the state-space framework - namely the transition function and observation function. By dividing the neural network into these discrete, purpose-specific modules, the model achieves adaptability for capturing non-linearities while maintaining computational manageability through the structured segmentation of computational tasks.
Solution Approach 2:
The patent employs universal approximator properties of neural networks within the constrained state-space framework. The neural network components serve multiple functions simultaneously: capturing non-linear dynamics, representing uncertainties, and maintaining temporal consistency. This multi-functionality reduces the need for separate specialized components, thereby managing computational complexity while achieving high adaptability.
3Reliability
If sampling-based methods are used to represent uncertainties, then both aleatoric and epistemic uncertainties can be captured, but the computational complexity becomes prohibitive
Solution Approach 1:
The patent substitutes the mechanical sampling-based uncertainty representation with a parametric probabilistic approach. Instead of using computationally intensive sampling methods to represent uncertainties, the model employs analytical probability distributions parameterized by the neural network outputs. This substitution maintains accurate uncertainty representation while dramatically improving computational efficiency by replacing iterative sampling with closed-form probabilistic calculations.
Data Source
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AI summary
The presently disclosed subject matter provides a state-space model which is comprised of one or more neural networks. The state-space model is configured to stochastically model a technical system by modelling uncertainties both in latent states of the technical system and in weights of the one or more neural networks. Thereby, the state-space model may be able to capture both aleatoric uncertainty (inherent unpredictability in observations) and epistemic uncertainty (uncertainty in the model's parameters or weights. During the training and during subsequent use for model-predictive control, moment matching across neural network layers is used, which may ensure that the model's predictions are consistent and close to real system behavior. The above measures may improve the control and safety of many technical systems.