Spiking Neural Koopman Operator Approximation for On-Board Inference
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Solution Overview
Problem
Existing methods for approximating Koopman operators, such as Dynamic Mode Decomposition and Artificial Neural Networks, face challenges in capturing nonlinear system complexities, computational intensity, and inefficiency in resource-constrained environments, particularly for applications like autonomous vehicles and drones.
Innovation Solution
A spiking neural network (SNN) based architecture is used to approximate Koopman operators, comprising a spiking encoder block, a Koopman block, and a spiking decoder block, utilizing Leaky Integrate-and-Fire-neuron layers to provide a sparse-spike domain representation and estimate eigenvalues, with a loss function optimization for efficient computation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If Dynamic Mode Decomposition is used to approximate Koopman operator, then computational complexity is reduced, but ability to capture nonlinear system complexities deteriorates
Solution Approach 1:
The system segments the computational task into two distinct modules: (1) an SNN-based encoder that captures nonlinear features from raw sensor data, and (2) a DMD-based linear operator that performs efficient dynamic mode decomposition. This segmentation allows each component to specialize - the SNN handles nonlinear complexity while DMD provides computational efficiency, resolving the contradiction between capturing nonlinearities and maintaining low computational complexity.
Solution Approach 2:
The spiking neural network acts as an intermediary transformation layer that converts raw nonlinear sensor data into a latent representation space. This intermediate representation is then processed by the linear DMD operator. The SNN intermediary enables the subsequent linear operator to work efficiently on transformed data that already encodes nonlinear characteristics, thus achieving both nonlinear capture and computational efficiency.
2Adaptability or versatility
If Artificial Neural Network based approaches are used to discover eigenfunctions, then representation capability is improved, but computational resource consumption increases
Solution Approach 1:
The patent substitutes traditional artificial neural networks with spiking neural networks that operate on event-driven spike trains rather than continuous activations. This substitution replaces the energy-intensive continuous computation mechanism with a sparse, event-based mechanism where neurons only fire when necessary, dramatically reducing computational resource consumption while maintaining representation capability for discovering Koopman eigenfunctions.
Solution Approach 2:
The spiking neural network employs periodic firing patterns and threshold-based activation mechanisms where neurons accumulate input over time and fire periodically when thresholds are reached. This periodic action pattern creates sparse computation windows separated by rest periods, reducing overall computational resource consumption compared to continuous activation in traditional ANNs, while still achieving effective representation of nonlinear dynamics.
3Adaptability or versatility
If traditional neural networks are used for real-time system adaptation, then adaptability to environmental changes is improved, but energy consumption increases
Solution Approach 1:
The spiking neural network implements self-service through adaptive threshold mechanisms and homeostatic plasticity where neurons automatically adjust their firing thresholds and connection weights based on recent activity patterns. This self-adjustment occurs without requiring external retraining or supervision, enabling real-time adaptation to environmental changes in energy-efficient autonomous systems while maintaining low power consumption through sparse spiking activity.
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AI summary
Koopman operator theory is a widely used method to analyze, control, and predict the behavior of the states of a non-linear dynamical system using measurement functions in Hilbert space. Real time approximation of the Koopman operator is crucial in order to adapt and understand behavior of underlying non-linear dynamical system. Traditional approaches leverage matrix-based methods or artificial neural networks to approximate Koopman operator. However, such methods necessitate significant power and computational resources, therefore may not be suitable for applications that require real-time on-board processing. The problems of the conventional approaches are resolved based on a recent development of brain inspired spiking neural networks and neuromorphic computing platforms, as these offer extremely low-energy computation and real-time responses. Embodiments of the present disclosure provide implementation of a Spiking Neural Network (SNN) based architecture that efficiently approximate Koopman operator with minimal length of data and demonstrates significant computational savings.