Implicit Physics Model Recovery Under Low-Sampling Constraints
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Solution Overview
Problem
Existing model recovery techniques struggle with real-world constraints such as low sampling rates, perturbed systems with human inputs, sparsity structure uncertainty, implicit dynamics, and input timing errors, leading to performance degradation and inaccurate model coefficient estimation.
Innovation Solution
The system employs a liquid time constant neural network (LTC-NN) architecture to recover physics models by incorporating automatic differentiation, dense layers for sparsity preservation, and an ODE solver-guided loss function to handle perturbations and input uncertainties, enabling accurate model coefficient estimation under real-world conditions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If model recovery techniques are applied at sub-Nyquist sampling rates, then productivity is improved by reducing sampling requirements, but measurement precision deteriorates due to insufficient information about model coefficients
Solution Approach 1:
The system performs preliminary action by incorporating external knowledge about sparsity structure of non-linear dynamics before the model recovery process. This prior information is embedded into the recovery algorithm through regularization terms and constraints that guide the estimation process, enabling accurate coefficient recovery even when sampling data contains insufficient information
Solution Approach 2:
The system introduces an intermediary regularization mechanism that mediates between the limited sampling data and the target model coefficients. The sparsity-promoting regularization terms act as an intermediary that bridges the information gap, allowing the algorithm to infer missing coefficient information from the available sub-Nyquist samples
2Measurement precision
If more variables and differentials of input observations are included to compensate for input timing errors, then measurement precision improves, but device complexity increases due to additional computational requirements
Solution Approach 1:
The system applies partial action by selectively including only the necessary variables and differentials required to model input timing errors, rather than comprehensively adding all possible terms. The regularization framework identifies and retains only the minimal set of terms that significantly contribute to modeling accuracy, avoiding the computational burden of excessive variables
Solution Approach 2:
The system performs preliminary analysis to identify which input perturbation terms are most critical for accuracy before running the full model recovery. This preliminary selection process reduces the computational complexity by pre-filtering the variable set to include only those terms that provide meaningful improvement in measurement precision
Data Source
AI summary
Examples including a system described herein implement a novel liquid time constant neural network (LTC-NN) based architecture to recover an underlying model of physical dynamics from real world data. The automatic differentiation property of LTC-NN nodes overcomes problems associated with low sampling rate, the input dependent time constant in the forward pass of the hidden layer of LTC-NN nodes creates a massive search space of implicit physical dynamics, the physics model solver based data reconstruction loss guides the search for the correct set of implicit dynamics, and drop out in dense layer ensures extraction of the sparsest model. Further, to account for perturbation timing error, the LTC-NN based architecture of the system utilizes dense layer nodes to search through input shifts that results in the lowest reconstruction loss.