Neural Model Recovery for Low-Sampling Dynamical Systems

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Solution Overview

Problem

Existing model recovery techniques struggle to accurately recover model coefficients from dynamical systems when data is sampled at low frequencies, as the information content is insufficient, leading to increased generalization error and poor performance.

Innovation Solution

Employ a neural architecture, such as liquid time constant neural network (LTC-NN), continuous time recurrent neural network (CT-RNN), or neural ordinary differential equation (NODE), to incorporate sparsity structure and utilize an ODE solver for model coefficient estimation, transforming hidden states into model coefficient estimates and input shift values, and iteratively update to minimize loss.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Productivity

If data is sampled at low frequencies to reduce sampling constraints, then sampling rate is reduced, but information content is insufficient leading to increased generalization error

Engineering Contradiction:

Improvesampling rateVSAvoidmodel coefficient estimation accuracy

Core Design Contradiction:

ProductivityVSMeasurement precision

Solution Approach 1:

The neural network architecture is pre-configured with knowledge of the sparsity structure of the dynamical system before training. This preliminary incorporation of structural information allows the network to effectively learn from limited low-frequency samples by constraining the solution space to physically plausible models, thereby maintaining estimation accuracy despite reduced sampling rates

Inventive Principle:

Principle #10Preliminary action

Solution Approach 2:

A neural network architecture serves as an intermediary between the low-frequency measurement data and the model coefficient estimation. The network transforms the limited observational data into accurate coefficient estimates by leveraging its embedded knowledge of system sparsity structure, effectively bridging the information gap created by subsampling

Inventive Principle:

Principle #24Intermediary (Mediator)

2Measurement precision

If external knowledge such as sparsity structure is incorporated to reduce estimation error, then model recovery performance improves, but device complexity increases

Engineering Contradiction:

Improvemodel coefficient estimation accuracyVSAvoidneural architecture complexity

Core Design Contradiction:

Measurement precisionVSDevice complexity

Solution Approach 1:

Rather than incorporating complex global constraints throughout the entire modeling process, the sparsity structure knowledge is locally integrated into specific components of the neural network architecture. This localized incorporation maintains overall system simplicity while achieving improved estimation accuracy from the limited data

Inventive Principle:

Principle #3Local quality

Data Source

PatentUS20260044649A1Systems and methods for model recovery from real world data

Publication Date: 2026.02.12 THE ARIZONA BOARD OF REGENTS ON BEHALF OF THE UNIV OF ARIZONA

AI summary

A system and associated methods extend neural architectures such as liquid time constant neural network (LTC-NN) or continuous time recurrent neural networks (CT-RNN) or neural ordinary differential equations (NODE) to obtain advanced neural structures (LTC-NN-MR, CT-RNN-MR, NODE-MR) that can recover model coefficients of a dynamical system under low sampling rate conditions. The forward pass of these advanced neural structures has the same form as bilinear approximations of nonlinear dynamics. Measurements of real data can be used to convert the set of non-linear dynamics to an over-determined system of equations that are linear in terms of the model coefficients.