Autoencoder Reduced-Order Modeling for Nonlinear PDE Control
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Solution Overview
Problem
Existing control methods for high-dimensional physical systems with nonlinear dynamics face challenges in designing accurate and physics-informed models, particularly in real-time applications, due to the need for large data sets and the intrusive nature of traditional model reduction techniques, which require access to proprietary software and full model solvers.
Innovation Solution
A computer-implemented method using a neural network model with an autoencoder architecture, including an encoder, a linear or nonlinear operator, and a decoder, trained to represent system dynamics as parameterized ordinary differential equations, allowing for reduced-order modeling and control without requiring access to full model solvers, and leveraging data-driven and physics-informed loss functions for accurate representation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If traditional model reduction techniques (POD-Galerkin projection) are used to reduce system complexity, then device complexity is reduced, but ease of operation deteriorates because access to proprietary software and full model solvers is required
Solution Approach 1:
The patent extracts only the essential dynamic characteristics of the system by training a neural network model on operational data, separating the model creation process from proprietary software dependencies. The neural network learns system dynamics directly from data without requiring access to full model solvers or proprietary simulation tools, thus extracting the necessary information while eliminating the operational burden.
Solution Approach 2:
The patent replaces traditional mechanical model reduction methods (POD-Galerkin projection requiring full model access) with a data-driven neural network approach. This substitution eliminates the need for proprietary software and full model solvers by using operational data to directly train the predictive model, making the system easier to operate while maintaining reduced complexity.
2Ease of operation
If data-driven control methods are used to avoid model-building, then ease of operation is improved, but measurement precision deteriorates due to potential requirement of large quantities of data
Solution Approach 1:
The patent performs preliminary model training during an offline phase using historical operational data. This preliminary action creates a trained neural network model that captures system dynamics accurately before real-time control is needed. By pre-processing and pre-training the model offline, the system achieves both ease of operation during control and high measurement precision without requiring large quantities of data during real-time operation.
3Productivity
If neural network model with autoencoder architecture is used for reduced order modeling, then productivity is improved through faster real-time control, but device complexity increases due to encoder-decoder architecture
Solution Approach 1:
The patent employs a dynamic neural network architecture where the encoder learns to compress system states into a reduced latent space representation, and the decoder reconstructs the full system behavior from this compressed form. This dynamic adaptation allows the model to achieve reduced-order modeling effectiveness with faster real-time computation, balancing productivity improvement against the inherent architectural complexity through learned optimization rather than fixed structural complexity.
Data Source
AI summary
A system and method are provided for training neural network for controlling operation of system having non-linear dynamics represented by partial differential equations (PDEs). The method comprises collecting digital representation of time series data indicative of instances of function space of the system and measurements of state of the operation of the system. Collocation points corresponding to solutions of the PDE are generated. The neural network is trained using training data including the collected time series data and the collocation points to train parameters of non-linear operator. The neural network has autoencoder architecture including encoder to encode each instance of the training data into latent space, the non-linear operator to propagate the encoded instances into the latent space with transformation determined by parameters of the non-linear operator, and decoder to decode the transformed encoded instances of the training data to minimize a hybrid loss function.