Physics-Informed Neural Network Adaptive Design Optimization
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Solution Overview
Problem
Deep neural networks (DNNs) face challenges in multi-cycle development for engineering products due to their reliance on big data and limited generalization capability in complex physics simulations, particularly in scenarios requiring detailed physics simulations where data generation is costly and high-dimensionality issues arise.
Innovation Solution
The implementation of physics-informed neural networks (PINNs) that embed partial differential equations (PDEs) and boundary/initial conditions into the loss function, allowing for adaptive design and optimization by dynamically resampling collocation points and adjusting network parameters, thereby reducing reliance on training data and improving convergence.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Power
If deep neural networks are used for engineering design, then computational power and data processing capability are improved, but reliance on big data and limited generalization capability in complex physics simulations worsen
Solution Approach 1:
The patent transforms the neural network training approach by changing the parameter optimization objective from purely data-driven error minimization to physics-constrained optimization. The loss function is reparameterized to include PDE residuals and boundary condition violations, fundamentally altering how network weights are updated to satisfy physical laws rather than just fitting training data.
Solution Approach 2:
The patent introduces physics equations (PDEs, boundary conditions, initial conditions) as intermediary constraints between the neural network and the physical system being modeled. These equations act as mediators that guide the network's learning process, ensuring solutions adhere to physical principles while still leveraging the network's computational capabilities.
2Loss of information
If data-driven approaches are used, then learning from available data is improved, but performance in scenarios with limited or costly data generation worsens
Solution Approach 1:
The physics-informed neural network performs self-correction by automatically enforcing physical constraints through the loss function. The network self-regulates its predictions to satisfy PDEs and boundary conditions without requiring extensive labeled training data, enabling it to learn effectively from limited data while maintaining physical consistency.
Solution Approach 2:
Physical laws and boundary conditions are incorporated a priori into the loss function before training begins. This preliminary embedding of domain knowledge constrains the solution space from the outset, allowing the network to converge faster with less data by leveraging pre-established physical principles rather than learning them from scratch.
3Adaptability or versatility
If traditional neural networks are used for physics simulations, then flexibility in modeling is improved, but convergence speed and solution accuracy in complex scenarios worsen
Solution Approach 1:
The loss function provides continuous feedback on how well the neural network's predictions satisfy physical equations and boundary conditions. During training, gradients from the PDE residuals and boundary condition violations guide weight updates, creating a feedback loop that steers the network toward physically consistent solutions and accelerates convergence compared to unconstrained training.
Data Source
AI summary
The present disclosure relates to systems, methods, and products for adaptive design and optimization using a physics-informed neural network (PINN). The system includes a non-transitory memory and a processor. The processor executes instructions to cause the system to: input collocation points and design parameters into the PINN to obtain an output; calculate a loss function based on a set of governing equations and the output; determine whether the PINN is convergent based on the calculated loss function; in response to the PINN being convergent, export the PINN; and in response to the PINN not being convergent: determine whether to resample the collocation points; determine an optimum number of collocation points; determine a set of optimal network parameters for adjusting the PINN; and input the collocation points and the set of optimal network parameters to the PINN for a next iteration.