Physical Field Prediction Across Complex Geometries and PDE Scales
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Solution Overview
Problem
Existing machine learning approaches for solving partial differential equations (PDEs) struggle with complex geometries, require flexible handling of multiple input functions and boundary conditions, and fail to capture multiscale behavior accurately, leading to computational inefficiencies and inaccuracies.
Innovation Solution
A method involving geometric and topological embeddings, combined with physics-informed neural networks, to infer physical fields by encoding designs into latent spaces, using a hybrid loss function that includes physics and data losses, enabling fast and accurate prediction of physical fields across complex geometries and scales.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional numerical methods (FEA) are used to solve PDEs, then accuracy is maintained, but computational speed and efficiency deteriorate
Solution Approach 1:
The patent replaces traditional mechanical numerical solving methods (FEA, FDM) with a machine learning-based system. A neural network is trained to learn the mapping between problem parameters and PDE solutions, substituting the iterative numerical computation process with a trained model that can predict solutions directly, thereby achieving both speed and accuracy.
Solution Approach 2:
The patent performs preliminary training of the neural network model using synthetic data generated from traditional numerical solvers. This preliminary action creates a pre-trained model that encapsulates the solution patterns, allowing rapid prediction without repeating the full numerical computation process for each new problem.
2Productivity
If machine learning models are used for PDE solving, then computational speed improves, but handling of complex geometries and multiscale behavior deteriorates
Solution Approach 1:
The patent transforms complex geometric problems into a different representation space using coordinate transformations and domain mapping techniques. By mapping complex geometries to simpler reference domains and using dimensionless parameters, the neural network can handle varied geometries without requiring geometry-specific processing for each case.
Solution Approach 2:
The patent develops a universal neural network framework that can handle multiple types of PDEs, boundary conditions, and geometric configurations through a single model architecture. The use of dimensionless parameters and normalized formulations allows the same model to generalize across different problem types, achieving versatility without sacrificing speed.
3Device complexity
If conventional geometry models are used, then boundary representation is sufficient, but entire design domain modeling deteriorates
Solution Approach 1:
The patent uses synthetic data generation to create virtual copies of physical scenarios. By generating synthetic training data that includes the entire design domain (not just boundaries) through numerical solvers, the neural network learns to predict fields throughout the volume, effectively copying the complete physical behavior without requiring explicit material models for every point.
Data Source
AI summary
Variants of the method can include determining a design, generating a geometric representation of the design, generating a topological representation of the design, determining a context value set, predicting a physical field using a trained physics model, optionally verifying the physical field, optionally generating a corrected physical field, and optionally training the physics model based on the corrected physical field.