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Adaptive Physics-Guided Neural Network

David Shulman, Itai Dattner

TL;DR

An adaptive physics-guided neural network framework for predicting quality attributes from image data by integrating physical laws into deep learning models is introduced, demonstrating the potential of adaptive physics-guided learning to integrate physical constraints effectively, even in challenging real-world contexts with diverse environmental conditions.

Abstract

This paper introduces an adaptive physics-guided neural network (APGNN) framework for predicting quality attributes from image data by integrating physical laws into deep learning models. The APGNN adaptively balances data-driven and physics-informed predictions, enhancing model accuracy and robustness across different environments. Our approach is evaluated on both synthetic and real-world datasets, with comparisons to conventional data-driven models such as ResNet. For the synthetic data, 2D domains were generated using three distinct governing equations: the diffusion equation, the advection-diffusion equation, and the Poisson equation. Non-linear transformations were applied to these domains to emulate complex physical processes in image form. In real-world experiments, the APGNN consistently demonstrated superior performance in the diverse thermal image dataset. On the cucumber dataset, characterized by low material diversity and controlled conditions, APGNN and PGNN showed similar performance, both outperforming the data-driven ResNet. However, in the more complex thermal dataset, particularly for outdoor materials with higher environmental variability, APGNN outperformed both PGNN and ResNet by dynamically adjusting its reliance on physics-based versus data-driven insights. This adaptability allowed APGNN to maintain robust performance across structured, low-variability settings and more heterogeneous scenarios. These findings underscore the potential of adaptive physics-guided learning to integrate physical constraints effectively, even in challenging real-world contexts with diverse environmental conditions.

Adaptive Physics-Guided Neural Network

TL;DR

An adaptive physics-guided neural network framework for predicting quality attributes from image data by integrating physical laws into deep learning models is introduced, demonstrating the potential of adaptive physics-guided learning to integrate physical constraints effectively, even in challenging real-world contexts with diverse environmental conditions.

Abstract

This paper introduces an adaptive physics-guided neural network (APGNN) framework for predicting quality attributes from image data by integrating physical laws into deep learning models. The APGNN adaptively balances data-driven and physics-informed predictions, enhancing model accuracy and robustness across different environments. Our approach is evaluated on both synthetic and real-world datasets, with comparisons to conventional data-driven models such as ResNet. For the synthetic data, 2D domains were generated using three distinct governing equations: the diffusion equation, the advection-diffusion equation, and the Poisson equation. Non-linear transformations were applied to these domains to emulate complex physical processes in image form. In real-world experiments, the APGNN consistently demonstrated superior performance in the diverse thermal image dataset. On the cucumber dataset, characterized by low material diversity and controlled conditions, APGNN and PGNN showed similar performance, both outperforming the data-driven ResNet. However, in the more complex thermal dataset, particularly for outdoor materials with higher environmental variability, APGNN outperformed both PGNN and ResNet by dynamically adjusting its reliance on physics-based versus data-driven insights. This adaptability allowed APGNN to maintain robust performance across structured, low-variability settings and more heterogeneous scenarios. These findings underscore the potential of adaptive physics-guided learning to integrate physical constraints effectively, even in challenging real-world contexts with diverse environmental conditions.

Paper Structure

This paper contains 60 sections, 23 equations, 6 figures.

Table of Contents

  1. Introduction
  2. Methodology
  3. Problem Definition
  4. Integration of Physical Models in Latent State Analysis
  5. Modeling Framework:
  6. Conceptual Framework for Physically-Informed Mapping
  7. Predictive Modeling from Observed Data to Target Measurements
  8. Method 1: Direct Prediction
  9. Method 2: Inverse Prediction via Estimated Latent State
  10. Effectiveness of the Inverse Prediction Approach
  11. Method 3: Adaptive Prediction Approach
  12. Advantages of the Adaptive Prediction Approach
  13. Comparative Performance Evaluation
  14. Implementation
  15. Methodological Adaptation for Vegetable Images
  16. ...and 45 more sections

Figures (6)

  • Figure 2: Average RMSE Score vs. Training Size for regressions task.
  • Figure 3: Average F1 Score vs. Training Size for classifications task.
  • Figure 4: Mean RMSE across different training sizes for each model on the cucumber dataset. The PGNN consistently outperforms the ResNet model, with the Adaptive Prediction approach showing the best performance overall.
  • Figure : (a) Indoor Material Classification
  • Figure : (a) Indoor Material Classification
  • ...and 1 more figures