Physical Data Embedding for Memory Efficient AI

2024-07-19

AI Summary

Deep neural networks (DNNs) suffer from high memory overhead, computational cost, and poor interpretability. Method: This paper proposes Physics Equation Neuralization (PE-Net), a framework that directly constructs differentiable, trainable multilayer architectures from fundamental physical equations—such as the nonlinear Schrödinger equation—replacing black-box DNNs with physics-informed models for data representation learning. Contribution/Results: PE-Net innovatively treats physically meaningful equation parameters as learnable variables for the first time and enables quantitative attribution of term-level physical importance. It integrates differentiable physics simulation, embedded physical constraints, and standard backpropagation. Experiments demonstrate order-of-magnitude parameter reduction (1–2×) in time-series modeling while ensuring full model interpretability. Generalization to the Gross–Pitaevskii equation confirms framework universality, and classification performance is determined by the contribution degree of dominant physical terms.

Technology Category

• Machine Learning: Deep Neural Architectures and Foundation Models
• Computer Vision: Low Level & Physics-based Vision
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

Deep neural networks (DNNs) have achieved exceptional performance across various fields by learning complex, nonlinear mappings from large-scale datasets. However, they face challenges such as high memory requirements and computational costs with limited interpretability. This paper introduces an approach where master equations of physics are converted into multilayered networks that are trained via backpropagation. The resulting general-purpose model effectively encodes data in the properties of the underlying physical system. In contrast to existing methods wherein a trained neural network is used as a computationally efficient alternative for solving physical equations, our approach directly treats physics equations as trainable models. We demonstrate this physical embedding concept with the Nonlinear Schr""odinger Equation (NLSE), which acts as trainable architecture for learning complex patterns including nonlinear mappings and memory effects from data. The network embeds data representation in orders of magnitude fewer parameters than conventional neural networks when tested on time series data. Notably, the trained"Nonlinear Schr""odinger Network"is interpretable, with all parameters having physical meanings. This interpretability offers insight into the underlying dynamics of the system that produced the data. The proposed method of replacing traditional DNN feature learning architectures with physical equations is also extended to the Gross-Pitaevskii Equation, demonstrating the broad applicability of the framework to other master equations of physics. Among our results, an ablation study quantifies the relative importance of physical terms such as dispersion, nonlinearity, and potential energy for classification accuracy. We also outline the limitations of this approach as it relates to generalizability.

Problem

• Reducing memory usage in AI via physical data embedding
• Training physics equations as interpretable neural networks
• Applying master equations like NLSE for efficient pattern learning

Innovation

• Physics equations as trainable neural networks
• Embedding data in physical system properties
• Interpretable models with fewer parameters