Perception-Informed Neural Networks: Beyond Physics-Informed Neural Networks

TL;DR

PrINNs address limitations of physics-informed neural networks in handling perception-based uncertainty by introducing a general precisiation framework that supports singular, probabilistic, possibilistic, interval, and fuzzy representations of knowledge. The method integrates perception into neural network learning through loss terms and residuals, allowing both known differential equations and cases with unknown dynamics to be modeled or discovered. Key contributions include MOEINNs, TKINNs, and FINNs, plus the concept of Z-differential equations and sureness as meta-information to fuse diverse expert views. This framework enables uncertainty-aware, data-driven modeling and potential discovery of new forms of differential equations in complex dynamical systems, with online training capabilities.

Abstract

This article introduces Perception-Informed Neural Networks (PrINNs), a framework designed to incorporate perception-based information into neural networks, addressing both systems with known and unknown physics laws or differential equations. Moreover, PrINNs extend the concept of Physics-Informed Neural Networks (PINNs) and their variants, offering a platform for the integration of diverse forms of perception precisiation, including singular, probability distribution, possibility distribution, interval, and fuzzy graph. In fact, PrINNs allow neural networks to model dynamical systems by integrating expert knowledge and perception-based information through loss functions, enabling the creation of modern data-driven models. Some of the key contributions include Mixture of Experts Informed Neural Networks (MOEINNs), which combine heterogeneous expert knowledge into the network, and Transformed-Knowledge Informed Neural Networks (TKINNs), which facilitate the incorporation of meta-information for enhanced model performance. Additionally, Fuzzy-Informed Neural Networks (FINNs) as a modern class of fuzzy deep neural networks leverage fuzzy logic constraints within a deep learning architecture, allowing online training without pre-training and eliminating the need for defuzzification. PrINNs represent a significant step forward in bridging the gap between traditional physics-based modeling and modern data-driven approaches, enabling neural networks to learn from both structured physics laws and flexible perception-based rules. This approach empowers neural networks to operate in uncertain environments, model complex systems, and discover new forms of differential equations, making PrINNs a powerful tool for advancing computational science and engineering.

Figures (7)

• Figure 1: Some of the modes of precisiation in generalized theory of uncertainty
• Figure 2: Some instances of IDEs.
• Figure 3: The precisiation of IDEs in different modes.
• Figure 4: Perception informed neural networks.
• Figure 5: FINN-based controller in a closed-loop control system.