Long He

Tongfei Chen, Jingying Yang, Linlin Yang et al.

Deep learning architectures are fundamentally inspired by neuroscience, particularly the structure of the brain's sensory pathways, and have achieved remarkable success in learning informative data representations. Although these architectures mimic the communication mechanisms of biological neurons, their strategies for information encoding and transmission are fundamentally distinct. Biological systems depend on dynamic fluctuations in membrane potential; by contrast, conventional deep networks optimize weights and biases by adjusting the strengths of inter-neural connections, lacking a systematic mechanism to jointly characterize the interplay among signal intensity, coupling structure, and state evolution. To tackle this limitation, we propose the Kirchhoff-Inspired Neural Network (KINN), a state-variable-based network architecture constructed based on Kirchhoff's current law. KINN derives numerically stable state updates from fundamental ordinary differential equations, enabling the explicit decoupling and encoding of higher-order evolutionary components within a single layer while preserving physical consistency, interpretability, and end-to-end trainability. Extensive experiments on partial differential equation (PDE) solving and ImageNet image classification validate that KINN outperforms state-of-the-art existing methods.

Nikhil Muralidhar, Jie Bu, Ze Cao et al.

Physics-based simulations are often used to model and understand complex physical systems and processes in domains like fluid dynamics. Such simulations, although used frequently, have many limitations which could arise either due to the inability to accurately model a physical process owing to incomplete knowledge about certain facets of the process or due to the underlying process being too complex to accurately encode into a simulation model. In such situations, it is often useful to rely on machine learning methods to fill in the gap by learning a model of the complex physical process directly from simulation data. However, as data generation through simulations is costly, we need to develop models, being cognizant of data paucity issues. In such scenarios it is often helpful if the rich physical knowledge of the application domain is incorporated in the architectural design of machine learning models. Further, we can also use information from physics-based simulations to guide the learning process using aggregate supervision to favorably constrain the learning process. In this paper, we propose PhyDNN, a deep learning model using physics-guided structural priors and physics-guided aggregate supervision for modeling the drag forces acting on each particle in a Computational Fluid Dynamics-Discrete Element Method(CFD-DEM). We conduct extensive experiments in the context of drag force prediction and showcase the usefulness of including physics knowledge in our deep learning formulation both in the design and through learning process. Our proposed PhyDNN model has been compared to several state-of-the-art models and achieves a significant performance improvement of 8.46% on average across all baseline models. The source code has been made available and the dataset used is detailed in [1, 2].